tag:blogger.com,1999:blog-26798646359813490202024-03-17T22:58:58.605-04:00 Greater Than Plus MinusAnonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.comBlogger25125tag:blogger.com,1999:blog-2679864635981349020.post-26270085840382518892018-09-25T13:59:00.003-04:002018-09-25T14:02:30.529-04:00New site coming soon...A new, revamped Greater Than Plus Minus is coming soon! Follow Brian on LinkedIn (<a href="https://www.linkedin.com/in/bmacgtpm/">bmacGTPM</a>) or Twitter (<a href="https://twitter.com/bmacGTPM">@bmacGTPM</a>) for updates.Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-42083490186482646422015-08-09T08:10:00.001-04:002015-08-09T08:10:45.032-04:00Goodbye, @GreaterThanPM. Hello, @bmacNHL. I recently changed my Twitter handle, which I'm sure caused millions of people, or possibly 0 people, large quantities of distress and sleepless nights, and provoked questions like "how could you do such a thing?", "why?", and "why ask why?". So I thought I'd explain.<br />
<br />
<b>Why not @GreaterThanPM?</b><br />
The original GreaterThanPM handle was chosen because my website, this website, was www.GreaterThanPlusMinus.com. The handle @GreaterThanPlusMinus was too long, so I shortened PlusMinus to PM.<br />
<br />
Sadly, I didn't realize at the time, and only realized after I started hanging out with Canadians more often, that PM is an abbreviation that is commonly used for Prime Minister. So to the people seeing my handle for the first time, especially those in the Great White North, it sounds as though I am asserting that I'm somehow better than a prime minister. So I decided to make the name change.<br />
<br />
<b>So why @bmacNHL? </b><br />
Here is an in-depth explanation using some complicated formulae:<br />
<br />
b = Brian<br />
mac = Macdonald<br />
bmac = a nickname commonly used when referring to me <br />
NHL = a nickname commonly used when referring to the National Hockey League. <br />
@ = required by Twitter <br />
<br />
<br />
<b>FAQ</b><br />
Q. Why not @bmacFLA? <br />
A. It was already taken. #sadface.<br />
<br />
<br />
<br />
<br />Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-47146674422230181312015-01-05T00:01:00.001-05:002015-01-05T00:32:24.756-05:00A real life application of Venn Diagrams, or How I spent my Sunday afternoon.<div>
<div>
</div>
I was at the local neighborhood pool today, working on the
all-important sun tan before heading inside to watch the FLA at WSH game
at 3pm. It started drizzling, kind of like this:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizpiLnc1k6uscB6OMxBD36nIeKMRmaZIgevssnoL8TiQkJobeXnJ3Qx3Fn8HxiwdwJVg4R9VUyi09y0bw8AYJSzKztPQSgnnQHwD9r_hxOgeyGTdENVz-YW1_E4UCp5N_OAINQT1YKiGer/s1600/no.octagons.slow.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizpiLnc1k6uscB6OMxBD36nIeKMRmaZIgevssnoL8TiQkJobeXnJ3Qx3Fn8HxiwdwJVg4R9VUyi09y0bw8AYJSzKztPQSgnnQHwD9r_hxOgeyGTdENVz-YW1_E4UCp5N_OAINQT1YKiGer/s1600/no.octagons.slow.gif" height="320" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhreX9Yq2mhbb8yNCt8zywFtbU21Mpa9pDUdFWyL7_KVUzXyqoPBpUXi2vHxXt7frwCmG0b7gpakxmQ-nC-n0zCiRPteRz4ADqeOO4l_jrCxyMNflcqoxaGUDkRsFmS4XWMfj-T16hI8TF/s1600/no.octagons.slow.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br /></a></div>
<div>
After
briefly looking around for a rainbow in the sky, and after overcoming the minor disappointment of not seeing one, I
noticed that the drizzle was becoming more and more like a steady rain:<br />
<br />
<a name='more'></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjluwtIMC9lkLowOYMzZOGLZyRJ5PFA8vsdR27r3cgAVci3PKnHKLb5mll57fzLuVpQDyQytjmdliZnBvs0LOVQAH5e7grdBNgryWFBgizW5bDECCAKsoTfwJNE9G4Q6rJSC2gGkgsdTdyD/s1600/no.octagons.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjluwtIMC9lkLowOYMzZOGLZyRJ5PFA8vsdR27r3cgAVci3PKnHKLb5mll57fzLuVpQDyQytjmdliZnBvs0LOVQAH5e7grdBNgryWFBgizW5bDECCAKsoTfwJNE9G4Q6rJSC2gGkgsdTdyD/s1600/no.octagons.gif" height="320" width="320" /></a></div>
<div>
I decided to migrate towards the nearby umbrella, which was casting its large octagon-shaped shadow over a table and some chairs:</div>
<div>
</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgV9ZI3L3Enpb4LBhVYnxBTVSPL9pjzrLKc_09AKE4MXd0GlAKsRsPe3pG9e0zhHkoQyfw0BykHckj1Pz51gFoe9EvjUL23lz6WsSGXxZE5Izr8RcwmQtGDyvLoBW3Cmqxh71Y13cojaNmp/s1600/shadow.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgV9ZI3L3Enpb4LBhVYnxBTVSPL9pjzrLKc_09AKE4MXd0GlAKsRsPe3pG9e0zhHkoQyfw0BykHckj1Pz51gFoe9EvjUL23lz6WsSGXxZE5Izr8RcwmQtGDyvLoBW3Cmqxh71Y13cojaNmp/s1600/shadow.png" height="200" width="200" /></a></div>
<div>
(The table and chairs can't be seen in the figure above because the shade is extremely dark). As
I was moving myself and my belongings, I noticed that because of the
umbrella, the pattern of rain on the ground looked something like this:
</div>
<div>
</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh62VkYNKK11XZsUzkvC4HyfgFyHy4fKKv7yn6j6oZpbIdvDb-fI2sz2_8f5NX3ghyB6cpEPS9aEVisessoHbyznoSPLRkxhlhZznRi0UkcFEMBtK0te9fJf27Sp-BT92xFI1H_yeDvZWOb/s1600/rain.outside.octagon.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh62VkYNKK11XZsUzkvC4HyfgFyHy4fKKv7yn6j6oZpbIdvDb-fI2sz2_8f5NX3ghyB6cpEPS9aEVisessoHbyznoSPLRkxhlhZznRi0UkcFEMBtK0te9fJf27Sp-BT92xFI1H_yeDvZWOb/s1600/rain.outside.octagon.gif" height="320" width="320" /></a></div>
<div>
</div>
<div>
But the sun was still out also, and since the angle of the
sun's rays was different than the angle at which the rain was falling,
the umbrella cast a octagonal shadow that didn't exactly overlap with the dry
areas:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxUdhUAajhRle4brV4_8DJvkRFmfsHSOE3s9GsWiedhtOMPrel3pJYXCCBZKxKkXMOUlIl1S1yRCSuXqRscz2acue6NIcZ-xGVV4X76fAu11H4hIAyipvzvZ-Q6ZmexcqhqWxAVIho5RRl/s1600/all.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxUdhUAajhRle4brV4_8DJvkRFmfsHSOE3s9GsWiedhtOMPrel3pJYXCCBZKxKkXMOUlIl1S1yRCSuXqRscz2acue6NIcZ-xGVV4X76fAu11H4hIAyipvzvZ-Q6ZmexcqhqWxAVIho5RRl/s1600/all.gif" height="320" width="320" /></a></div>
<div>
<br /></div>
<div>
So <a href="https://www.youtube.com/watch?v=rPFuf94om_Y&feature=youtu.be&t=20s" target="_blank">I says to myself, I says</a>, I can have the best
of both worlds. I can be both sunny and dry if I just sit in the region</div>
<div>
<div style="text-align: center;">
Sunny ∩ Rainy<b>'</b>, </div>
<div style="text-align: left;">
<br />
where the "prime" symbol is used here to denote "complement". The above line is typically read "Sunny intersect Rainy complement", and means "Sunny and Not Rainy". In other words, I should sit in the region outside the grey octagon, but inside the rainless octagon: </div>
</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipuxgCABuqmnhfEBOkBtgc7WUSCa8RYGzbi5pQ4bA7dT6TmtWltqIx6ndUGgNbrSpk1iaRGNRKYUtSe4S8_6naZgItvvf98wt66_53COwI-G7bt7WHMXA5rAIlb-3y3SwDstICMOONfKpa/s1600/all-final-edit.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipuxgCABuqmnhfEBOkBtgc7WUSCa8RYGzbi5pQ4bA7dT6TmtWltqIx6ndUGgNbrSpk1iaRGNRKYUtSe4S8_6naZgItvvf98wt66_53COwI-G7bt7WHMXA5rAIlb-3y3SwDstICMOONfKpa/s1600/all-final-edit.png" height="320" width="320" /></a></div>
<div>
</div>
So I did exactly that until the rain stopped, and successfully got a nice tan while keeping dry.<br />
<br />
Then it started getting hot, so I jumped into the pool.<br />
<br />
The end. <br />
<br />
*Special thanks to Venn and his diagrams for their assistance with this article, and for helping me figure out how to get a sun tan without getting wet.* <br />
<br />Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com2tag:blogger.com,1999:blog-2679864635981349020.post-22380351147397654132014-04-30T08:28:00.000-04:002014-04-30T08:28:19.149-04:00NHL Heat map@StatsbyLopez posted a photo on Twitter from a recent presentation where I showed an NHL heat map. So I thought I'd give a quick explanation of said heat map.<br />
<br />
First, here's the heat map: it's for all 5-on-5 shots in the NHL: <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxuu3Tb8rW_wuRu8DEKQzDyEjqZEavAhfYHLsylJ48hUS99y_h7fZfK18VLumqynk3x4ORle806jcZCL3KqMDCIiG24GXSda9SjDfDNyNGShyuXf0AqJGbYVNAtQW48oaGVeICLrf-1FWA/s1600/heat-map-bin-3-ft.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxuu3Tb8rW_wuRu8DEKQzDyEjqZEavAhfYHLsylJ48hUS99y_h7fZfK18VLumqynk3x4ORle806jcZCL3KqMDCIiG24GXSda9SjDfDNyNGShyuXf0AqJGbYVNAtQW48oaGVeICLrf-1FWA/s400/heat-map-bin-3-ft.png" height="400" width="400" /> </a></div>
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<br /></div>
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The size of each rectangle
represents the number of shots taken at that location (bigger rectangle = more shots). The color
represents the percentage of shots that were goals (red = high percentage, blue = low percentage). </div>
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<br /></div>
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Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com2tag:blogger.com,1999:blog-2679864635981349020.post-64470512515764593562013-10-11T10:26:00.000-04:002014-01-04T07:28:48.947-05:00Bayesian approach to analyzing goalies, Part 4: Regression to the Mean, Luongo vs Schneider, Thomas vs Rask, Hiller vs Fasth<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfZDR7m-2o8WHdiq6CNXWb92zJAi3FxuOmb8IGALDfIZKTcSQJqB0LNHl6Uf65dia0VD-poWRxXqr2Hb1cDyjoJU0_cBmEZJWa4Gg38Ftr2qQ8DwunJyaJHImA9X8tCs4A7NFS2gF_a3r_/s1600/Cory+Schneider-observed-and-true-vs-time.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div>
Last time, in <a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_7222.html">Part 3</a> of this series, we saw what our Bayesian estimate for Luongo's true ESSV% looks like over time; i.e. when we get more and more information and use more and more data. See <a href="http://www.greaterthanplusminus.com/p/goalies.html">here</a> for links to all posts in this series. <br />
<br />
<br />
<div class="MsoNormal">
In this article, we'll show results for more goalies than just Luongo. I haven’t really heard much analysis of the goaltending
situation in the Vancouver (joke). I’ve felt burdened by this obvious need that
the hockey world has (joke), so I thought I’d start with a little
statistical analysis of Roberto Luongo and Cory Schneider (not meant to be a
joke, though you may disagree after reading this). Really, I just want to use them as an example to help
illustrate this approach to analyzing goalies.<span style="mso-spacerun: yes;">
</span></div>
<br />
<br />
One of the things we noticed in Part 3 is that there is some regression to the
mean going on. Luongo's Bayesian estimate was always between his
observed ESSV% and the league average ESSV%. Let's start with a figure that shows that this "regression to the mean" happens for all goalies. <br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq20rvx9f3lQ0sR02gUNoUBoX0VMaKntI9FJy2k79l4LS1_jCw1kPSrnObrXfNZaIwoWziv8eva3SzGzLfEYeFl0e3OWKjdfC507RwuBvEA8s7BxqO90s3LMdqtEVAmXdnYNjGOIAhWzLi/s1600/estimated-vs-true-with-luongo-and-schneider.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-48WkxsdFThS6n6Vo20ScEMQGW9BgYKxNeqRnN_prU9eyS_QQMCEF39_YcJnfxPGDoHkpjaQCPqBlAhHAk9XjMJiVkym02Ci-SHwJc5pswR1rV_m72oF1iS3DKShxT7zFMq-BSL1tuBg6/s1600/estimated-vs-true.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-48WkxsdFThS6n6Vo20ScEMQGW9BgYKxNeqRnN_prU9eyS_QQMCEF39_YcJnfxPGDoHkpjaQCPqBlAhHAk9XjMJiVkym02Ci-SHwJc5pswR1rV_m72oF1iS3DKShxT7zFMq-BSL1tuBg6/s400/estimated-vs-true.png" width="400" /></a></div>
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</div>
<a name='more'></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgvgAUJMmzbBGU626PXHSJQyJ33A8nK5mDS0s2OIo1D98t0efdcLv0zgse17bxqFruS-XUE5tbbK5p_JPP43GaFdNC1D4hTu4yCqC8JyJvJer3Kp_HZoC7gHqCzZ67kGcUOrJo9MGyGybW/s1600/estimated-vs-true.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><br />
In this figure, each gray dot corresponds to a goalie. The horizontal position of the gray dot is based on the goalie's observed ESSV%, and the vertical position of the gray dot corresponds to our estimate of their true ESSV%. The blue dots correspond to observed ESSV% and the red line is league average.<br />
<br />
The key observation is that for each goalie, their gray dot is between their blue dot and the red line. This means for every goalie in the league, our estimate is between their observed ESSV% and the league average. Above average goalies (right side) are automa<i>g</i>ically pulled down towards league average, and below average goalies (left side) are automa<i>g</i>ically pulled up towards league average. <br />
<br />
Notice that some goalies are closer to the league average than others. We have sized the dots by shots faced. Notice that the small dots are typically closer to league average. We saw this before in <a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_7222.html">Part 3</a>. When the number of shots is small, our estimate tends to be close to league average. When the number of shots is large, our estimate tends to be closer to observed ESSV%. The extent to which our estimate is pulled towards the mean is automa<i>g</i>ically determined by the model. <br />
<br />
One thing we didn't previously stress is that this method is pretty useful for comparing goalies who have faced different quantities of shots. It is most useful when those goalies played on the same team so that we can assume they faced roughly the same quality of shots. We'll adjust for quality of shots in a future series, which will be better for comparing goalies on different teams.<br />
<br />
As an example, let's start with Luongo and Schneider, who both played for VAN during the seasons we used for this series (2008-09 thru 2012-13). <span style="font-size: small;"><span style="font-family: inherit;"><span style="line-height: 115%;">Luongo
and Schneider had roughly the same even strength save percentage (.933, and .931) during the seasons that we are using. </span></span></span><span style="font-family: inherit;"><span style="font-size: small;"><span style="line-height: 115%;">Since Luongo has faced about 3000 more shots
than Schneider, we<span style="font-size: small;"> a</span>re more sure of Luongo’s ability. But how sure are we?
