I recently got around to updating my database for the 09-10 season and, in looking over the EV stats for each team, I noticed that the Leafs continue to have one of the best corsi ratios in the league at EV with the score tied.

I think that this is unusual for a couple reasons.

For one, the 08-09 Leafs were a poor team according to this metric. While last year's squad outshot the opposition in a general sense, their corsi ratio with the score tied was 0.94, good for 21st in the league. Thus, if one considers corsi ratio with the score tied to be a crude measure of a team's ability at even strength, the Leafs would appear to be one of the most improved teams in the NHL (looking strictly at EV play, of course).

Secondly, despite soundly outshooting the opposition, the Leafs have one of the worst EV goal differentials in the league. I haven't filtered out empty netters yet, but only the Lightning, Oilers, and Jackets are worse than Toronto in terms of goal differential at even strength. This despite directing some 500 more shots towards the other team's net at EV than their opponent over the course of the season. The effect isn't as extreme when the score is tied -- they're only -7 -- but the unusual profile remains.

The tendency to outshoot without outscoring has led some to question whether the Leafs do, in fact, outplay the opposition at even strength, or whether the shot numbers are deceiving.

One way to settle the issue is to look at the Leafs scoring chance numbers. If Toronto's scoring chance ratio broadly parallels its shot ratio at EV, then that ought to dispel notions that the Leafs don't legitimately outplay the opposition, or that they shoot from everywhere.

Slava Duris, whose blog can be found here, has been recording scoring chances for Toronto over the course of the season. To date, he's posted 53 of the games for which he's recorded chances.

Taking those 53 games in particular, I looked at how many even strength scoring chances the Leafs had with the score tied, and how many their opponents had. I then determined how many shots the Leafs directed towards the opposition's net -- again, only at EV with the score tied -- in those same 53 games, and did the same for their opponents. The raw data can be viewed below.

Overall, there were 474 even strength scoring chances with the score tied in the 53 games sampled. Of those 474 chances, Leafs generated 252, whereas the opposition generated the remaining 222. Thus, the Leafs scoring chance ratio with the score tied was 1.14.

In terms of corsi with the score tied, the Leafs directed 1008 shots towards the opposition's goal, and had 915 directed toward their own, thus giving them a corsi ratio of 1.10.

In other words, the Leafs actually did better in terms of scoring chances than in terms of corsi over the 53 games examined.

Granted, this doesn't allow one to conclude that the Leafs are a better team than their corsi ratio would suggest. For example, if we assume that Toronto's underlying scoring chance ratio is identical to its corsi ratio (1.10), then the probability of it generating at least 252 chances out of 474 randomly selected chances is 0.376 (or, if one prefers, the probability of it having a corsi ratio at least as good as 1.14 in a sample of 474 chances). In other words, the two values are not significantly different from each other.

Nevertheless, it would appear that the Leafs have managed to outplay the opposition at even strength over the course of the season, their rotten goal differential notwithstanding.

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## 7 comments:

Aren't you the clever one. If you don't mind me asking, what do you study in school, Jlikens?

Wow, so Vesa Toskala was really *that* bad?

Vic:

I'm currently in law school, but I also have an undergraduate degree in history.

Olivier:

Probably, although playing to the score effects are relevant, too.

The Leafs have played from behind for much of 2009-10 and the same was true last year (although not, interestingly, in 07-08).

And as Vic demonstrated last fall, the Leafs continued to play aggressively when holding the lead last season.

Both of those factors have adversely affected Toskala's numbers to some degree, I think.

I wouldn't have guessed that, I would have gone with commerce, or perhaps a physical science. I suppose the lesson learned is that I should assume that everyone posting on the Oilogosphere is a lawyer or law student until there is evidence to the contrary.

I like the order test, I think that's reasonable. I'd model that as an urn full of black and white balls. A white ball (1008 of them) for every TOR corsi+, and a black ball (915 of them) for every corsi-. Then we'd have TOR draw 474 balls from the urn, without replacing them after each draw. That's the total number of scoring chances in the games recorded, while the score was tied of course.

And we'd ask the question: what are the chances that TOR picks 252 or fewer white balls?

That model is represented by the cumulative form of the hypergeometric distribution. It's simple math, arithmetic really, but computers won't like the gigantic integers used ... I doubt that either a spreadsheet or the PHP math addon will work these. The former will probably give an error and the former may yield rogue values.

You could use 'R', which is free.

this function:

phyper(252, 1008, 915, 474, lower.tail = TRUE, log.p = FALSE)

yields p = .665.

So TOR fits in the 67th percentile.

Now we do the same for every other team. Even the ones for whom we only have 10 games or so. The underlying sample size is accounted for with the model here, only the error increases.

Then we'd be on our way.

Makes sense, no?

Vic:

Your way seems like the better way to do it.

My method was somewhat simpler (although less rigorous).

I 'simulated' 474 chances in which the probability of the Leafs generating each individual chance was 0.525 (i.e. 1008/(1008+915); their Corsi percentage).

I looked at 500 simulations in total. Out of those 500 simulations, the Leafs had at least 252 of the 474 chances in 188 of the simulations (188/500=0.376).

If that figure is doubled in order to take into account the other half of the distribution (which I forgot to do in my post), I get 0.752, which is in the ballpark of your p-value.

Good stuff JLikens. Terrible luck for the Leafs that Toskala was so poor. I'd be more convinced that style was negatively effecting him if the other goalies weren't so much better. At EV:

Toskala: .898

Others: .915

That's just awful. The WOWY for Toskala is pretty damning as well:

Record when Toskala plays: 7-15-4

Record when Toskala out: 23-23-10

The Leafs had other problems for sure but Toskala sure as heck wasn't helping.

I think that it is great that you are updating you database. You can find interesting data to go back to it.

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