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A few hours ago, I asked for some data. Almost immediately, http://war-on-ice.com/ came through.

Now, before I tell you what I did and what my results were, I had a certain expectation. My expectation is that once I had all the shots taken (and allowed) split into 4 categories, then I’d be able to weight each category based on its relevance to future goals.

This was my expectation, baselined to goals as “1”

1.0 Shots that were Goals

0.3 Shots that were Saved

0.2 Shots that were Wide

0.1 Shots that were Blocked

That is, what predicts future goals best is past goals. The reason is that shots-that-were-goals contains alot of information about the talent of the team. Shots-that-were-saved contains SOME information, but not as much as goals. Wide shots have some information, and Blocked shots have the least. With Blocked Shots, you can even argue that it is NEUTRAL, since it tells you alot about the shooting team (put themselves in a position to shoot) as it does about the defending team (executed a block, but also put themselves to allow a shot). So, I figured that Shots-that-were-blocked was close to neutral, but in favor of the shooting team.

Anyway, now we need a way to test the correlation to future goals. For each full-season, I put games 0001 through 0615 into “1st half” and games 0616 through 1230 into “2nd half”. Then for each team, I figured their 1st half Goal differential, and Save differential, and Wide Differential, and Blocked Differential (all from the perspective of the offense minus defense). And for the 2nd half, I just figured Goal Differential.

Then, I ran a regression of the four types of shot differential against future goals. The results for the 4 full seasons from 2009-10 through to 2013-14:

1.00 Shots that were Goals

0.23 Shots that were Saved

0.15 Shots that were Wide

0.43 Shots that were Blocked

As expected, all non-goal shots have to be severely underweighted. What was interesting though is that they didn’t follow the pattern I expected.

When I repeated for the 4 full seasons from 2005-06 to 2008-09

1.00 Shots that were Goals

-0.08 Shots that were Saved

0.54 Shots that were Wide

0.03 Shots that were Blocked

Again, the non-goal shots were all over the place.

I did one last one, and that was to take not only all 8 full seasons, but also to include regressing set 2 against set 1 (that is, “predicting” past goals of set 1, from the 4 types of shots in set 2).

1.00 Shots that were Goals

0.14 Shots that were Saved

0.20 Shots that were Wide

0.25 Shots that were Blocked

Basically, it really comes down to this as to how to weight the various shots:

1.0 Shots that were Goals

0.2 Shots that were Not Goals

As a reminder, this was my prior:

1.0 Shots that were Goals

0.3 Shots that were Saved

0.2 Shots that were Wide

0.1 Shots that were Blocked

While I think my prior makes more sense, we either have to respect the results of the data, or the limitations to the data as recorded by the data recorders.

A metric that EQUALLY weights all shots is not a good metric (I’m looking right at you Corsi and Fenwick). It first ignores our prior that says that shots-that-are-goals contains more information than non-goal-shots. Secondly, it’s not supported by empirical research.

Now, I know what you are going to say: how come all-shots correlate so much better than only-goals? That’s easy. The best way to increase correlation is to increase the number of trials. It’s really that simple. 100 shots is not as good a forecaster as 500 shots, which is not as good as 2000 shots. So, if you have 10 non-goal shots and 1 goal-shot, then naturally, the 10 non-goal shots will correlate better with future goals.

And indeed, this is consistent with the above results! Since we weight each non-goal shot at 0.2 and each goal at 1.0, and if you have 2 EV goals and 20 EV non-goals, then guess what. The 2 EV goals count as “2 trials”, while the 20 EV goals count as “4 trials”. So, naturally, the 20 EV non-goals will correlate better than the 2 EV goals. But, that still doesn’t mean you can weight both the same. Not at all.

The weights are the weights. And right now, you need to weight goals at “1” and non-goals at “0.2”. Welcome to our new metric, the Weighted Shots Differential. To keep up with all the silliness, I’m calling this Tango. Once Corsi et al disappear as names, we can call it Weighted Shots Differential (or wSH+/-).

Subject to further research and testing. We’re just getting started.