</span></span></span><br />
<br />
Let's look at the same figure as above, with Luongo and Schneider highlighted:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZtOne-LsDZkTHpUE7nsxMR3LUD43Zf1XQ4b2a7fFQ1tcO113Dx-4TSXw-zeKzhQx2zOg6fJSGg7PDK1UxXuJ6hdFLrKpFWZ6Us_a4e0YAJy6uOznlsdx2fF61gijCkpqVTxKSDQ6Nj0tj/s1600/estimated-vs-true-with-luongo-and-schneider.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="391" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZtOne-LsDZkTHpUE7nsxMR3LUD43Zf1XQ4b2a7fFQ1tcO113Dx-4TSXw-zeKzhQx2zOg6fJSGg7PDK1UxXuJ6hdFLrKpFWZ6Us_a4e0YAJy6uOznlsdx2fF61gijCkpqVTxKSDQ6Nj0tj/s400/estimated-vs-true-with-luongo-and-schneider.png" width="400" /></a></div>
<div style="text-align: center;">
</div>
Luongo's observed save percentage is greater than Schneider's, and since Schneider faced fewer shots, his Bayesian estimates get automa<i>g</i>ically pulled more strongly towards the league average. The result is that our estimates for Luongo (.930) and Schneider (.926) are farther apart (difference of .004) than their observed ESSV% (.933 and .931, difference of .002).<br />
<br />
<br />
Let's look at the curves for Luongo and Schneider as well: <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3A5LTZ24CGw1sjHDJD8lXDQjoWJcGvsvesyq_Qob-vkEsRghLr2Nw37K9IFfMnBEbcqnnL3uoPsXK4VVr_EyVBShT5rg_C8Ds1y3vTs-jx_NBDV65Ni1SIJNX0JWa0Ed6w8UARMKeTbGB/s1600/curves-luongo-schneider.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="330" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3A5LTZ24CGw1sjHDJD8lXDQjoWJcGvsvesyq_Qob-vkEsRghLr2Nw37K9IFfMnBEbcqnnL3uoPsXK4VVr_EyVBShT5rg_C8Ds1y3vTs-jx_NBDV65Ni1SIJNX0JWa0Ed6w8UARMKeTbGB/s400/curves-luongo-schneider.png" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4nRPHrNuJKaxfLZUHe7pqCS_oFbMJsV7I7x4bR3q4JaYkQwd-tOSWM3ujTVed3yMOCaHB05OOEhoxBxKrr6CkMczVOnSHkk59_hqj3dvCVdd_5Us3mAyQ8XK0mLvyoUzbxraItqZBRVnz/s1600/curves-luongo-schneider.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijt0K_egO40ZSGTz6jNUFIR0nGTOSvxM_0lKzLl-3sez8v-lrt3I1SiBlIAzX1aoWOVCGF03jwh2smOSMmnDEu033C8y-oT6sknDgjcpHjU4OyViTmoPK-TdRGu-M9-ZYEw-xobpitxEZg/s1600/curves-luongo-schneider.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div>
The blue is Luongo, the red is Schneider, and the gray lines are the rest of the league's goalies. Luongo's curve is to the right of Schneider's, indicating our estimate for Luongo is higher. His curve is more narrow and has a higher peak, indicating that we are more sure of his estimate than we are of Schneider's. In other words, Luongo's estimate is more precise. Here's a table summarizing the results:<br />
<span style="font-family: "Courier New",Courier,monospace;"><span style="font-size: small;"> TrueESSV% Err ESSV% Shots<br />Roberto Luongo .930 .003 .933 5239<br />Cory Schneider .926 .004 .931 1932</span></span><br />
<br />
The Err column indicates that the error bound for Luongo's estimate is smaller than that of Schneider, as we would expect. <br />
<br />
<br />
In this case of Luongo and Schneider, though the gap between the two goalies changes, the
order of the two goalies stays the same: Luongo has both a higher
observed ESSV% and a higher Bayesian ESSV%. In other words, using both methods we would conclude that Luongo is the better goalie. But as we saw in the OTT and BUF write-ups in the <a href="http://www.greaterthanplusminus.com/2013/09/more-places-to-buy-2013-14-hockey.html">2013-14 Hockey Prospectus book</a>, this isn't always the case. Often, the order of your goalies will switch. Let's give an example here, and highlight Tim Thomas and Tuukka Rask:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8mmL-szewJinWmHpooNPiEeuK9O1Xc4VsWfQGUCGN5GlkqrUYrD0N26Mnlv1hvNB9WgbIZFZ6g9Br7_9hAkCmsrdFZ-BtuHrL3HPOT_9aJPpxmzlK9fIz6uyKvFE50Cjjsp_MsDTGDfGF/s1600/estimated-vs-true-thomas-and-rask.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8mmL-szewJinWmHpooNPiEeuK9O1Xc4VsWfQGUCGN5GlkqrUYrD0N26Mnlv1hvNB9WgbIZFZ6g9Br7_9hAkCmsrdFZ-BtuHrL3HPOT_9aJPpxmzlK9fIz6uyKvFE50Cjjsp_MsDTGDfGF/s400/estimated-vs-true-thomas-and-rask.png" width="400" /></a></div>
In this case, Rask has a higher observed ESSV% (.935) than Thomas (.934), but Thomas (.930) has a higher Bayesian ESSV% than Rask (.929). In the figure, Rask is further to the right, but Thomas is higher. Here's a table for Thomas and Rask:<br />
<br />
<span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: #e1e2e5; border-collapse: separate; color: black; font-family: 'Lucida Console'; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; orphans: 2; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px;"></span><br />
<pre class="GNVMTOMCABB" style="-webkit-user-select: text; border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; font-family: 'Lucida Console'; font-size: 10pt !important; line-height: 1.2; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: none; outline-width: initial; white-space: pre-wrap !important;" tabindex="0"> TrueESSV% Err ESSV% Shots
Tim Thomas .9303 .0032 .9346 4723
Tuukka Rask .9294 .0038 .9356 2824</pre>
<br />
The gap between them isn't huge in either case, but the order did switch. See the OTT and BUF team pages in the <a href="http://www.greaterthanplusminus.com/2013/09/more-places-to-buy-2013-14-hockey.html">2013-14 Hockey Prospectus book</a> for more extreme examples. <br />
<br />
What about the goalie situation in ANA? Here are the results for Hiller and Fasth:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAYlmP6NpXNZ33OAz0779nGWYWNWb90kX1mexas-87_h3L7KVZiq9JYdja1SDMk3R28E5WMDRnf6Xa4Nx_AoIOdeDQdVmBNjTDMobIL1Ti2iKz1oaC0nUVMPR-ZFHz__APStBXmQs3eUKw/s1600/estimated-vs-true-hillar-and-fasth.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAYlmP6NpXNZ33OAz0779nGWYWNWb90kX1mexas-87_h3L7KVZiq9JYdja1SDMk3R28E5WMDRnf6Xa4Nx_AoIOdeDQdVmBNjTDMobIL1Ti2iKz1oaC0nUVMPR-ZFHz__APStBXmQs3eUKw/s400/estimated-vs-true-hillar-and-fasth.png" width="397" /></a></div>
<div style="text-align: center;">
<span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: #e1e2e5; border-collapse: separate; color: black; font-family: 'Lucida Console'; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; orphans: 2; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px;"></span></div>
<div style="text-align: center;">
<pre class="GNVMTOMCABB" style="border-style: none; font-family: 'Lucida Console'; font-size: 10pt ! important; line-height: 1.2; margin: 0px; outline-style: none; white-space: pre-wrap ! important;" tabindex="0"> TrueESSV% Err ESSV% Shots
Jonas Hiller .9259 .0030 .9278 5234
Viktor Fasth .9226 .0053 .9272 508</pre>
</div>
<br />
<br />
Hiller and Fasth have almost the same ESSV%, with a slight edge to Hiller. But Fasth has far fewer shots, so our estimate of Fasth's true ESSV% is pretty close to the league average. The gap between Hiller and Fasth according to true ESSV% (.0033) is larger than the gap in observed ESSV% (.0004). Also, Hiller's estimate is more precise (smaller Err). This analysis suggests that ANA shouldn't overreact to Fasth's strong performance last season and do something like trade Hiller. (Well, that's the conclusion if we are focusing only on performance and are ignoring contract status and cap hit.) <br />
<br />
These kinds of conclusions are not new to the analytics community. You can eyeball their ESSV% and notice they are almost the same, you can notice the huge difference in the number of shots that these two goalies have faced (5000 vs 500). Analysts familiar with the idea of "regression to the mean" would expect Fasth's ESSV% to regress.<br />
<br />
But what <i>is</i> new is that we now have a way to quantify these qualitative ideas. We also have error bounds on our estimates. We'll continue with examples like this next time. We'll also use our results to answer the question "What is the probability that Goalie A has a higher true ESSV% than Goalie B?" <br />
<br />
<br />
Links to other parts:<br />
<a href="http://www.greaterthanplusminus.com/2013/09/bayesian-approach-to-analyzing-goalies.html">Part 1</a><b> - </b>Introduction<br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies.html">Part 2</a> - An example using only 10 shots <br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_7222.html">Part 3</a> - Updating estimates with more information<br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_11.html">Part 4</a> - Regression to the mean, Luongo vs Schneider, Thomas vs Rask, Hiller vs Fasth<br />
<br />
Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com22tag:blogger.com,1999:blog-2679864635981349020.post-63931431658797677642013-10-10T17:05:00.001-04:002014-01-04T07:28:01.333-05:00Bayesian approach to analyzing goalies, Part 3: Updating estimates with more dataIn <a href="http://www.greaterthanplusminus.com/2013/09/bayesian-approach-to-analyzing-goalies.html">Part 1</a> of this series, we gave an introduction to the series, and the motivation behind this new method of analyzing goalies. In <a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies.html">Part 2</a>, we started with an example of Luongo's first 10 shots to build some intuition for what estimates this method gives and the advantages it has over traditional SV% or even strength save percentage (ESSV%). We got a picture like this:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB1LrTwsV9t7OsbFgbTwxoOuOHIE4m_-Yxr_Vf1LcHGpMeND5o4KITKZXT32Aa-m0iW06HMg9MYjWpShS_aCqlOjladuQxh_ssqyToXliJboL32Kwp-p2itFr3zkqq2g7vOeD727V0rRDy/s1600/luongo-curves_Page_001.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB1LrTwsV9t7OsbFgbTwxoOuOHIE4m_-Yxr_Vf1LcHGpMeND5o4KITKZXT32Aa-m0iW06HMg9MYjWpShS_aCqlOjladuQxh_ssqyToXliJboL32Kwp-p2itFr3zkqq2g7vOeD727V0rRDy/s400/luongo-curves_Page_001.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
After 10 shots, Luongo's curve (black) is still very similar to what our prior expectation was based on typical ESSV% in the NHL. Since he saved 10 out of his first 10 shots, his curve (and the corresponding dot) is shifted slightly to the right. <br />
<br />
In this article, we'll continue this example and discuss the animation that we showed at the end of Part 2. The animation shows what Luongo's curve looks like after 20 shots, 30 shots, 40 shots, etc.:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuIRHYN9yecE1uNzHD_OoVIbYM5q3B2GZILqpVot9ViThKpZ1FZQygJ7QBVHOeqx-TnP12GPsTYjeTJQSAL2mhfPEOVqC69pZL2TOsBNoUbc9vptmxCIh1xPoxFUzF-X4ivFbqhmMXZTBt/s1600/luongo.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuIRHYN9yecE1uNzHD_OoVIbYM5q3B2GZILqpVot9ViThKpZ1FZQygJ7QBVHOeqx-TnP12GPsTYjeTJQSAL2mhfPEOVqC69pZL2TOsBNoUbc9vptmxCIh1xPoxFUzF-X4ivFbqhmMXZTBt/s400/luongo.gif" width="400" /></a></div>
<br />
<a name='more'></a><br />
Luongo's distribution curve goes to the left, but quickly moves back to the right, and seems to stabilize pretty quickly.... the black dot seems to bounce around .930-ish area after the first 500 or 1000 shots. As we add more and more shots, the curve gets narrower, and the peak of the curve gets higher. This indicates that as time goes on, and we get more and more information (i.e. we use more and more shots in the model), we are becoming more and more certain of our estimate of Luongo's true ESSV%. In other words, our estimate is getting more and more precise. <br />
<br />
We added a blue dot to this animation which represents the observed ESSV%. In the very beginning, it starts out off the screen to the right. (Recall that in Part 2, we said that with 10 saves in his 10 shots, Luongo's ESSV% was only 1.000.) Luongo allowed 3 goals in the first 7 shots of his second game, so the blue dot swings off the screen to the left. The blue dot then swings back to the right and bounces around there for a while, way up past .940. After a while, it stabilizes a bit, and is pretty close to the black dot. This blue dot is kind of showing what we know about ESSV%: extreme values when the number of shots is small, very unstable in the beginning, but with a significant number of shots, it begins to stabilize. <br />
<br />
Another observation is that the black dot is always between the blue dot and the red dot. This is true in the beginning when the blue dot is off the screen to the left, and when the blue dot crosses over to the right half of the figure, so does the black dot. This is illustrating the "regression to the mean" that is going on. Our Bayesian estimate for Luongo's true ESSV% is closer to the mean than his observed ESSV%, whether his ESSV% is higher or lower than the mean. <br />
<br />
During the beginning of the animation, the regression is pretty heavy. In other words, the black dot is pulled <i>way </i>towards the red dot. The prior distribution is dominating and has a big influence on our estimate. This is probably preferred... we don't have much data, so our prior information has more influence on our estimate. The blue dot, which is based solely on the limited data, is pretty erratic in the beginning with pretty extreme values. <br />
