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.
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 @pcunneen19 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.
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