Great Expectations

It happened awhile ago, but Game 2 really got me thinking a lot about shot quality.

The perception persists that the Habs stole the game, that they were outplayed by Boston. Boston held the edge in shots, 39-31, and 21-14 at EV. That's where the positives begin and end for the Bruins.

There were two breakaways (Kovalev and AKost) stopped by Tim Thomas. The Bruins had none. Letting highly skilled opponents skate in alone on Thomas was probably not part of the Bs game plan. Hamrlik and Brisebois both hit goalposts. The Bruins had none. This was a game in which the Bruins got all the breaks (perhaps excepting penalties, which were atrociously called on both sides), but still lost in overtime.

Obviously, the scoring chance quality was not equal for both clubs. This is where Javageek's nifty little tables come in.

The expected goals in game 2 were 5.6 for Montreal, 2.0 for Boston. Expected goals are defined in Alan Ryder's Shot Quality study. Basically, he figures out an average probability that a shot will find the net for shots of different types at different distances in different situations. He finds that tip-ins, shots off rebounds, shots made close to the net and shots on the PP are all more likely to go in than normal. That sort of stuff. Adding up the goal probability for all of your shots in a game gives you an expected goal total. It's far from perfect, but it's better than just counting shots.

This table from Hockey Numbers shows a lot of interesting pieces of data for the 30 teams' performance at even strength this season.

The columns are, in order: Expected Goals For per 60, Expected Goals Against per 60, Expected Goal Differential per 60, Shot Quality Neutral Save%, Actual Goals For per 60, Actual Goals Against per 60, Relative Shot Quality For, Shots For per 60, Relative Shot Quality Against, Shots Against per 60, Actual Goal Differential per 60, Expected Total (season?) Goals For, Expected Total Goals Against, Expected Total Goal Differential.

I'm not sure one season is enough data to be able to draw conclusions, but I will anyway.

Scoring Goals

Correlation between SF (shots for per 60) and GF (goals for per 60): 0.33
Makes sense. The more shots you take, the more goals you score.

Correlation between SF and SQF (team average shot quality, relative to league average): -0.19
Small, but negative. It looks like there is a trade-off between shot quality and number of shots.

Correlation between SQF and GF: 0.32
This surprised me. The SQF number is just an average - it doesn't take number of shots into consideration at all, and it's as good a goal predictor as number of shots.

Correlation between EGF (expected goals for, product of SQF and SF) and GF: 0.53
Strong correlation. EGF is a better predictor of GF than shots-for or shot quality alone. Makes sense.

Correlation between SF and SA: -0.26
'The best defense is a good offense' rings true. When you're getting chances, the other guys aren't.

So, EGF is better at measuring offense than simple SF. This is a step toward the elusive measure of scoring chances without having to resort to counting them subjectively.

Preventing Goals
Correlation between SA and GA: 0.57
Strong - the more shots you allow, the more goals you're likely to allow. But why so much stronger than the correlation between SF and GF?

Correlation between SA and SQA: 0.41
Bad defense is bad defense: teams allowing more shots tend to allow better shots. If there are clubs who defensively rely on allowing a greater number of lower quality shots, they aren't the norm.

Correlation between SQA and GA: 0.38
Teams allowing better chances allow more goals against, but it's not as strong as simple shots against. More ammo against the low shot quality team defense.

Correlation between EGA and GA: 0.57
Expected goals against is no better a predictor of GA than simple SA. Still more ammo against the low shot quality team defense.

On defense, EGA and SA are equally good at predicting GA. That's not good news for proponents of the high-SA/low-SQA theory of defense. Ryder's paper says pretty much the same thing. In the season he studied, it looked like team defense (or lack thereof) could drive shot quality up or down by ~10% tops. It's the guys on offense who are driving most of the shot quality. Good defense and good offense both shift shots out of the SA column and into the SF column.

Javageek has posted the expected goal numbers for 46 of the 1st round games. Small sample, but nevertheless:

Correlation btw Expected Goals and GF: 0.44
Btw Shots for and GF: 0.28
Btw Shots directed at the net (incl attempts blocked and misses) and GF: 0.07

The team with the higher EGF won 35 of the 46 games.
The team with the higher shot total won 31 of the 46.
The team with the higher shots directed total won 26 of the 46.

The team with the greater EGF series total won all eight first round series.
The team with the greater SOG total won six of eight.
The team with the greater shots directed series total went 4-4.

It's not an entirely fair comparison because EGF has PP factors built in while the shot totals don't.

I'm liking this EGF number. As a measure of a team's offensive potential, it has a greater predictive value than shots. Looking at boxscores, it provides an OK scoring chance count that is 100% objective.


Blogger Phoff said...

This is neat stuff. A little over my Arts degree head, but fascinating nonetheless.

I wonder if, when looking into the quality of shots taken, the player taking the shot is factored in the equation? It might be impossible to factor in, but, IMO, it matters a gerat deal who actually is taking the shot.

4/23/2008 5:36 p.m.  
Anonymous Anonymous said...

Awesome post.

I have been checking hockeynumbers every day over the course of this years playoffs in order to see his expected goal data.

You note that the team with the greater EGF has won 35 out of the 46 games played in the first round -- roughly 76% of the time. Impressive as this figure is, it actually understates the predictive validity of expected goals.

Javageek calculated that, over the course of a large sample of games, the team with more expected goals wins 84% of the time.

4/23/2008 7:10 p.m.  
Blogger Jeff J said...

If I recall Ryder's document correctly, the individual player is not factored in. Somewhere in Javageek's work, he says there are some teams/players who consistently outperform their expected goals. I think the Montreal PP is a good example. In that situation from some areas of the ice, Kovalev is a bigger threat to score than an awful lot of other players. Yeah, the individual player is a real factor.

It would be very difficult to work that into EGF because individual players just don't score enough goals. Over the course of the season, you have a lot of data for shots in all situations all over the rink. Adding in individual players could really throw it off. Consider how many slapshots Nick Lidstrom took from exactly 103' away in SH situations all season. There was probably just the one, and he happened to score. If it ever happened again, the shot would have an expected goal value of 1.0 - probably triple the value of a breakaway. That is, if you factor individual players into EGF. There might be a way to deal with the sample size problem, but I can't think of a way to smooth it out and retain the excellent objectivity of the stat.

4/23/2008 9:40 p.m.  

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