<br />
But as time goes on, the black dot moves further from the red dot and gets closer and closer to the blue dot. The more data we get, the less influence the prior has, and the more influence the data has. This method is automa<i>g</i>ically regressing Luongo to the mean by an appropriate amount based on how much data there is. <br />
<br />
It might be helpful to look at a non-animated figure to emphasize what is going on. Here's the position of the blue dot and black dot over time:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSELGGIwOMijZCerimpsvwIjmkvLKIPtSYE4AbzgQVDktbIj8Y_KyVEN3mJcMADtd3sO2QX-Wzbn8DZMQjW9tK6zCgkRR2MTVCaAwVXdfW0PBDzmyTl2D-cITW8kpxN9L4jicZtdz7TXRC/s1600/observed-and-true-vs-time.png" style="margin-left: 1em; margin-right: 1em;"></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiffWa0aKl5qX_SnaCKdQDW-zMy63ITQBHiOlV7EKW4Hfkw__dmzAjgcji71dwL5OvhLyM_DY6PiQ1yRBzn142GfczHu-maSSJ7VdJQeefLjrpnguugzYivsNGNOoon5EWQLJDHzBNNdIkK/s1600/Roberto+Luongo-observed-and-true-vs-time.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiffWa0aKl5qX_SnaCKdQDW-zMy63ITQBHiOlV7EKW4Hfkw__dmzAjgcji71dwL5OvhLyM_DY6PiQ1yRBzn142GfczHu-maSSJ7VdJQeefLjrpnguugzYivsNGNOoon5EWQLJDHzBNNdIkK/s400/Roberto+Luongo-observed-and-true-vs-time.png" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSELGGIwOMijZCerimpsvwIjmkvLKIPtSYE4AbzgQVDktbIj8Y_KyVEN3mJcMADtd3sO2QX-Wzbn8DZMQjW9tK6zCgkRR2MTVCaAwVXdfW0PBDzmyTl2D-cITW8kpxN9L4jicZtdz7TXRC/s1600/observed-and-true-vs-time.png" style="margin-left: 1em; margin-right: 1em;"></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSELGGIwOMijZCerimpsvwIjmkvLKIPtSYE4AbzgQVDktbIj8Y_KyVEN3mJcMADtd3sO2QX-Wzbn8DZMQjW9tK6zCgkRR2MTVCaAwVXdfW0PBDzmyTl2D-cITW8kpxN9L4jicZtdz7TXRC/s1600/observed-and-true-vs-time.png" style="margin-left: 1em; margin-right: 1em;"></a></div>
The horizontal axis is time in the animation. More precisely, it is the number of shots used in the model. The vertical axis is ESSV%. So the curves are showing ESSV% after <i>n</i>
shots, where <i>n</i> ranges from 10 to 5230. The colors are the same as in the animation: the blue curve corresponds to the blue
dot (observed ESSV%), the gray/black curve corresponds to our Bayesian
estimate, and the red line is league average. <br />
<br />
The black appears to be pretty well-behaved and stabilizes quickly. The blue is much more erratic in the beginning, with large swings, and it appears as a pretty noisy signal before stabilizing. The black is always between the blue and the red. In the beginning, the regression to the mean is heavy and the black is closer to the red. After a while, when we have more data, the black is closer to the blue, and the two curves pretty much move in tandem. <br />
<br />
In <a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_11.html">Part 4</a>, we'll talk about the regression to mean a little more, and start showing some results for the rest of the league's goalies. We might even compare Luongo and Schneider, since that's never been done before. This will be an example of a couple of other benefits of our Bayesian ESSV%:<br />
<ol>
<li>it is useful when comparing goalies who have faced different numbers of shots. </li>
<li>it is useful for answering questions like "what is the probability that Luongo's true ESSV% is greater than Schneider's?"</li>
</ol>
<br />
Links to other Parts:<br />
<a href="http://www.greaterthanplusminus.com/2013/09/bayesian-approach-to-analyzing-goalies.html">Part 1</a><b> - </b>Introduction<br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies.html">Part 2</a> - An example using only 10 shots <br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_7222.html">Part 3</a> - Updating estimates with more information<br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_11.html">Part 4</a> - Regression to the mean, Luongo vs Schneider, Thomas vs Rask, Hiller vs Fasth <br />
<ol>
</ol>
Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-67215517404632238362013-10-09T19:59:00.002-04:002014-01-04T07:28:26.268-05:00Bayesian approach to analyzing goalies, Part 2: An exampleIn <a href="http://www.greaterthanplusminus.com/2013/09/bayesian-approach-to-analyzing-goalies.html">Part 1</a> of this series, we gave an introduction to this method of analyzing goalies and the motivation behind it. We discussed why many analysts use even strength save percentage (ESSV%) instead of traditional SV%, and talked about two problems that ESSV% has which we'd like to deal with. This series focuses on Problem 1: ESSV% tends to be very inconsistent especially for goalies who have faced a relatively small number of shots. Our approach is a Bayesian analysis, where we can use "prior information". <br />
<br />
Let's begin with a simple example. Let's consider the first 10 shots that Roberto Luongo faced during the 2008-09 season. None of these shots were goals. If this is the only information we have about Luongo, what should our estimate of his true ESSV% be? In other words, what should we expect his ESSV% to be going forward? We knew a lot about Luongo at the beginning of the 2008-09 season, but for the sake of explaining what's going on, let's pretend we didn't.<br />
<br />
One approach to answering this question is to use his observed ESSV%. In this case, his ESSV% is 1.000 since he had 10 saves on these 10 shots. This estimate is pretty high... 1.000 is way higher what any typical NHL goalie would ever have. This is a pretty extreme example, since we are using only 10 shots, and it's sort of obvious that observed ESSV% should not be our estimate in this case. But it will help us explain what is going on, and this kind of thing can still happen when using 100, 500, or 1000 shots, though the observed ESSV% won't typically be as extreme. <br />
<br />
Instead of using observed ESSV%, we could use a Bayesian estimate. Suppose we know that the league's ESSV% are typically distributed like this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQndrj9n39g7aPD9X_b_WgPb1Q8kVvWdhTspu2RJD6NXlRulZH8yEw4zyQnDVcL6nRDBEKCvGpQoAIHNx8enJbICm0eSCl2KZM5pFFK0Z4ITLdY3lTHbSzLb-ni4nGret6uPUPGnUHQfwT/s1600/observed-and-true-vs-time.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7VKh4Pd_QkSmoO-GXF8eKglAHMEI9hzfscV1gylXAh_qZQ0z7NayvnQMnVbptFQiZrXrq-8U1CFgfvI8PmUae7P3lslGK11Us3GW4f3-wtlRorsLYUKuMCoEh59qGY-bQuaj05_zx4ZnZ/s1600/luongo-curves-beta-prior-only.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="330" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7VKh4Pd_QkSmoO-GXF8eKglAHMEI9hzfscV1gylXAh_qZQ0z7NayvnQMnVbptFQiZrXrq-8U1CFgfvI8PmUae7P3lslGK11Us3GW4f3-wtlRorsLYUKuMCoEh59qGY-bQuaj05_zx4ZnZ/s400/luongo-curves-beta-prior-only.png" width="400" /></a></div>
<br />
<a name='more'></a><br />
The horizontal axis is ESSV% and the vertical axis indicates how likely each ESSV% is. We expect an NHL goalie will hardly ever have an ESSV% less than .900 or greater than .940, and most of the time, ESSV% is between .910 and .930. If we
get a goalie that has an ESSV% much higher or lower than what is
expected, then our method will tend to pull a goalie's ESSV% towards the
mean.<br />
<br />
(Note: There are different ways to get this curve, but let's pretend we got it from observed ESSV% for NHL goalies during the seasons in question. This isn't exactly what we did, but we don't want to take the time to explain what we did just yet.) <br />
<br />
If we use this prior information in a particular way, we can get a Bayesian estimate of Luongo's true ESSV% after 10 shots that is much more conservative than his observed ESSV% of 1.000:<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgk5NU6a9uG-8cmQaUq2A4IpffWu6UKnlRw7W6fgogsJonYgHdK0Lw3HvsW-QM3tOYxCmACbQ9cp0knl7BZbOh8HoadsLcyzbu02n4AFbR_sBAngSN7uibd73-x6vorzKAb9sqlqDkR3Gl1/s1600/luongo-curves_Page_001.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgk5NU6a9uG-8cmQaUq2A4IpffWu6UKnlRw7W6fgogsJonYgHdK0Lw3HvsW-QM3tOYxCmACbQ9cp0knl7BZbOh8HoadsLcyzbu02n4AFbR_sBAngSN7uibd73-x6vorzKAb9sqlqDkR3Gl1/s400/luongo-curves_Page_001.png" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjStRRdByXzXTBAZSkry3Yx-Sa-ecZKWb3cYtv28AbbOc5CFc62UL6z278roSkHkD9rkXyq6RaiKPuZWggbaOi_L6lwIb5RzOjRzAq288om09I96tpzPm33NdfuPT6kn0LDZcfnUZzTj-M0/s1600/luongo-curves-10-shots.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br /></a></div>
The red is our prior expectation for a goalie's ESSV% from the previous figure, and the black is our updated curve for Luongo after 10 shots. The dots at the bottom are the mean for the prior (red) and the mean for Luongo (black). <br />
<br />
Note that this distribution curve for Luongo is very close to the prior distribution. We only have 10 shots worth of information, and although Luongo had some pretty extreme results, there is not overwhelming evidence that Luongo is much different than an average goalie. <br />
<br />
Also note that Luongo's curve is slightly shifted to the right, and that his dot is slightly to the right of the red dot. This is expected since he saved 10 out of his first 10 shots. Our estimate should be <i>slightly </i>higher than league average, since in this limited time period he had good results. And that's what we see here.. slightly higher, but not much higher.<br />
<br />
Luongo's curve is still pretty wide too. A wider curve means we still aren't very sure about Luongo's ability. In other words, we haven't narrowed down our beliefs much yet. And we probably shouldn't after only 10 shots. <br />
<br />
What happens when we get more information? Let's see what Luongo's curve looks like after 20 shots, 30 shots, etc., all the way up to 5230 shots:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuIRHYN9yecE1uNzHD_OoVIbYM5q3B2GZILqpVot9ViThKpZ1FZQygJ7QBVHOeqx-TnP12GPsTYjeTJQSAL2mhfPEOVqC69pZL2TOsBNoUbc9vptmxCIh1xPoxFUzF-X4ivFbqhmMXZTBt/s1600/luongo.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuIRHYN9yecE1uNzHD_OoVIbYM5q3B2GZILqpVot9ViThKpZ1FZQygJ7QBVHOeqx-TnP12GPsTYjeTJQSAL2mhfPEOVqC69pZL2TOsBNoUbc9vptmxCIh1xPoxFUzF-X4ivFbqhmMXZTBt/s400/luongo.gif" width="400" /></a></div>
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<div class="separator" style="clear: both; text-align: center;">
</div>
<div style="text-align: center;">
(Issues uploading the 5200 shot version,<br />
but here's the 4800 shot version for now... basically the same.)</div>
<br />
We'll save the discussion of this animation for <a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_7222.html">Part 3</a>. <br />
<br />
Links to other parts:<br />
<a href="http://www.greaterthanplusminus.com/2013/09/bayesian-approach-to-analyzing-goalies.html">Part 1</a><b> - </b>Introduction<br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies.html">Part 2</a> - An example using only 10 shots <br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_7222.html">Part 3</a> - Updating estimates with more information<br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_11.html">Part 4</a> - Regression to the mean, Luongo vs Schneider, Thomas vs Rask, Hiller vs Fasth<br />
<br />Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-83244263002252595142013-09-26T21:39:00.001-04:002014-01-04T07:27:39.635-05:00Bayesian approach to analyzing goalies, Part 1<div style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;">
</div>
<br />
Save percentage (SV%) is a statistic that is commonly used to analyze goalies. Analysts have started using even strength save percentage (ESSV%) instead, for various reasons. One reason is that there isn't much data for special teams, so it's hard to draw any conclusions about performance or ability on the penalty kill.<br />
<br />
Another is that a goalie doesn't control how many special teams situations he has to face, and so doesn't control how many special teams shots he has to face. If a goalie's team takes a lot of (non-coincidental) minor penalties, that goalie will face a lot of shots on the penalty kill. Those shots are tougher to stop, and this will tend to drag down the goalie's SV%. Even if he is one of the league's top goalies, his SV% may not reflect that because he is facing so many more short handed situations than the other top goalies in the league. ESSV% avoids all this.<br />
<br />
There are still a couple issues with ESSV% though. <br />
<br />
<div class="MsoNormal">
<b>Problem 1</b>: ESSV% still tends to be very inconsistent especially for goalies who have faced a relatively small number of shots. This has been noted by several analysts. The <a href="http://hockeyanalysis.com/2013/06/18/estimating-actual-randomness-in-goal-data/">top</a>
<a href="http://www.broadstreethockey.com/2013/7/4/4487304/save-percentage-variability-regression-defense">three</a>
<a href="http://www.arcticicehockey.com/2011/12/20/2648333/pdo-regression-to-the-mean-or-why-you-should-ignore-shooting">results</a>
