One of the bizarre things about hockey is that the current standings system gives teams extra points for winning shootouts, which is something almost entirely orthogonal to, you know, actually being a good hockey team. I can’t think of another comparable situation in sports. Penalty shootouts in soccer are sort of similar, but they only apply in knockout situations, whereas shootouts in hockey only occur in the regular season.

Is this stupid? Yes, and a quick Google will bring up a fair amount of others’ justified ire about shootouts and their effect on standings. I think the best solution is something along the lines of a 10 minute overtime (loser gets no points), and if it’s tied after 70 then it stays a tie. Since North Americans hate ties, though, I can’t imagine that change being made, though.

What makes it so interesting to me, though, is that it opens up a new set of metrics for evaluating both skaters and goalies. Skaters, even fourth liners, can contribute a very large amount through succeeding in the shootout, given that it’s approximately six events and someone gets an extra point out of it. Measuring shooting and save percentage in shootouts is pretty easy, and there’s very little or no adjustment needed to see how good a particular player is.

The first question we’d like to address is: is it even reasonable to say that certain players are consistently better or worse in shootouts, or is this something that’s fundamentally random (as overall shooting percentage is generally thought to be in hockey)? We’ll start this from the goalie side of things; in a later post, I’ll move onto the skaters.

Since the shootout was introduced after the 2004-05 lockout, goalies have saved 67.1% of all shot attempts. (Some data notes: I thought about including penalty shots as well, but those are likely to have a much lower success rate and don’t occur all that frequently, so I’ve omitted them. All data come from NHL or ESPN and are current as of the end of the 2012-13 season. UPDATE: I thought I remembered confirming that penalty shots have a lower success rate, but some investigations reveal that they are pretty comparable to shootout attempts, which is a little interesting. Just goes to show what happens when you assume things.)

Assessing randomness here is pretty tricky; the goalie in my data who has seen the most shootout attempts is Henrik Lundqvist, with 287. That might seem like a lot, but he’s seen a little over 14,000 shots in open play, which is a bit less than 50 times as many. This means that things are likely to be intensely volatile, at least from season to season. This intuition is correct, as looking at the year-over-year correlation between shootout save percentages (with each year required to have at least 20 attempts against) gets us a correlation of practically 0 (-0.02, with a wide confidence interval).

Given that there are only 73 pairs of seasons in that sample, and the threshold is only 20 attempts, we are talking about a very low power test, though. However, there’s a different, and arguably better, way to do this: look at how many extreme values we see in the distribution. This is tricky when modelling certain things, as you have to have a strong sense of what the theoretical distribution really is. Thankfully, given that there are only two outcomes here, if there is really no goaltender effect, we would expect to see a nice neat binomial distribution (analogous to a weighted coin). (There’s one source of heterogeneity I know I’m omitting, and that’s shooter quality. I can’t be certain that doesn’t contaminate these data, but I see no reason it would introduce bias rather than just error.)

We can test this by noting that if all goalies are equally good at shootouts, they should all have a true save percentage of 67% (the league rate). We can then calculate the probability that a given goalie would have the number of saves they do if they performed league average, and if we get lots of extreme values we can sense that there is something non-random lurking.

There have been 60 goalies with at least 50 shootout attempts against, and 14 of them have had results that would fall in the most extreme 5% relative to the mean if they in fact performed at a league average rate. (This is true even if we attempt to account for survivorship bias by only looking at the average rate for goalies that have that many attempts.) The probability that at least that many extreme values occur in a sample of this size is on the order of 1 in 5 million. (The conclusion doesn’t change if you look at other cutoffs for extreme values.) To me, this indicates that the lack of year over year correlation is largely a function of the lack of power and there is indeed something going on here.

The tables below shows some figures for the best and worst shootout goalies. Goalies are marked as significant if the probability they would get that percentage if they were actually league average is less than 5%.

So, some goalies are actually good (or bad) at shootouts. This might seem obvious, but it’s a good thing to clear up. Another question: are these the same goalies that are better at all times? Not really, as it turns out; the correlation between raw save percentage (my source didn’t have even strength save percentage, unfortunately) and shootout save percentage is about 0.27, which is statistically significant but only somewhat practically significant—using the R squared from regressing one on the other, we figure that goalie save percentage only predicts about 5% of the variation in shootout save percentage.

You may be asking: what does all of this mean? Well, it means it might not be fruitless to attempt to incorporate shooutout prowess into our estimates of goalie worth. After all, loser points are a thing, and it’s good to get more of them. To do this, we should estimate what the relationship between a shootout goal and winning the shootout (i.e., collecting the extra point) is. To do this, I followed the basic technique laid in this Tom Tango post. Since shootouts per season are so small, I used lifetime data for each of the 30 franchises to come up with an estimate for the number of points that one shootout goal is worth. Regressing goal difference per game on winning percentage, we get a coefficient of 0.368. In other words, one shootout goal is worth about 0.368 shootout wins (that is, points).

