PLAY: A Playmaking Metric, Part 3 - Results

In Part 2 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 teammates (excluding the player’s own shots) when he is on the ice versus off the ice.  It’s kind of like a shot-based WOWY that doesn’t include the player's own shots.  If a player's teammates take more shots when he is on the ice versus off the ice, his altruistic contribution will be high.

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.  

Playmaking Metric

Ah, finally... we can talk about the playmaking metric.  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.  To determine the best way to combine assists and altruistic contribution, we use a multiple linear regression.  The expected assists per 60 minutes that we get from this regression model are what we call our playmaking metric, PLAY.  See the paper for details of the regression. 

We built models for forwards and defensemen, and built models for half seasons and full seasons.  In all cases, PLAY was (1) more consistent than assists and (2) better than assists at predicting future assists.  Here are the half season to half season correlations of assists and PLAY for forwards and defensemen:

PLAY is more consistent than assists for both forwards and defensemen.  Results for full seasons were similar, but slightly higher across the board.  For forwards, year-to-year correlation of PLAY was 0.54.     

PLAY was also a better predictor in every way we tested it, which included cross-validation.  See the paper for the boring details.  Unless you are a statistician, in which case see the paper for the exciting details.

Top playmakers

As an example, here are the top playmakers from 2010-11, according to PLAY:
       Player Pos Team  PLAY60   A60
 Henrik Sedin   C  VAN    1.56  2.21
Claude Giroux  RW  PHI    1.40  1.82
 Anze Kopitar   C  L.A    1.37  1.78
Sidney Crosby   C  PIT    1.35  1.81
  Martin Erat  RW  NSH    1.31  1.53

We’ve shown assists per 60 minutes here also.  The one surprise here, for me at least, is Martin Erat.  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.   
Let’s look deeper.  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.  He ranked 17th, 22nd, 13th, and 13th 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.  

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.  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.  

The other players in that top 5 are players you would expect to see…  pretty standard, really.  Henrik Sedin led the league in PLAY in 3 of the 4 seasons were considered (2008-09, 2009-10, and 2010-11) and was 4th in 2007-08 (Joe Thornton was first that year).  It was nice to see Giroux 2nd.  This high rating is for 2010-2011, the year before he was second in the league in assists. 

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.  This is like a per season version of PLAY.
                         2010-11   2009-10 Difference
       Player Pos Team   PLAY  A   PLAY  A    PLAY  A
 Henrik Sedin   C  VAN     31 44     32 53       1  9
 Anze Kopitar   C  L.A     25 33     22 18       3 15
Claude Giroux  RW  PHI     25 33     17 15       9 18
 Daniel Sedin  LW  VAN     24 35     22 36       2  1
   Bobby Ryan  RW  ANA     24 28     19 17       5 11 
                   (This table was taken from the paper and edited.)

The two new names are D. Sedin and Ryan.  Crosby and Erat are out of the top 5 because of playing time (both missed games due to injury that year).  Notice we’ve also included 2009-10 stats, as well as the difference between the two seasons.  As we saw in the picture above, PLAY tends to be much more consistent than assists.

Future work

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.  So that's why we used only up to 2010-11.  We’ll eventually be updating this to include 2011-12 and 2012-13 data in the model, and get PLAY for those seasons.  But I didn't want to keep holding onto this new metric, so I just figured I'd post without the updated stats.  Forgiveness, please.

There are a couple ways this could be improved.  We could use a different measure for marginal contribution that accounts for zone starts and quality of opponents, like Adjusted Plus-Minus.  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.  We could use Fenwick or Corsi instead of shots to compute the altruistic contribution. 

Ideally, zone starts and strength of opponents would be accounted for, so PLAY is not perfect.  But fortunately, we can say that PLAY is better than assists, even the way it currently is computed, without these modifications.  

We also could do something similar with just 1st assists instead of using all assists. Since 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.

No comments:

Post a Comment