in a google search for “save percentage regression to the mean hockey” are a
good sample of articles that discuss these issues, and why ignoring these
issues can lead an analyst to draw questionable conclusions about the ability
of a goalie or about the other players on a goalie’s team.<br />
<br />
<a name='more'></a></div>
<b>Problem 2</b>: When we use ESSV%, we treat every shot the same. Basically, we assume that all shots are created equal. In other words, every shot has an equal probability of being a goal. A shot from 5 feet is the same as a shot from 50 ft. A shot from the center of the ice is the same as a shot from a wide angle.<br />
<br />
Intuitively, this isn't true. There is also statistical evidence that this isn't true. Various analysts have shown that things like distance and angle, or alternatively, shot location, are related to the probability that a shot will be a goal. For example, here is goal percentage by distance:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip6Ufq_BOp8sIkec6TgwVRqAkQpklECyCUXlPaOvF2IC1VM2YYy63R1i0TCAYlr9qIKS4_RQpTENXIuc6D9sz5MrdbqGjCpGHTCwUa1s3O3u_XjlrAPl9DltS-a8QoVVEi6KgNQ7O8Uzur/s1600/GoalPercentageByDistanceColorSquare.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="358" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip6Ufq_BOp8sIkec6TgwVRqAkQpklECyCUXlPaOvF2IC1VM2YYy63R1i0TCAYlr9qIKS4_RQpTENXIuc6D9sz5MrdbqGjCpGHTCwUa1s3O3u_XjlrAPl9DltS-a8QoVVEi6KgNQ7O8Uzur/s400/GoalPercentageByDistanceColorSquare.png" width="400" /></a></div>
<br />
Goal percentage decreases as distance increases. <br />
<br />
<br />
In this series we'll focus on Problem 1. This work is based on joint work with Nick Clark. We'll save Problem 2 and discussions about shot quality for another series of articles. That will be based on a project that one of my students, Calla Glavin, is working on. The figure above is courtesy Calla. <br />
<br />
We note that Problem 1 was also discussed in the BUF and OTT team write-ups in the new 2013-14 Hockey Prospectus book. Information about purchasing that book can be found <a href="http://www.greaterthanplusminus.com/2013/09/more-places-to-buy-2013-14-hockey.html">here</a>. In this series, we'll go into a little more detail about how the method works and what kind of results we get. We'll also have additional figures and an animation.<br />
<br />
We'll also analyze the goalie situations of some NHL teams. We won't do BUF and OTT again, see <a href="http://www.greaterthanplusminus.com/2013/09/more-places-to-buy-2013-14-hockey.html">the book</a> for those. We'll focus on a couple of other teams, and also focus on a couple of individual players. <br />
<br />
<b>A Bayesian</b> <b>approach </b><br />
<br />
If we know ESSV% is fairly inconsistent, and we know that extremely high or low save percentages typically regress heavily to the league's mean ESSV%, perhaps we could develop a metric that is more conservative and less subject to large fluctuations. One approach is to use a Bayesian statistical analysis. In this kind of analysis, we still use data about the goalie's saves, and the number of shots he's faced. But we also use some "prior information". More specifically, we can use information about the known distribution of save percentages in the NHL. For example, if we know that save percentages are typically distributed something like this, we can use that information:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6fRH0iqg58vJAAnEu_BWPEJK_ySV7ms0CMAyQczy0HNFcmMiGntoSmCuN9DGC3FljkBlCKpD-lMRHM71SofoBJauWE9ZbbpsqOFFyeBUI9DNAqck4HUWT_4PZ4rxbXIGepeMIDVuiti1L/s1600/hist-of-sv.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="372" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6fRH0iqg58vJAAnEu_BWPEJK_ySV7ms0CMAyQczy0HNFcmMiGntoSmCuN9DGC3FljkBlCKpD-lMRHM71SofoBJauWE9ZbbpsqOFFyeBUI9DNAqck4HUWT_4PZ4rxbXIGepeMIDVuiti1L/s400/hist-of-sv.png" width="400" /></a></div>
Almost everyone is between .900 and .940, and most are still between .910 and .930. If we use this prior information in an appropriate way, a goalie whose save percentage is far away from this region will get pulled in towards the league average. The extent to which he gets pulled towards the league average will depend on how many shots he has faced. Goalies with lots of shots won't get pulled towards the mean as much as goalies with fewer shots. <br />
<br />
That's just the big picture for now. Next time, we'll use Roberto Luongo as an example to illustrate what kinds of results our Bayesian approach gives. And we'll talk more about this "regression to the mean" and show some figures illustrating this effect.<br />
<br />
And since I can't help myself, I'll give a teaser. We'll also discuss this animation later in the series:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVfSpYDTL_R9GQiClxkRnb1rOUX18uwCnkLFa1GKDP1BGXjwSbyAm1VEIP-SCTE2RDRY1mNLRQ3zI8V5sKQhVzgo2b4zy57hQgrwM80kevxImFGXRGA8IsZYOPeLcczVSib7yxRSjIEcjX/s1600/luongo.gif" imageanchor="1"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVfSpYDTL_R9GQiClxkRnb1rOUX18uwCnkLFa1GKDP1BGXjwSbyAm1VEIP-SCTE2RDRY1mNLRQ3zI8V5sKQhVzgo2b4zy57hQgrwM80kevxImFGXRGA8IsZYOPeLcczVSib7yxRSjIEcjX/s400/luongo.gif" width="400" /></a></div>
<br />
<div style="text-align: center;">
(If the animation isn't working, try refreshing your browser.)</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
Links to other parts:<br />
<a href="http://www.greaterthanplusminus.com/2013/09/bayesian-approach-to-analyzing-goalies.html">Part 1</a><b> - </b>Introduction<br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies.html">Part 2</a> - An example using only 10 shots <br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_7222.html">Part 3</a> - Updating estimates with more information<br />
<a href="http://www.greaterthanplusminus.com/2013/10/bayesian-approach-to-analyzing-goalies_11.html">Part 4</a> - Regression to the mean, Luongo vs Schneider, Thomas vs Rask, Hiller vs FasthAnonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-39644797936316704492013-09-19T09:59:00.000-04:002013-09-19T09:59:26.464-04:00More places to buy 2013-14 Hockey Prospectus<br />
See <a href="http://www.hockeyprospectus.com/article.php?articleid=1579">here</a> for links to various places to buy the book. There are .pdf versions and paperback versions.<br />
<br />
<br />
As noted at that link, the cheapest paperback is <a href="https://www.createspace.com/4442623">available from CreateSpace</a> using the discount code <b><span style="font-family: inherit;">7B8F3CZ7</span></b>. It is $22.95 after discount. <br />
<br />
The .pdf version is $12.95. <br />
<br />
<br />Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com4tag:blogger.com,1999:blog-2679864635981349020.post-66995392920514904222013-09-13T11:59:00.000-04:002013-09-13T11:59:04.831-04:00Hockey Prospectus 2013-14 now availableHockey Prospectus 2013-14 is now available for purchase. See <a href="http://www.hockeyprospectus.com/article.php?articleid=1577">here</a> for details on how to make said purchase. <br />
<br />
For those interested, I contributed to the BUF, OTT, and WPG pages. For WPG, I wrote about stuff related to realignment, and how WPG's travel will be affected. For BUF and OTT, I analyzed their goalie situations using a new technique. <br />
<br />
I'll write more about those techniques in a forthcoming post, but the basic idea is that the approach automagically regresses a goalies estimated true Sv% towards the league average, especially for those goalies who have faced relatively few shots. <br />
<br />
<br />Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com5tag:blogger.com,1999:blog-2679864635981349020.post-51454484297132534182013-08-05T20:51:00.002-04:002013-08-07T13:11:17.559-04:00PLAY - More analysis and top 10 PLAYersIn Parts 1 thru 3, we developed a new playmaking metric that is (1) more consistent than assists and (2) better than assists at predicting future assists. <a class="twitter-atreply pretty-link" dir="ltr" href="https://twitter.com/spamventura"><s>@</s><b>spamventura</b></a> had an observation about the results that we'll study a little further in this article. Along the way, we'll give the top 10 PLAYers (capitalization and pun intended) from 2009-10, and how they did in 2010-11.<br />
<br />
<br />
<a name='more'></a><br />
<br />
After looking at the results I posted in Part 3, <a class="twitter-atreply pretty-link" dir="ltr" href="https://twitter.com/spamventura"><s>@</s><b>spamventura</b></a> said this:<br />
<blockquote class="twitter-tweet">
<a href="https://twitter.com/GreaterThanPM">@GreaterThanPM</a> Hmm. But if it's consistently lower (is it? Haven't looked at full results) then some effect must be missing, right?<br />
— Sam (@spamventura) <a href="https://twitter.com/spamventura/statuses/363967539807649792">August 4, 2013</a></blockquote>
<script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script>
So what Sam is saying is that he observed that the PLAY from 2009-10, which can be thought of as expected assists for 2010-11, was always lower than actual assists from 2010-11, at least for the top 5 listed there. (Or maybe he meant PLAY from 2010-11... not sure). If PLAY is always lower for the top players, or always higher for the bottom players, that could indicate a problem with the model. It seems a little worrisome, so let's look into this further.<br />
<br />
First, it makes sense that PLAY from 2009-10 is usually lower than assists from 2009-10 (the same season) for the league's top playmakers. If PLAY uses goals and shots, and using shots sort of has a regressing effect, pulling everyone towards the mean. So you can kind of think of PLAY as sort of a regressed version of assists. If instead we looked at the players in the bottom half of the league, we'd see that their PLAY is typically <i>higher</i> than their assists, because they are getting pulled <i>up</i> towards the mean. We can see that affect here:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqVwvatGfSR95D8OoRcRNuAU0YNL6lh6T8mOf0RD3rN612ejs9mXkx5cizFF-8Dzd6dPDj8ykonB2e2eVUkO_TbjpV4-80-eChN2UcdS1iH1jEW5k_0s8UXvw7YWJbndOhSBIijeijwjOS/s1600/play-vs-assists-regression-to-mean.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqVwvatGfSR95D8OoRcRNuAU0YNL6lh6T8mOf0RD3rN612ejs9mXkx5cizFF-8Dzd6dPDj8ykonB2e2eVUkO_TbjpV4-80-eChN2UcdS1iH1jEW5k_0s8UXvw7YWJbndOhSBIijeijwjOS/s400/play-vs-assists-regression-to-mean.png" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtHPI4U2FkWMkRi8Q0PBXFEF2avFA0FOcJqfAiTIP0PuNn5rzkkRnDfYzg97Ojr-oNcWcDeBeMW737eLr3B29NHyJSaIvhTJ-eQJT27wyz6Pm8l4cwQrpP2l9mYck1peI78t11ArdyZ7ck/s1600/play-vs-assists-regression-to-mean.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br /></a></div>
Those two dots to the right are the Sedins. Let's remove them so we can zoom in a little more. <br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjc-0EZA9mLtkHy8nPtyWk1T7_cM0nR_xG2HMKG3Fsu24U0sEyszugktMXBaZKh7IEpmz719Vlto8HkZkprIb8rSFEIeswYqYHRa6mK2hz3Efx7DVJ9cxu-_A7GCJ2Fivk9Tb4r54LkwyCc/s1600/PLAY-vs-assists-regression-to-the-mean-sedins-removed.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjc-0EZA9mLtkHy8nPtyWk1T7_cM0nR_xG2HMKG3Fsu24U0sEyszugktMXBaZKh7IEpmz719Vlto8HkZkprIb8rSFEIeswYqYHRa6mK2hz3Efx7DVJ9cxu-_A7GCJ2Fivk9Tb4r54LkwyCc/s400/PLAY-vs-assists-regression-to-the-mean-sedins-removed.png" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcz-tOjqEDvRolgwcbCM0O1-fM0RKgstBeOAM_gSERLarAZY4bVhFeyhbqdxwThm5fkacziNGYdK9VUpDCZ9pC20aSo03bq5rH5K164Nb5CkuML-UCaUgo8WrBZQfi4oayC_6GIurQZrqj/s1600/PLAY-vs-assists-regression-to-the-mean-sedins-removed.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div>
<br />
Let's explain this figure a little. Each grey dot corresponds to a forward, and the vertical position of the dot indicates that forward's PLAY in 2009-10. Each blue dot along the blue line corresponds to the forward's assists per 60 minutes in 2009-10. The red horizontal line corresponds to the league average assists per 60 minutes in 2009-10. <br />
<br />
Notice that a player's gray dot is typically between their blue dot and the red line, which means that a player's PLAY is typically between their own assists and the league's average assists. Players with above average assists (right half) get pulled down, and players with below average assists (left half) get pulled up.<br />
<br />
This isn't always the case, because the model isn't just regressing, it's doing some other stuff too, like adjusting for strength of teammates. But there is a bit of a regression effect going on. So we expect PLAY from 2009-10 to be lower than assists in 2009-10 for the top players.<br />
<br />
But is PLAY from 2009-10 is always lower than assists from 2010-11? In our top 5 list from Part 3, that appeared to be the case. Let's show just those two columns, and their difference:<br />
