Predicting team SH% from player talent

For NHL teams, shooting percentage (SH%) doesn't seem to carry over all that well from year to year. Here repeated from last post, are the respective correlations: 

-0.19  2014-15 vs. 2013-14
+0.30  2013-14 vs. 2012-13
+0.33  2012-13 vs. 2011-12
+0.03  2011-12 vs. 2010-11
-0.10  2010-11 vs. 2009-10
-0.27  2009-10 vs. 2008-09
+0.04  2008-09 vs. 2007-08

(All data is for 5-on-5 tied situations. Huge thanks to puckalytics.com for making the raw data available on their website.)

They're small. Are they real? It's hard to know, because of the small sample sizes. With only 30 teams, even if SH% were totally random, you'd still get coefficients of this size -- the SD of a random 30-team correlation is 0.19.  

That means there's a lot of noise, too much noise in which to discern a small signal. To reduce that noise, I thought I'd look at the individual players on the teams.  (UPDATE: Rob Vollman did this too, see note at bottom of post.)

Start with last season, 2013-14. I found every player who had at least 20 career shots in the other six seasons in the study. Then, I projected his 2013-14 "X-axis" shooting percentage as his actual SH% in those other seasons.  

For every team, I calculated its "X-axis" shooting percentage as the average of the individual player estimates.  

(Notes: I weighted the players by actual shots, except that if a player had more shots in 2013-14 than the other years, I used the "other years" lower shot total instead of the current one. Also, the puckalytics data didn't post splits for players who spent a year with multiple teams -- it listed them only with their last team. To deal with that, when I calculated "actual" for a team, I calculated it for the Puckalytics set of players.  So the team "actual" numbers I used didn't exactly match the official ones.)

If shooting percentage is truly (or mostly) random, the correlation between team expected and team actual should be low.  

It wasn't that low. It was +0.38.  

I don't want to get too excited about that +38, because most other years didn't show that strong an effect. Here are the correlations for those other years:

+0.38  2013-14
+0.45  2012-13
+0.13  2011-12
-0.07  2010-11
-0.34  2009-10
-0.01  2008-09
+0.16  2007-08

They're very similar to the season-by-season correlations at the top of the post ... which, I guess, is to be expected, because they're roughly measuring the same thing.  

If we combine all the years into one dataset, so we have 210 points instead of 30, we get 

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+0.13  7 years

That could easily be random luck.  A correlation of +0.13 would be on the edge of statistical significance if the 210 datapoints were independent. But they're not, since every player-year appears up to six different times as part of the "X-axis" variable.

It's "hockey significant," though. The coefficient is +0.30. So, for instance, at the beginning of 2013-14, when the Leafs' players historically had outshot the Panthers' players by 2.96 percentage points ... you'd forecast the actual difference to be 0.89.  (The actual difference came out to be 4.23 points, but never mind.)

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The most recent three seasons appear to have higher correlations than the previous four. Again at the risk of cherry-picking ... what happens if we just consider those three?

+0.38  2013-14
+0.45  2012-13
+0.13  2011-12
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+0.34  3 years

The +0.34 looks modest, but the coefficient is quite high -- 0.60. That means you have to regress out-of-sample performance only 40% back to the mean.  

Is it OK to use these three years instead of all seven? Not if the difference is just luck; only if there's something that actually makes the 2011-12 to 2013-14 more reliable.  

For instance ... it could be that the older seasons do worse because of selective sampling. If players improve slowly over their careers, then drop off a cliff ... the older seasons will be more likely comparing the player to his post-cliff performance. I have no idea if that's a relevant explanation or not, but that's the kind of argument you'd need to help justify looking at only the three seasons.

Well, at least we can check statistical significance. I created a simulation of seven 30-team seasons, where each identical team had an 8 percent chance of scoring on each of 600 identical shots. Then, I ran a correlation for only three of those seven seasons, like here.

The SD of that correlation coefficient was 0.12. So, the +0.34 in the real-life data was almost three SDs above random.

Still: we did cherry-pick our three seasons, so the raw probability is very misleading.  If it had been 8 SD or something, we would have been pretty sure that we found a real relationship, even after taking the cherry-pick into account. At 3 SD ... not so sure.

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Well, suppose we split the difference ... but on the conservative side. The 7-year coefficient is 0.30. The 3-year coefficient is 0.60.  Let's try a coefficient of 0.40, which is only 1/3 of the way between 0.30 and 0.60.

If we do that, we get that the predictive ability of SH% is: one extra goal per X shots in the six surrounding seasons forecasts 0.4 extra goals per X shots this season.

For an average team, 0.4 extra goals is around 5 extra shots, or 9 extra Corsis.

In his study last month, Tango found a goal was only 4 extra Corsis.  Why the difference? Because our studies aren't measuring the same thing.  We were asking the same general question -- "if you combine "goals" and "shots," does that give you a better prediction than "shots" alone? -- but doing so by asking different specific questions.  

Tango asked how you predict half a team's games predict the other half. I was asking how you predict a team's year from its players' six surrounding years. It's possible that the "half-year" method has more luck in it ... or that other differences factor in, also.

My gut says that the answers we found are still fairly consistent.

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UPDATE: Rob Vollman, of "Hockey Abstract" fame, did a similar study last summer (which I read, but had forgotten about).  Slightly different methodology, I think, but the results seem consistent.  Sorry, Rob!