Two quick asides about this: one is that there’s an endemic flaw in this estimator even beyond sample size issues, and that’s that the skipping of an attempt when a team is up 2-0 (or 3-1) means that we are deprived of some potentially informative events simply due to the construction of the shootout. Another is that while this is not a perfect estimate, it does a pretty good job predicting things (R squared of 0.9362, representing the fraction of the variance explained by the goal difference).

Now that we can convert shootout goals to wins, we can weigh the relative meaning of a goaltender’s performance in shootouts and in actual play. This research says that each goal is worth about 0.1457 wins, or 0.291 points, meaning that a shootout goal is worth about 26% more than a goal in open play. However, shootouts occur infrequently, so obviously a change of 1% in shootout save percentage is worth much less than a change of 1% in overall save percentage. How much less?

To get this figure, we’re going to assume that we have two goalies facing basically identical, average conditions. The first parameter we need is the frequency of shootouts occurring, which since their establishment has been about 13.2% of games. The next is the number of shots per shootout, which is about 3.5 per team (and thus per goalie). Multiplying this out gets a figure of 0.46 shootout shots per game, a save on which is worth 0.368 points, meaning that a 1% increase in shootout save percentage is worth about 0.0017 points per game.

To compute the comparable figure for regular save percentage, I’ll use the league average figure for shots in a game last year, which is about 29.75. Each save is worth about 0.29 points, so a 1% change in regular save percentage is worth about 0.087 points per game. This is, unsurprisingly, much much more than the shootout figure; it suggests that a goalie would have to be 51 percentage points better in shootouts to make up for 1 percentage point of difference in open play. (For purposes of this calculation, let’s assume that overall save percentage is equal to a goalie’s even strength save percentage plus an error term that is entirely due to his team, just to make all of our comparisons apples to apples. We’re also assuming that the marginal impact of a one percentage point change on a team’s likelihood of winning is constant, which isn’t too true.)

Is it plausible that this could ever come into play? Yes, somewhat surprisingly. The biggest observed gap between two goalies in terms of shootout performance is in the 20-25% range (depends on whether you want to include goalies with 50+ attempts or only 100+). A 20% gap equates to a 0.39% change in overall save percentage, and that’s not a meaningless gap given how tightly clustered goalie performances can be. If you place the goalie on a team that allows fewer shots, it’s easier to make up the gap—a 15% gap in shootout performance is equivalent to a 0.32% change in save percentage for a team that gives up 27 shots a game. (Similarly, a team with a higher probability of ending up in a shootout has more use for the shootout goalie.)

Is this particularly actionable? That’s less clear, given how small these effects are and how much uncertainty there is in both outcomes (will this goalie actually face a shootout every 7 times out?) and measurement (what are the real underlying save percentages?). (With respect to the measurement question, I’d be curious to know how frequently NHL teams do shootout drills, how much they record about the results, and if those track at all with in-game performance.) Still, it seems reasonable to say that this is something that should be at least on the table when evaluating goalies, especially for teams looking for a backup to a durable and reliable #1 (the case that means that a backup will be least likely to have to carry a team in the playoffs, when being good at a shootout is pretty meaningless).

Moreover, you could maximize the effect of a backup goalie that was exceptionally strong at shootouts by inserting him in for a shootout regardless of whether or not he was the starter. That would require a coach to have a) enough temerity to get second-guessed by the press, b) a good enough rapport with the starter that it wouldn’t be a vote of no confidence, and c) confidence that the backup could perform up to par without any real warmup. This older article discusses the tactic and the fact that it hasn’t worked in a small number of cases, but I suspect you’d have to try this for a while to really gauge whether or not it’s worthwhile. For whatever it’s worth, the goalie pulled in the article, Vesa Toskala, has the worst shootout save percentage of any goalie with at least 50 attempts against (52.4%).

I still think the shootout should be abolished, but as long as it’s around it’s clear to me that on the goalie end of things this is something to consider when evaluating players. (As it seems that it is when evaluating skaters, which I’ll take a look at eventually.) However, without a lot more study it’s not clear to me that it rises to the level of the much-beloved “market inefficiency.”

EDIT: I found a old post that concludes that shootouts are, in fact, random, though it’s three years old and using slightly different methods than I am. The three years old portion is pretty important, because that means that the pool of data has increased by a substantial margin since then. Food for thought, however.