<br />
<pre><span style="font-family: "Courier New",Courier,monospace;"><span style="color: black;"><span style="mso-tab-count: 3;"> </span>2010-11<span style="mso-spacerun: yes;"> </span>2009-10</span></span></pre>
<pre><span style="font-family: "Courier New",Courier,monospace;"><span style="color: black;"><span style="mso-spacerun: yes;"> </span>Player Pos Team<span style="mso-spacerun: yes;"> </span> <span style="mso-spacerun: yes;"> </span>A <span style="mso-spacerun: yes;"> </span> PLAY<span style="mso-spacerun: yes;"> </span></span></span><span style="font-family: "Courier New",Courier,monospace;"><span style="color: black;"><span style="mso-spacerun: yes;"><span style="font-family: "Courier New",Courier,monospace;"><span style="color: black;">Difference</span></span></span>
Henrik Sedin<span style="mso-spacerun: yes;"> </span>C<span style="mso-spacerun: yes;"> </span>VAN<span style="mso-spacerun: yes;"> </span> 44<span style="mso-spacerun: yes;"> </span>32 12
Anze Kopitar<span style="mso-spacerun: yes;"> </span>C<span style="mso-spacerun: yes;"> </span>L.A<span style="mso-spacerun: yes;"> </span> 33<span style="mso-spacerun: yes;"> </span> 22 11
Claude Giroux<span style="mso-spacerun: yes;"> </span>RW<span style="mso-spacerun: yes;"> </span>PHI<span style="mso-spacerun: yes;"> </span> 33<span style="mso-spacerun: yes;"> </span> 17 16
Daniel Sedin<span style="mso-spacerun: yes;"> </span>LW<span style="mso-spacerun: yes;"> </span>VAN<span style="mso-spacerun: yes;"> </span> 35<span style="mso-spacerun: yes;"> </span> 22 13<span style="mso-spacerun: yes;">
</span>Bobby Ryan<span style="mso-spacerun: yes;"> </span>RW<span style="mso-spacerun: yes;"> </span>ANA<span style="mso-spacerun: yes;"> </span> 28<span style="mso-spacerun: yes;"> </span> 19 9</span></span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">
(This table was taken from </span><a href="http://www.academia.edu/4104016/Quantifying_playmaking_ability_in_hockey"><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">the paper</span></a><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> and edited.)</span></pre>
<pre><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> </span></pre>
<div style="text-align: left;">
In each case, PLAY predicted about 10 assists too low. But if we are going to check the model, we should look at this same table for the per 60 minutes version of each statistic. And we should sort by PLAY in 2009-10, not PLAY in 2010-11, because we are comparing PLAY from 2009-10 and assists from 2010-11. <br />
<br />
Here are the top 10 PLAYers (capitalization and pun intended) from 2009-10, and their assists in 2010-11:<br />
<br />
<span style="font-size: x-small;"><span class="Apple-style-span" style="border-collapse: separate; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Lucida Console'; line-height: 19px; white-space: pre-wrap;"></span></span></span><br />
<pre class="GD40030CLR" style="border-color: initial; border-style: none; border-width: initial; font-family: 'Lucida Console'; line-height: 1.3; margin: 0px; outline-color: initial; outline-style: none; outline-width: initial; white-space: pre-wrap ! important;" tabindex="0"><span style="font-size: x-small;"> 2009-10 2010-11</span></pre>
<pre class="GD40030CLR" style="border-color: initial; border-style: none; border-width: initial; font-family: 'Lucida Console'; line-height: 1.3; margin: 0px; outline-color: initial; outline-style: none; outline-width: initial; white-space: pre-wrap ! important;" tabindex="0"><span style="font-size: x-small;"> Player Pos Team PLAY A Diff
Henrik Sedin C VAN 1.63 2.21 0.58
Daniel Sedin LW VAN 1.49 1.83 0.34
Nicklas Backstrom C WSH 1.38 1.23 -0.15
Joe Thornton C S.J 1.35 1.26 -0.10
Paul Stastny C COL 1.34 0.95 -0.40
Wojtek Wolski LW NYR 1.34 1.31 -0.03
Scott Gomez C MTL 1.34 0.70 -0.64
Mikhail Grabovski C TOR 1.32 1.08 -0.24
Matt Stajan C CGY 1.31 1.43 0.11
Ryan Getzlaf C ANA 1.31 1.72 0.42</span></pre>
<br />
<br />
<br />
Fortunately, there is no noticeable trend of under- or over-estimating assists the next year. Some are over, some are under.<br />
<br />
<b>More discussion</b><br />
If you aren't interested in regression model diagnostics, you might prefer to skip this section.<br />
<br /></div>
<div style="text-align: left;">
</div>
<div style="text-align: left;">
If we go beyond the top 10, there is still no noticeable trend. Here is a plot of the Diff versus PLAY for all players. More precisely, we show the difference in the actual values and predicted values (assists in 2010-11 minus PLAY in 2009-10) in the vertical axis, and the fitted values (PLAY in 2009-10) along the horizontal axis:</div>
<div style="text-align: left;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaev938tWjLB9qPFFH9fB4gsjQKSj_MGr4Ms3GzbvsxSaJSEJBdzFAmTQsswUSQbY5jiK3GCfbcVYmLovyiaJ1FCcJkI_4FaQGrl67jU4ZzxRy5TglsrkgxyvHrmfWe-mAfVOZfFOyUHSm/s1600/resid-vs-fitted.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaev938tWjLB9qPFFH9fB4gsjQKSj_MGr4Ms3GzbvsxSaJSEJBdzFAmTQsswUSQbY5jiK3GCfbcVYmLovyiaJ1FCcJkI_4FaQGrl67jU4ZzxRy5TglsrkgxyvHrmfWe-mAfVOZfFOyUHSm/s400/resid-vs-fitted.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_k7vdu2wCkNj5Yv0yMbsWRaISPvsGAR24M9r7IHQrgLzGsZgG8A8kjAjVU7wyrXfkHk8cOQ583oXU5gFbUztPVpZd-jy5ZQyt9YH7rZe7VijeiBhcPQ01YUrFUGdJd01m9VNpheiLXmBe/s1600/resid-vs-fitted.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div>
If we saw a trend here, that would be a problem, but it looks pretty random. If, for example, all the high fitted values (points to the right) had high residuals (were above the blue line), then that would indicate some sort of problem. FWIW, the two outliers on the right are the Sedins.</div>
<div style="text-align: left;">
</div>
<div style="text-align: left;">
<br />
The reason for all of the 10's in the first table is that the table was sorted by PLAY in 2010-11, not PLAY in 2009-10. PLAY in 2010-11 uses assists from that season, so PLAY from 2010-11 is correlated with assists from 2010-11. Sorting by PLAY from 2010-11 is sort of like sorting by assists in 2010-11.<br />
<br />
Assists in 2010-11 were the <i>y</i>'s in our model. If we say that when <i>y</i> is high, the residuals are high, that's exactly what is supposed to happen if our model isn't an amazingly good fit. The residuals will be correlated with <i>y </i>to some degree<i>. </i>In fact, the correlation is \sqrt{1-R^2}, where R^2 is the multiple R^2 from the original model.<br />
<br />
So in <i>any</i> regression model that doesn't have a very high R^2, the residuals will be correlated with <i>y </i>to some degree. If we were to plot residuals vs y instead of residuals vs fitted values, we would expect to see a trend instead of the random blob of points like in the figure above.<br />
<br />
Since assists are pretty noisy, and since they depend on things other than talent (like teammates, opponents, and zone starts) that might change from year to year, our model does not have a very high R^2. We are trying to predict something that's really noisy, and we get a lot of unexplained variation. Our R^2 is low-ish, which means \sqrt{1-R^2} is high, and <i>y</i> and our residuals are correlated.<br />
<br />
<br />
But while PLAY isn't amazingly good at predicting assists, it is still better than assists at predicting assists. Plus, PLAY is more consistent than assists.<br />
<br />
<br />
<div style="text-align: left;">
</div>
Anywho, since we sorted by PLAY in 2010-11 in the table in Part 3, we have almost sorted by <i>y</i> since <i>y</i> and PLAY from 2010-11 are correlated. Since <i>y</i> and the residuals are correlated, we would expect the players in that table to have high residuals. <br />
<br />
I guess another way to think of it is that PLAY tends to give conservative predictions, so when <i>y </i>is very high, residuals tend to be high as well.<br />
<br /></div>
<pre></pre>
Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com3tag:blogger.com,1999:blog-2679864635981349020.post-20337866548348208112013-08-01T09:36:00.000-04:002013-08-01T13:28:17.048-04:00PLAY: A Playmaking Metric, Part 3 - Results<br />
In <a href="http://www.greaterthanplusminus.com/p/play.html">Part 2</a> of this series on a new playmaking metric PLAY, we talked about "altruistic contribution" based on shots. It is basically the difference in shots taken by a player’s <i style="mso-bidi-font-style: normal;">teammates</i> (excluding the player’s own shots) when he is on the ice
versus off the ice.<span style="mso-spacerun: yes;"> </span>It’s kind of like a
shot-based WOWY that doesn’t include the player's own shots. If a player's <i>teammates</i> take more shots when he is on the ice versus off the ice, his altruistic contribution will be high.<br />
<br />
Now we'll use this altruistic contribution to build our playmaking metric PLAY, and show that PLAY is better than
assists in two quantifiable ways: (1) it is more consistent than assists, and
(2) it is better than assists at predicting future assists.<span style="mso-spacerun: yes;"> </span><br />
<span style="mso-spacerun: yes;"></span><br />
<a name='more'></a><b style="mso-bidi-font-weight: normal;"><br />Playmaking Metric</b><br />
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Ah, finally... we can talk about the playmaking metric.<span style="mso-spacerun: yes;"> </span>We combine assists per 60 minutes and shot-based altruistic
contribution (also a per 60 minute rate stat) in one half of season to predict assists in the
second half of the season.<span style="mso-spacerun: yes;"> </span>To determine
the best way to combine assists and altruistic contribution, we use a multiple
linear regression.<span style="mso-spacerun: yes;"> </span>The expected assists
per 60 minutes that we get from this regression model are what we call our
playmaking metric, PLAY.<span style="mso-spacerun: yes;"> </span>See <a href="http://www.academia.edu/4104016/Quantifying_playmaking_ability_in_hockey">the
paper</a> for details of the regression. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
We built models for forwards and defensemen, and built
models for half seasons and full seasons.<span style="mso-spacerun: yes;">
</span>In all cases, PLAY was (1) more consistent than assists and (2) better
than assists at predicting future assists.<span style="mso-spacerun: yes;">
</span>Here are the half season to half season correlations of assists and PLAY
for forwards and defensemen:</div>
<div class="MsoNormal">
<span style="mso-spacerun: yes;"> </span></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
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</span><br />
<div class="MsoNormal">
PLAY is more consistent than assists for both forwards and
defensemen.<span style="mso-spacerun: yes;"> </span>Results for full seasons
were similar, but slightly higher across the board.<span style="mso-spacerun: yes;"> </span>For forwards, year-to-year correlation of
PLAY was 0.54.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
PLAY was also a better predictor in every way we tested it,
which included cross-validation.<span style="mso-spacerun: yes;"> </span>See <a href="http://www.academia.edu/4104016/Quantifying_playmaking_ability_in_hockey">the
paper</a> for the boring details.<span style="mso-spacerun: yes;"> </span>Unless
you are a statistician, in which case see <a href="http://www.academia.edu/4104016/Quantifying_playmaking_ability_in_hockey">the
paper</a> for the exciting details.<br />
<br /></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">Top playmakers</b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
As an example, here are the top playmakers from 2010-11,
according to PLAY:<span style="color: black; font-family: "Lucida Console";"><span style="mso-spacerun: yes;"><br /></span></span></div>
<pre><span style="font-family: "Courier New",Courier,monospace;"><span style="color: black;"><span style="mso-spacerun: yes;"> </span>Player Pos Team<span style="mso-spacerun: yes;"> </span>PLAY60<span style="mso-spacerun: yes;"> </span>A60
Henrik Sedin<span style="mso-spacerun: yes;"> </span>C<span style="mso-spacerun: yes;"> </span>VAN<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>1.56<span style="mso-spacerun: yes;"> </span>2.21
Claude Giroux<span style="mso-spacerun: yes;"> </span>RW<span style="mso-spacerun: yes;"> </span>PHI<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>1.40<span style="mso-spacerun: yes;"> </span>1.82
Anze Kopitar<span style="mso-spacerun: yes;"> </span>C<span style="mso-spacerun: yes;"> </span>L.A<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>1.37<span style="mso-spacerun: yes;"> </span>1.78
Sidney Crosby<span style="mso-spacerun: yes;"> </span>C<span style="mso-spacerun: yes;"> </span>PIT<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>1.35<span style="mso-spacerun: yes;"> </span>1.81
