Mar 152011
 

I thought this debate had been fully hashed out already but apparently some people still don’t believe that the game score has an impact on shooting percentage (and shot quality).  The following table shows the shooting percentages by game score over the past 3 seasons (2007-08 to 2009-10) during even strength situations where neither goalie is pulled for any reason (including delayed penalty situations).

Situation Shots Goals SH% Prob<= Prob>
Down2+ 23650 1852 7.83 0.3794 0.6206
Down1 30447 2356 7.74 0.1696 0.8304
Tied 60753 4427 7.29 0.0000 1.0000
Up1 26842 2288 8.52 0.9999 0.0001
Up2+ 19351 1779 9.19 1.0000 0.0000
Overall 161043 12702 7.89 0.5024 0.4976

The Situation, Shots, Goals, and SH% columns are self explanatory.  As you can see, shooting percentage is at its lowest in game tied situations, increases slightly for teams that are trailing and increases significantly for teams that are leading.

The second last column titled Prob<= show the probability (according to a binomial distribution) that that number of goals or fewer would be scored on that number of shots if the expected shooting percentage was 7.89%, the same as the overall 5v5 shooting percentage.  The last column titled Prob> is simply 1-Prob<= and shows the probability of getting more than that number of goals on that number of shots.  So, in down 2+ goal situations, there is a 37.94% chance of their being 1852 or fewer goals scored on 23650 shots which indicates that the down2+ shooting percentage isn’t different from the 5v5 mean at any reasonable confidence level.  The same conclusion can be drawn about down1 situations.  But, the shooting percentages in game tied, up1 and up2+ situations are statistically different at an extremely high confidence level.  Essentially there is zero chance that game tied, up1, or up2+ situations have the same natural shooting percentages as game overall 5v5 situations.  In no way can luck be the sole reason for these differences.

So, does this conclusively tell us that shot quality exists and varies according to game score?  It probably does, but I can’t say it is conclusive as it could mean that teams that trail a lot have bad goaltending (the reason they are trailing) and this results in the team leading having an inflated shooting percentage.  So, what if we looked at shots against a particular team.  Let’s say, for example, against the NY Rangers.  Here is what that looks like.

Situation Shots Goals SH% Prob<= Prob>
Overall 5159 386 7.48 0.5135 0.4865
Up1 843 73 8.66 0.9116 0.0884
Up2+ 485 46 9.48 0.9571 0.0429
Leading 1328 119 8.96 0.9800 0.0200
Tied 2004 138 6.89 0.1658 0.8342

I chose the Rangers because they use predominantly one goalie and that goalie is generally speaking a quality goalie.  As you can see, the confidence levels aren’t quite as strong as league wide mostly because of the smaller sample size but if we combine the up1 and up2+ categories we can say that shot quality against the Rangers when the opposing team is leading is statistically different than shooting percentage against the Rangers overall.

If you are interested in seeing what happens with a team that has had chronically bad goaltending, here is the same table for the Maple Leafs.  We see the same sort of things.

Situation Shots Goals SH% Prob<= Prob>
Overall 5309 491 9.25 0.5120 0.4880
Up1 938 94 10.02 0.8098 0.1902
Up2+ 906 100 11.04 0.9698 0.0302
Leading 1844 194 10.52 0.9712 0.0288
Tied 1985 149 7.51 0.0034 0.9966

So what have we learned.

  1. Shooting percentages vary according to game score.
  2. Those shooting percentage differences can’t be attributed to luck.
  3. Those shooting percentage differences can’t be attributed to goaltending.

That means, it must be the quality of the shots that varies across game scores.  In short, we can conclude that when teams get down in a game they open up and take more chances offensively which in turn gives up higher quality shots against which makes perfect sense to me.

When we combine this with my previous post on the Washington Capitals shooting percentage last season, it is probably safe to assume that shot quality exists and we can’t safely assume that all shots can be treated equal in all situations.

Jan 302011
 

Yesterday there was a post on the Behind the Net Blog which discussed the Washington Capital’s 2009-10 even strength shooting percentage of 11.0% and the conclusion was that it must be mostly luck which resulted in a shooting percentage that high.  But was it?  It was noted in the article that in 2007-08 the Capitals shot at 8.1%, in 2008-09 they shot at 8.2% and this season they are shooting at 8.2% again.  So clearly 2009-10 appears to be an anomaly, but was it a luck driven anomaly or something else?

Most people in the hockey analysis world have been using a simple binomial distribution to simulate luck so I’ll do that here too.  The thing is, if the Washington Capitals were really a 8.2% shooting team last year, the chances of them shooting 11.0% or better on 2045 shots is a mere 0.0042%.  That kind of luck we should expect once every 8000 NHL seasons.  In short, we can be pretty confident that the Capitals 11.0% shooting percentage wasn’t all luck driven.

So the next question is, how much of it is luck, and how much can we attribute to other factors?  Well, let’s assume that their good luck was significant to the point where there would only be a 5% chance they could have experienced even more luck.  We can do this by constructing a binomial distribution using centered on a shooting percentage where the chance of producing a shooting percentage of >11.0% is 5%.  The result is shown in the following chart:

The far left vertical line is the number of goals that Washington would produce if they had an 8.2% shooting percentage and the far right line is their actual shooting percentage.  The center vertical line is the theoretical shooting percentage we would need to meet the 5% luck conditions outlined above.  Under this scenario one could suggest of the extra 57 goals that Washington scored above what they would get if they shot at 8.2%, 22 of those goals can be attributed to luck and 35 can be attributed to skill.

But what if we assumed the Capitals were extremely lucky and there was only 1% chance of having greater luck.  Under that scenario their true talent level would be 9.49% shooting percentage and 26 goals would be due to skill and 31 would be due to luck.

Regardless of how you want to look at it, a significant portion of the Capitals elevated shooting percentage was likely due to non-luck factors, be they actual talent, playing style, score effects, etc.