Martin Erat<span style="mso-spacerun: yes;"> </span>RW<span style="mso-spacerun: yes;"> </span>NSH<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>1.31<span style="mso-spacerun: yes;"> </span>1.53</span></span></pre>
<pre></pre>
<div class="MsoNormal">
<br />
We’ve shown assists per 60 minutes here also.<span style="mso-spacerun: yes;"> </span>The one surprise here, for me at least, is
Martin Erat.<span style="mso-spacerun: yes;"> </span>His 2010-11 PLAY of 1.30
was his high mark among the 4 seasons we considered, but even in the other
seasons he was between 1.10 and 1.18, and is roughly a top-35 playmaking
according to PLAY.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
Let’s look deeper.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"></span>He led his
team in altruistic contribution for 3 of the 4 seasons, (2007-08, 2008-09,
2009-10), and was second only to J.P. Dumont in 2010-11.<span style="mso-spacerun: yes;"> </span>He ranked 17<sup>th</sup>, 22<sup>nd</sup>,
13<sup>th</sup>, and 13<sup>th</sup> in the NHL in altruistic contribution in
those seasons, so he's been roughly a top 15-20 player in that statistic. He also had a good year with assists in 2010-11 (1.53 assists/60 was 17th). High ratings in both gave him a high PLAY that season. Being 13th in Alt and 17th in assists might not sound that great, but only 3 other players were in the top 17 in both assists and altruistic contribution 2010-2011: H. Sedin, Giroux, and Kopitar. <span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Erat's high rating is indicating that he generates a lot of shots for his
teammates, though they may not capitalize on those shots, and suggests he may
be an underrated playmaker if we use assists alone.<span style="mso-spacerun: yes;"> </span>It’ll be interesting to see if anything
changes in Washington this year, especially if he ends up playing a significant
of time with Ovechkin at even strength.<span style="mso-spacerun: yes;">
</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The other players in that top 5 are players you would expect to see…<span style="mso-spacerun: yes;"> </span><a href="http://www.youtube.com/watch?v=qFGDCxKfBUY">pretty standard, really</a>.<span style="mso-spacerun: yes;"> </span>Henrik Sedin led the league in PLAY in 3 of
the<span style="mso-spacerun: yes;"> </span>4 seasons were considered (2008-09,
2009-10, and 2010-11) and was 4<sup>th</sup> in 2007-08 (Joe Thornton was first
that year).<span style="mso-spacerun: yes;"> It was nice to see Giroux 2nd. This high rating is for 2010-2011, the year <i>before </i>he was second in the league in assists. </span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Here are the top players in expected assists, which comes
from taking our playmaking metric (an expected assists per 60 minute stat) and multiplying by playing
time.<span style="mso-spacerun: yes;"> </span>This is like a per season version
of PLAY.</div>
<pre><span style="color: black; font-family: "Lucida Console";"><span style="mso-tab-count: 3;"></span></span><span style="font-family: "Courier New",Courier,monospace;"><span style="color: black;"><span style="mso-tab-count: 3;"> </span><span style="mso-spacerun: yes;"> </span>2010-11<span style="mso-spacerun: yes;"> </span>2009-10 Difference<span style="mso-spacerun: yes;">
</span>Player Pos Team<span style="mso-spacerun: yes;"> </span>PLAY<span style="mso-spacerun: yes;"> </span>A <span style="mso-spacerun: yes;"> </span>PLAY<span style="mso-spacerun: yes;"> </span>A<span style="mso-spacerun: yes;"> </span>PLAY<span style="mso-spacerun: yes;"> </span>A
Henrik Sedin<span style="mso-spacerun: yes;"> </span>C<span style="mso-spacerun: yes;"> </span>VAN<span style="mso-spacerun: yes;"> </span>31 44<span style="mso-spacerun: yes;"> </span>32 53<span style="mso-spacerun: yes;"> </span>1<span style="mso-spacerun: yes;"> </span>9
Anze Kopitar<span style="mso-spacerun: yes;"> </span>C<span style="mso-spacerun: yes;"> </span>L.A<span style="mso-spacerun: yes;"> </span>25 33<span style="mso-spacerun: yes;"> </span>22 18<span style="mso-spacerun: yes;"> </span>3 15
Claude Giroux<span style="mso-spacerun: yes;"> </span>RW<span style="mso-spacerun: yes;"> </span>PHI<span style="mso-spacerun: yes;"> </span>25 33<span style="mso-spacerun: yes;"> </span>17 15<span style="mso-spacerun: yes;"> </span>9 18
Daniel Sedin<span style="mso-spacerun: yes;"> </span>LW<span style="mso-spacerun: yes;"> </span>VAN<span style="mso-spacerun: yes;"> </span>24 35<span style="mso-spacerun: yes;"> </span>22 36<span style="mso-spacerun: yes;"> </span>2<span style="mso-spacerun: yes;"> </span>1<span style="mso-spacerun: yes;">
</span>Bobby Ryan<span style="mso-spacerun: yes;"> </span>RW<span style="mso-spacerun: yes;"> </span>ANA<span style="mso-spacerun: yes;"> </span>24 28<span style="mso-spacerun: yes;"> </span>19 17<span style="mso-spacerun: yes;"> </span>5 11</span></span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">
(This table was taken from </span><a href="http://www.academia.edu/4104016/Quantifying_playmaking_ability_in_hockey"><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">the paper</span></a><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> and edited.)<span style="color: black;"></span></span></pre>
<div class="MsoNormal">
<br />
The two new names are D. Sedin and Ryan.<span style="mso-spacerun: yes;">
</span>Crosby and Erat are out of the top 5 because of playing time (both missed
games due to injury that year).<span style="mso-spacerun: yes;"> </span>Notice
we’ve also included 2009-10 stats, as well as the difference between the two
seasons.<span style="mso-spacerun: yes;"> </span>As we saw in the picture above, PLAY tends to
be much more consistent than assists.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">Future work</b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
For the project, we only used stats up until 2010-2011. Sadly, we finished this project over a year ago, and finally finished writing it up<span style="mso-spacerun: yes;">. So that's why we used only up to 2010-11. </span>We’ll eventually be updating this to include
2011-12 and 2012-13 data in the model, and get PLAY for those seasons.<span style="mso-spacerun: yes;"> But I didn't want to keep holding onto this new metric, so I just figured I'd post without the updated stats. <a href="http://www.youtube.com/watch?v=W647gDp-u-s">Forgiveness, please</a>.</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
There are a couple ways this could be improved.<span style="mso-spacerun: yes;"> </span>We could use a different measure for marginal
contribution that accounts for zone starts and quality of opponents, like <a href="http://www.greaterthanplusminus.com/p/adjusted-plus-minus.html">Adjusted
Plus-Minus</a>.<span style="mso-spacerun: yes;"> </span>If zone starts are
accounted for, Henrik Sedin might not be at the top of the list by such a wide
margin, or maybe not at the top of the list at all.<span style="mso-spacerun: yes;"> We could use Fenwick or Corsi instead of shots to compute the altruistic contribution. </span><br />
<br />
<span style="mso-spacerun: yes;">Ideally, zone starts and strength of opponents would be accounted for, so PLAY is not perfect. But fortunately, we can </span><span style="mso-spacerun: yes;">say that PLAY is better than assists, even the way it currently is computed, </span><span style="mso-spacerun: yes;">without these modifications. </span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
We also could do something similar with just 1st assists instead of using all assists.<span style="mso-spacerun: yes;"> Since </span><span style="mso-spacerun: yes;"><a class="account-group js-account-group js-action-profile js-user-profile-link js-nav" data-user-id="537438873" href="https://twitter.com/pcunneen19"> <span class="username js-action-profile-name"><s>@</s><b>pcunneen19</b></span></a> recently asked about this, we took the liberty of doing this right away. They were no significant improvements if we replace assists with 1st assists. If we use both 1st assists and 2nd assists, but keep them separated in our regression model instead of combining them into one "assists" category, we also see no significant improvements in PLAY. It is interesting to note that in that case, 1st assists did have a larger coefficient in the regression than 2nd assists. Not surprising, since hockey analysts regard 1st assists as more predictive. </span><br />
<span style="mso-spacerun: yes;"><br /></span></div>
<br />Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-41702067496476778062013-07-30T11:19:00.000-04:002013-07-30T11:19:26.149-04:00PLAY: A playmaking metric, Part 2 - Altruistic Contribution<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.blogger.com/blogger.g?blogID=2679864635981349020" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div>
<a href="http://www.greaterthanplusminus.com/2013/07/play-playmaking-metric-part-1-intro.html">Part 1</a> of this series on a new playmaking metric PLAY, we gave an overview, and discussed marginal contribution, which is basically some form of WOWY. See <a href="http://www.greaterthanplusminus.com/2013/07/play-playmaking-metric-part-1-intro.html">here</a> for Part 1 and <a href="http://www.academia.edu/4104016/Quantifying_playmaking_ability_in_hockey">here</a> for the full paper. In this part, we'll discuss competitive and altruistic contributions. Altruistic contribution is what we'll use to compute PLAY.<br />
<br />
<a name='more'></a><br />
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">Competitive and
Altruistic Contributions </b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
So we have this WOWY for every player, and we are going to
decompose it into two parts, competitive contribution (Comp) and altruistic contribution
(Alt).<span style="mso-spacerun: yes;"> </span>A player’s competitive
contribution is simply the goals per 60 minute that he scores.<span style="mso-spacerun: yes;"> </span>A player’s altruistic contribution is
everything else, or his WOWY with his goals per 60 minutes taken out:</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="text-align: center;">
Alt<span style="mso-spacerun: yes;"> </span>= WOWY – Comp</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Altruistic contribution is basically the difference in the
goals scored by a player’s <i style="mso-bidi-font-style: normal;">teammates</i>
(not including the goals that the player himself scored) when he is in on the
ice versus when he is off the ice.<span style="mso-spacerun: yes;"> </span>In
other words, it is a measure of how he affects his teammates’ goal scoring.<span style="mso-spacerun: yes;"> </span>If his <i style="mso-bidi-font-style: normal;">teammates</i>
score more goals with him than without him, he’ll have a high altruistic
contribution, regardless of whether or not he scores many of the goals.<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
So his WOWY is broken into two parts:</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="text-align: center;">
WOWY = Comp + Alt</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The competitive and altruistic contribution could also be
thought of as selfish and unselfish contributions, although we kind of think
selfish has too negative of a connotation to use this terminology.<span style="mso-spacerun: yes;"> </span>Scoring goals should not have a negative
connotation.<span style="mso-spacerun: yes;"> </span>Thinking of altruistic
contributions as unselfish contributions is ‘aight though. </div>
<div class="MsoNormal">
<br /></div>
Let’s look at a couple of pictures.<span style="mso-spacerun: yes;"> </span>First, since this altruistic contribution is
a measure of how a player affects his teammates’ goal scoring, it should be
correlated with assists.<span style="mso-spacerun: yes;"> </span>Here’s a
scatter plot, using data for forwards from the 2010-11 season:<br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-pcg_12D8_3hGL4i315R4o0RbBdox5YpUGLaKjG32C933XdfrqZpJT8Alml2pCpE895BtL90C7C3LHnEvX_-50gJeA-EqTj0cL01GFI-Ps4LwWW1c2dx5gW-P30HFY3TM6P4CBgHfNfSh/s1600/alt-vs-assists-60.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-pcg_12D8_3hGL4i315R4o0RbBdox5YpUGLaKjG32C933XdfrqZpJT8Alml2pCpE895BtL90C7C3LHnEvX_-50gJeA-EqTj0cL01GFI-Ps4LwWW1c2dx5gW-P30HFY3TM6P4CBgHfNfSh/s400/alt-vs-assists-60.png" width="400" /></a></div>
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<br />
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Yup, they are pretty correlated.<span style="mso-spacerun: yes;"> </span>Now let’s plot competitive versus altruistic
contributions.<br />
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSCmeS5oEbxfPXzYDVwQ0O6b_Cx1Ae9CK12TYZwetL1jkKO1cI4lp2h0rQ-vTa2kZx9Any0UNmVpmS9Mrzs9ZqxMA4-LouyH8bB4jW2_ZqibgrFSNGxEYxM-330iVda_PoT-3ZSOkQ8w6W/s1600/comp-vs-alt-F-and-D.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSCmeS5oEbxfPXzYDVwQ0O6b_Cx1Ae9CK12TYZwetL1jkKO1cI4lp2h0rQ-vTa2kZx9Any0UNmVpmS9Mrzs9ZqxMA4-LouyH8bB4jW2_ZqibgrFSNGxEYxM-330iVda_PoT-3ZSOkQ8w6W/s400/comp-vs-alt-F-and-D.png" width="400" /></a></div>
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<br /></div>
<br />
Forwards and defensemen appear in two distinct groups. This isn’t terribly surprising. Since a defenseman typically scores fewer goals than a forward, his competitive contribution is typically lower, and his altruistic contributions tend to be higher.<br />
<br />
It’s also not surprising that Crosby is an outlier. But he’s even more of an outlier than usual because the season that we used for this plot (2010-11) was one of the seasons that Crosby missed time because of concussions. So we have a small sample size in his case. He was also on a ridiculous scoring pace during the first half of that season. <br />
<br />
Now let’s plot competitive versus altruistic contributions just for forwards:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9jByiIpx7iPaBx84_8Gc3AvxCXoYa8CgX1brvpDaeZFSidi_0gIewOv84EUn7xY_QaprqswPx3YbKu8GuGWFolZUxlS8mFvyYLSwg-LYD64lHrBogZUG0spWTNIrGxO9dbsCa6sL8l6BK/s1600/comp-vs-alt-forwards.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9jByiIpx7iPaBx84_8Gc3AvxCXoYa8CgX1brvpDaeZFSidi_0gIewOv84EUn7xY_QaprqswPx3YbKu8GuGWFolZUxlS8mFvyYLSwg-LYD64lHrBogZUG0spWTNIrGxO9dbsCa6sL8l6BK/s400/comp-vs-alt-forwards.png" width="400" /></a></div>
<br />
Actually let’s remove Crosby… we won’t have all that blank space, and we’ll have room to add some more names:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEAfgYVahxTj5JVz2GPuUUdRobGjw24TjNwq_JhQEd56bxgFgWng27Gy8Ga_XHGO_tqCuyX_5y2bgPs2PaFDDtM1Hv5gyq5nIHPD1HSO9AKrH_U1LSMfsX__r8SYd0QYreSJtMvuE4_SRK/s1600/comp-vs-alt-forwards-no-Crosby.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEAfgYVahxTj5JVz2GPuUUdRobGjw24TjNwq_JhQEd56bxgFgWng27Gy8Ga_XHGO_tqCuyX_5y2bgPs2PaFDDtM1Hv5gyq5nIHPD1HSO9AKrH_U1LSMfsX__r8SYd0QYreSJtMvuE4_SRK/s400/comp-vs-alt-forwards-no-Crosby.png" width="400" /></a></div>
<br />
Notice that competitive and altruistic contributions are pretty uncorrelated, which is some evidence that they are measuring different skills. Let’s add more to this picture… let’s divide this into 4 quadrants:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmtTKEvGfOFMsOlL9hA07vfk8zsy0F0x0u8_J3Mvv-n-o5Vj9PpynZfIzUiuJI0hoMWYwltHZk3lRUWokQOyB04DB6Mi1wv-5pNrDS3DtfZ_l4kgWoiKvn9jbUgI6Jlx8qTj_Pv56GGb-Q/s1600/comp-vs-alt-4-quadrants.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmtTKEvGfOFMsOlL9hA07vfk8zsy0F0x0u8_J3Mvv-n-o5Vj9PpynZfIzUiuJI0hoMWYwltHZk3lRUWokQOyB04DB6Mi1wv-5pNrDS3DtfZ_l4kgWoiKvn9jbUgI6Jlx8qTj_Pv56GGb-Q/s640/comp-vs-alt-4-quadrants.png" width="640" /></a></div>
<br />
We could use this Comp vs Alt stuff to classify players as goal scorers, playmakers, both, or neither, and here is one way to visualize it. Players with high Comp and low Alt (upper left) are goal scorers, while players with high Alt and low Comp (lower right) are playmakers. The middle (more transparent dots) is average, and the further away from the middle (more opaque dots) a player is, the further from average he is. Dots were sized by playing time.... bigger dot means more playing time.<br />
<br />
Since this only uses one season of data, some of the results are a little wacky… Grabner wouldn’t have such a high Comp if this weren’t the season he went on the ridiculous goal scoring spree. Ovechkin would still be in “Both” but would be further from the middle and probably closer to the “Goal Scorer” region. Zherdev is a pretty big outlier, but his playing time was pretty limited (Zherdev’s dot is pretty small).<br />
<br />
<b>Using Shots instead of Goals </b><br />
<br />
That’s all well and good, but we actually aren’t going use any of these goal-based Comp and Alt stats for the playmaking metric. Assists are already a goal-based measure of playmaking ability that we can use, and assists measure playmaking ability a little more directly than altruistic contribution does. What we’ll use is altruistic contribution based on <i>shots</i>. <br />
<br />
The same thing we did in <a href="http://www.greaterthanplusminus.com/2013/07/play-playmaking-metric-part-1-intro.html">Part 1</a> and above in this article can be done if we replace “goals” with “shots” everywhere. WOWY can be defined using shots. A player’s competitive contribution is simply his shots per 60 minutes. His altruistic contribution is his WOWY minus his competitive contribution based on shots.<br />
<br />
A player's altruistic contribution is the difference in shots taken by his <i>teammates </i>(not including his own shots) when he is on the ice versus when he is off the ice. If his teammates take more shots with him than without him, he’ll have a high altruistic contribution, regardless of whether or not he himself took a lot of shots. This quantity is what we’ll use, along with assists, to develop the playmaking metric. We'll (finally) talk about the playmaking metric next time.<br />
<br />Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-15188121095233840972013-07-28T13:00:00.000-04:002013-07-28T16:36:47.366-04:00PLAY: A Playmaking Metric, Part 1 – Intro<!--[if !mso]>
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I wanted to share a recent project I did with friends and
colleagues Chris Weld and Chris Arney titled "<a href="http://www.academia.edu/4104016/Quantifying_playmaking_ability_in_hockey">Quantifying playmaking ability in hockey</a>". <span style="mso-spacerun: yes;"> </span>The one sentence summary is that we developed
a metric for quantifying playmaking ability in hockey that is better than
assists in two quantifiable ways: (1) it is more consistent than assists, and
(2) it is better than assists at predicting future assists.<span style="mso-spacerun: yes;"> </span></div>
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<br /></div>
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<span style="mso-spacerun: yes;">In this article, we'll give an overview of what we're doing, and the motivation behind it. </span></div>
<div style="mso-element: comment-list;">
<a name='more'></a><br />
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One reason for the improvement is that our playmaking metric
is based on both shots and goals.<span style="mso-spacerun: yes;"> </span>Since
shots are often more consistent than goals, and better predictors of future
performance than goals, including shots helps a lot.<span style="mso-spacerun: yes;"> </span>Assists, which are based only on goals, are
subject to the same randomness as goals for small sample sizes.<span style="mso-spacerun: yes;"> </span>Also, we have accounted for strength of
teammates for our playmaking metric.</div>
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Using shots isn’t completely straightforward.<span style="mso-spacerun: yes;"> </span>While assists count the number of a player’s
passes that lead to a teammate’s goal, there is no analogous statistic that is
tracked for shots.<span style="mso-spacerun: yes;"> </span>We don’t know how
many of a player’s passes lead directly to a teammate’s shot.<span style="mso-spacerun: yes;"> </span>We note that Rob Vollman <a href="http://www.hockeyprospectus.com/article.php?articleid=1417">developed a
way to estimate passes</a> that lead to a teammate’s shot, and it works pretty
well.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;">That article also has a good </span><span style="mso-spacerun: yes;"><span style="mso-spacerun: yes;">description and </span>discussion of quantifying playmaking ability, and some interesting stuff about pass-to-shot ratios. </span></div>
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In order to develop our playmaking metric, we first develop
an “altruistic contribution” metric for players that is based on shots. It is basically the difference in shots taken by a player’s <i style="mso-bidi-font-style: normal;">teammates</i> (excluding the player’s own shots) when he is on the ice
versus off the ice.<span style="mso-spacerun: yes;"> </span>It’s kind of like a
shot-based WOWY that doesn’t include the player's own shots.<span style="mso-spacerun: yes;"> </span>This is a different approach from Vollman’s,
but I imagine this gives similar results to Vollman’s estimated passes. We'd have to take only estimated passes at even strength, and then divide by playing time at even strength (our metric is a per 60 minute statistic). I haven’t checked this though.</div>
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Then, we combine this altruistic contribution with assists to
form the playmaking metric. So the metric is based on both goals and shots, and
has the two advantages over assists mentioned in the first paragraph.<span style="mso-spacerun: yes;"> </span></div>
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<br /></div>
We'll finish Part 1 by discussing "marginal contribution" which is the first step in computing PLAY. <br />
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Next article, we’ll talk about some of the background
required to compute the playmaking metric, and look at some pictures like this:</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPtdrbdhvt1JjGBLhHl6Jf3iI81pC47ePS2PFAmetlHQNDY8q_ElrpfFSorO92xkgkxu_vBU_Ar8wGpVdWh-_eOsmdvbxa0kWmC6gKyWHpn7Mae-ECVBGvyuI5wfi9Fu4RtjsUnpb1fnKT/s1600/comp-vs-alt-4-quadrants.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPtdrbdhvt1JjGBLhHl6Jf3iI81pC47ePS2PFAmetlHQNDY8q_ElrpfFSorO92xkgkxu_vBU_Ar8wGpVdWh-_eOsmdvbxa0kWmC6gKyWHpn7Mae-ECVBGvyuI5wfi9Fu4RtjsUnpb1fnKT/s400/comp-vs-alt-4-quadrants.png" width="400" /></a></div>
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<span style="mso-no-proof: yes;"></span></div>
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Then, we’ll talk about the playmaking metric itself.<span style="mso-spacerun: yes;"> </span></div>
<span style="mso-spacerun: yes;"></span><span style="mso-spacerun: yes;"></span><span style="mso-spacerun: yes;"> </span></div>
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<b style="mso-bidi-font-weight: normal;">Marginal Contribution </b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
We start by defining a player’s “marginal contribution”, or
his total contribution to his team.<span style="mso-spacerun: yes;"> </span>It
is similar to WOWY or WOWY-like analysis, <a href="http://www.puckprospectus.com/article.php?articleid=454">which</a> <a href="http://hockeynumbers.blogspot.ca/2006/07/introduction-shift-analysis.html">have</a>
<a href="http://www.hockeyprospectus.com/article.php?articleid=238">been</a> <a href="http://hockeyanalysis.com/2013/04/11/how-are-hockeyanalysis-com-ratings-haro-hard-hart-calculated/">discussed</a>
<a href="http://www.puckprospectus.com/article.php?articleid=254">in</a> <a href="http://www.insidethebook.com/ee/index.php/site/article/with_or_without_you_at_the_win_loss_game_level/">these</a>
<a href="http://www.hockeyprospectus.com/article.php?articleid=763">seven</a>
places, for example. Marginal contribution m is defined like this:</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
m = GF<sub>on</sub> – GF<sub>off</sub></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
GF<sub>on</sub> is the goals scored by the team when player
A is on the ice.<span style="mso-spacerun: yes;"> </span>GF<sub>off</sub> is
computed by taking the average GF<sub>on</sub> of all of A’s teammates during
only the times in which they are not on the ice with A.<span style="mso-spacerun: yes;"> </span>But this average is actually a weighted
average… weighted by time on ice with player A.<span style="mso-spacerun: yes;">
</span>Some people average like this, and some don’t.<span style="mso-spacerun: yes;"> </span>We chose this method so the stats of players
who hardly play with A have a weight near 0 and do not factor into the
computation of GF<sub>off</sub>.<span style="mso-spacerun: yes;"> </span></div>
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<br /></div>
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In any case, you can just pretend this is WOWY, however you
have seen it calculated, or however you calculate it yourself, and you’ll get
the basic idea.<span style="mso-spacerun: yes;"> </span>In fact, let’s just call
it WOWY for the rest of these articles instead of marginal contribution.<span style="mso-spacerun: yes;"> </span>Also, remember we are only
considering offense, and only considering 5-on-5 play.</div>
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<br /></div>
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We could have chosen other ways to define marginal contribution.
For example, we could have used <a href="http://www.greaterthanplusminus.com/p/adjusted-plus-minus.html">Adjusted
Plus-Minus</a> (APM).<span style="mso-spacerun: yes;"> </span>I prefer APM over
WOWY (admittedly, I’m biased), but WOWY is faster to compute, especially when
we do pairs of players in the future, so we went with that instead.<span style="mso-spacerun: yes;"> </span></div>
<br />
The next step is that this WOWY will be divided into competitive contribution and altruistic contribution. We'll save this for next time. <br />
<br />
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<span style="mso-comment-author: bmac;"><a href="http://www.blogger.com/null" name="_msocom_1"></a></span></div>
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Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-65848452652881782212013-03-28T14:04:00.000-04:002013-03-28T14:04:11.001-04:00Trade deadline article at ESPN.comRyan Wagman (@RAWagman) and I recently wrote an ESPN.com article on trade deadline fixes for each of the Atlantic Division teams. Check it out <a href="http://insider.espn.go.com/nhl/story/_/id/9095366/nhl-trade-deadline-moves-rangers-penguins-devils-islanders-flyers">here</a> if you have ESPN Insider, or <a href="http://www.hockeyprospectus.com/article.php?articleid=1486">here</a> if you are a member at HockeyProspectus.com. For the other divisions, there are links on the right hand side of the ESPN article. <br />
<br />
Disclaimer: we finished the article before the Pens' flurry of trades. We picked Adrian Aucoin for the Pens, suggesting the Pens biggest need was a depth defenseman. Since then the Pens acquired a different defenseman, Doug Murray, so that sort of coincides. Of course, the Pens did some other stuff too. Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-23613362821971619392013-03-26T23:07:00.000-04:002013-03-26T23:07:05.302-04:00Wired.com article on realignment<a class="g-profile" href="http://plus.google.com/101679125736382308464" target="_blank">Samuel Arbesman</a> (@arbesman) wrote a nice article at <a href="http://www.wired.com/">Wired.com</a> titled <a href="http://www.wired.com/wiredscience/2013/03/algorithmically-realigning-sports-leagues/">Algorithmically Realigning Sports Leagues</a>. The article is a nice summary of the realignment project that Bill Pulleyblank and I worked on. Check it out <a href="http://www.wired.com/wiredscience/2013/03/algorithmically-realigning-sports-leagues/">here</a>, and the rest of our realignment stuff <a href="http://www.greaterthanplusminus.com/p/realignment.html">here</a>. Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-75750765276166101702013-03-14T22:41:00.002-04:002013-03-14T22:41:51.283-04:00Analysis of NHL's realignment planI just finished up an article over at HockeyProspectus.com, <a href="http://www.hockeyprospectus.com/article.php?articleid=1474">analyzing the NHL's new realignment plan</a>. <br />
<br />
At first glance, the new plan might appear bad for the teams in the northeast and the Florida teams, who are all in a division together. But we show, among other things, that the new plan has a fairly small impact on their travel... just a small increase over what their travel would have been in the the "best" 4-conference solution (if by "best" we mean the solution that would minimize travel). <br />
<br />
Links to all of the realignment articles are on the <a href="http://www.greaterthanplusminus.com/p/realignment.html">realignment page</a>. <br />
<br />
Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-46862181191545252442013-02-25T16:46:00.004-05:002013-03-14T22:42:33.660-04:00More realignment figuresJust wanted to post some figures that are related to the discussion going on over at <a href="http://tangotiger.com/index.php/site/comments/realignment-to-reduce-travel">Tom Tango's blog</a> about realignment. I'd encourage you to read the discussion there first. (I encourage you to read the rest of his blog regularly also.)<br />
<br />
<a name='more'></a><br />
<br />
These are pictures similar to the ones found in the paper, except they are<br />
actual distance vs weighted distance, instead of<br />
actual distance vs predicted distance. <br />
<br />
Predicted distance was a rescaled version of weighted distance, based on the linear relationship between weighted distance and actual distance. Here, we give just raw weighted distance along the x-axis. <br />
<br />
Let's start with the NFL. <br />
<div style="text-align: center;">
<img alt="" height="350" 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" width="400" /></div>
<br />
The slope of this line is nearly 1, which makes sense since in the NFL teams go back and forth for every road game. In the other leagues, they do not, so we should not expect a slope of 1. Here's the NHL:<br />
<br />
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<img alt="" height="350" 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" width="400" /></div>
<br />
Still very linear, but definitely not a slope of 1. Here's MLB: <br />
<br />
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<img alt="" height="350" 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" 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Again, linear, but the slope is less than 1. Here's the NBA:<br />
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" 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Definitely the worst of the bunch. Something seems to be going on with the two groups of teams in the ovals. The small oval is all the West Coast teams. This method underestimates travel for those teams by a lot. This is potentially because the schedulers work extra hard to make efficient schedules for those teams, giving them multiple-game road trips when they have to travel long distances. But without knowing more information, that's just a guess. </div>
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I've disable comments so that the discussion stays at <a href="http://tangotiger.com/index.php/site/comments/realignment-to-reduce-travel">Tango's blog.</a> </div>
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Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.comtag:blogger.com,1999:blog-2679864635981349020.post-55602418416048086912013-02-20T17:02:00.000-05:002013-03-14T22:42:20.396-04:00NHL Realignment I recently finished a paper on realignment with friend and colleague
Bill Pulleyblank. The purpose of the project was to determine solutions to realignment that minimize travel for the league. We also compare our best solutions to the NHL 4-conference proposal from around a year ago. <br />
<br />
I also wrote a couple of articles about it on Hockey
Prospectus. Links to everything, plus some animations that are discussed in the second Hockey Prospectus article, can be found on the <a href="http://www.greaterthanplusminus.com/p/realignment.html">Realignment</a> page.<br />
<br />Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com1tag:blogger.com,1999:blog-2679864635981349020.post-18565834375985809782013-02-15T13:12:00.000-05:002013-03-14T22:42:06.050-04:00Realignment AnimationsI'll be writing some articles on realignment shortly. In the mean time, here's a preview... I posted some animations related to this project on the <a href="http://www.greaterthanplusminus.com/p/realignment.html">Realignment</a> page, including the top 100 solutions for each of the 4 major sports leagues.<br />
<br />
Details about our method of generating and ranking these realignments is coming soon...Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-44520024718239130912012-11-23T15:56:00.000-05:002012-11-23T15:56:31.384-05:00Nashville Preds surprise youth hockey gameThought this was pretty cool. <br />
<blockquote class="tr_bq">
The Nashville Predators surprise a youth hockey game by bringing the
full NHL experience to the rink. The families and kids are stunned to
see and hear the NHL announcer, Paul McCann, the national anthem, Gnash,
and about 250 fans take over the game.</blockquote>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/wBMjPc69Tuk?feature=player_embedded' frameborder='0'></iframe></div>
Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-34345035476771253962012-11-16T20:17:00.000-05:002012-11-25T12:27:12.860-05:00The nhlnumbers.com Reference LibraryOver at nhlnumbers.com, Eric T. has been compiling a nice <a href="http://nhlnumbers.com/2012/11/1/stats-article-reference-library">Reference Library</a> with "articles that have advanced our understanding of the game in some small way." Quality.Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-8584662775483017962012-11-16T20:10:00.000-05:002013-07-05T11:30:56.394-04:00Adjusted Plus-MinusMany of the projects I've worked on are related to Adjusted Plus-Minus (APM), so I thought I'd make that my first real, actual post. <br />
<br />
APM is a plus-minus-like statistic that improves over plus-minus in many ways. Over at <a href="http://behindthenethockey.com/">behindthenethockey.com</a> and/or <a href="http://arcticicehockey.com/">arcticicehockey.com</a>, I wrote a four-part blog series describing how the statistic is calculated, the improvements that it is has over plus-minus, and some of the results for best offensive, defensive, and overall players at even strength. Here are links to those posts: <br />
<br />
<a name='more'></a><br />
<br />
<a href="http://www.arcticicehockey.com/2011/9/22/2441898/nhl-adjusted-plus-minus-part-01">NHL Adjusted Plus-Minus Part 1</a> (an introduction)<br />
<a href="http://www.arcticicehockey.com/2011/9/22/2441898/nhl-adjusted-plus-minus-part-01">NHL Adjusted Plus-Minus P</a><a href="http://www.arcticicehockey.com/2012/1/16/2711979/nhl-adjusted-plus-minus-part-2-even-strength-offense">art 2, Even Strength Offense</a><br />
<a href="http://www.arcticicehockey.com/2012/1/29/2756500/nhl-adjusted-plus-minus-part-3-even-strength-defense">NHL Adjusted Plus-Minus Part 3, Even Strength Defense</a><br />
<a href="http://www.arcticicehockey.com/2012/5/20/3032244/nhl-adjusted-plus-minus-part-4-even-strength-overall">NHL Adjusted Plus-Minus Part 4, Even Strength Overall</a><br />
<br />
At some point I'll post some special teams results too.<br />
<br />
Recently, my updated version of APM was published. See the version at Journal of Quantitative Analysis in Sports <a href="http://www.degruyter.com/view/j/jqas.2012.8.issue-3/1559-0410.1447/1559-0410.1447.xml?format=INT">here</a> or if you don't have access to that, see the version <a href="http://academia.edu/2483598/Adjusted_Plus-Minus_for_NHL_Players_using_Ridge_Regression_with_Goals_Shots_Fenwick_and_Corsi">here</a>.<br />
<br />
This updated version uses a different statistical technique than the previous version (ridge regression instead of ordinary least squares regression). It also computes APM for goals, and also some statistics other than goals: Shots, Fenwick (shots + missed shots), and Corsi (shots+ missed shots+ blocked shots). The results are more stable. The improvement is greatest for the single-season results and the special teams results, since they use less data. <br />
<br />
In the paper, I also give some updated lists of APM's picks for various awards for 2007-2011: best defensive forward (Selke), best defensemen (Norris), best player overall (Hart). Spoiler alert: Pavel Datsyuk is the man. I'll be posting some other results here from time to time, like award winners for 2011-12 and the aforementioned special teams results, but not before posting about some other topics first...<br />
<br />
<br />Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-13148590086270267472012-10-19T23:35:00.000-04:002012-11-25T12:43:53.809-05:00Why "Greater Than Plus Minus"?When I started thinking of a website name, I had a lot of "great" ideas:<br />
<br />
anarcticicehockey.com<br />
nhlnumerals.com<br />
infrontofthenet.ca<br />
nhlprospectus.com<br />
thehockeybook.com (by limbolion)<br />
<br />
Little did I know <a href="http://www.arcticicehockey.com/">they </a>were <a href="http://www.hockeyprospectus.com/">similar </a>to <a href="http://www.insidethebook.com/">existing</a> <a href="http://www.behindthenet.ca/">website</a> <a href="http://www.nhlnumbers.com/">names</a>. The other ideas that I had clearly illustrated my lack of creativity in word-related endeavors... I studied mathematics for a reason. So I polled some friends, who were much more creative than me.<br />
<br />
<a name='more'></a><br />
Friend and spades/bridge partner Matthew T. Sitomer came up with my favorite, Greater Than Plus Minus. GTPM has three properties that I was looking for:<br />
<ol>
<li>A pun, play on words, or something else mildly (or tremendously)
amusing. </li>
<li>Some sort of reference to hockey/goals/shots/dekes/goons/etc.</li>
<li>Some sort of reference to math/stats/analysis/analytics/<wbr></wbr>etc/.</li>
</ol>
It also has the potential for a cheesy/hilarious/ridiculous logo involving >, +, and -.<br />
<br />
Since a lot of hockey analysis centers around developing statistics that are similar to plus-minus, but better than plus-minus in some way (like, for example, <a href="http://arxiv.org/abs/1201.0317">Adjusted Plus-Minus</a>), the named seemed appropriate.<br />
<br />
Many thanks to Sito, Schwooz, Saldog, and Todd for their ideas. Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0tag:blogger.com,1999:blog-2679864635981349020.post-67122840116135859942012-10-19T23:07:00.000-04:002013-01-27T10:35:51.833-05:00Introduction<div style="text-align: justify;">
Welcome to GreaterThanPlusMinus.com! </div>
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GTPM is a place for friends, colleagues, analysts, and fellow sports fans to discuss and analyze sports, and especially hockey.<br />
<br />
<div style="text-align: justify;">
While most discussion will be
quantitative on some level, we'll discuss other stuff too. And while
hockey will be a focus, we'll talk about <span style="font-size: small;"><span style="font-family: inherit;">baseball and </span></span>other sports too. </div>
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Enjoy!</div>
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Brian</div>
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Anonymoushttp://www.blogger.com/profile/07071975735587550601noreply@blogger.com0