One of the first posts that I wrote on this website was about pulling the goalie. I’d noticed that Andy Murray seemed to be awfully aggressive in pulling his goalie and tied it into the fact that some papers had been written of which the Kings of an earlier generation were aware.
If hockeymetrics has an equivalent to the sabrmetrics loathing of the sacrifice bunt and trading outs for bases, it should probably be the ingrained refusal of hockey coaches to pull their goalie earlier in the game. There was an interesting paper published out of Simon Fraser University a few years back that I thought might be of interest to readers. I’m not going to review it at length but I’ll go through and pluck out some highlights.
Coaches simply rely on conventional wisdom, or on what has been done for decades in the world of hockey. According to St. Louis Blues head coach Andy Murray, \I think a guide rule is if you’re down by two goals, you pull him with about two minutes remaining. Or if you’re down by one goal, you’re looking at the one-minute mark.”
It’s kind of funny that the authors cite an Andy Murray quote in explaining the conventional wisdom – as you can see from the post that I linked above, Murray had some extraordinarily aggressive goalie pulls in the time period that I was looking at. What intrigues me, and the authors of the paper, is the question of which is the right strategy. Does it make sense to pull the goalie earlier in the game?
The authors rely on data from the 2007-08 season. I don’t propose to delve into their math too much – there are some tweaks and changes that I’d make to what they’re doing and maybe some unnecessary complexity at some points but, on the whole, it seems like a reasonable way to come up with an estimate of what should be done. They basically built a simulator, a way to try out different strategies in terms of pulling the goaltender. Let’s go to the guts of the thing:
An analysis of the time when goaltenders were pulled by their coaches during the 2007-2008 NHL season shows that this move is typically done with 1 minute remaining if a team is trailing by one goal and with 1:30 remaining in the case of a two-goal deficit.
The strategy is generally adopted by NHL coaches no matter the game situation, except for shorthanded situations, in which case the goaltender is almost never pulled. Let us call the above decision rules the current strategy. In Tables 4 through 7, we investigate four scenarios along with various strategies which are listed in order of eectiveness as
measured by their ANP.
“ANP” means “average number of points.” What the authors have done is built a simulator that they can use to test out certain strategies against what they call “the current strategy” and set out in the excerpt that I’ve quoted. They set out four different situations in which they tested a number of different strategies. I’ll go through them all, because I think that they’re interesting.
The road team is trailing by 1 goal with 3 minutes left. Both teams are playing at full strength (5-on-5).
So, ANP is average number of points. What the authors have done is simulate each of those strategies for this situation 150 million times and then calculated the average points earned with each of the four strategies. As you can see, the current strategy – pull the goalie with a minute left – is the worst strategy. Pulling your goalie until the score is tied nets you an extra 0.05 points per game.
The home team is trailing by 2 goals with 6 minutes left. Both teams are playing at full strength (5-on-5).
Again, the current strategy is the worst one. Going in all-in isn’t quite the best strategy that they found but it gets you about 55% more points in the long run than pulling the goalie with 1:30 left.
The home team is trailing by 1 goal with 1:54 minutes left. The home team is playing shorthanded (4-on-5) as they just got called for a penalty.
The road team is trailing by 3 goals with 12:22 left. The road team has a 5-on-3 power-play with 2:00 minutes and 1:16 minutes remaining in the penalties.
There’s a trend here: the authors are finding that the strategies employed by NHL coaches are too conservative and don’t produce the best outcomes. In their words:
In summary, the simulations suggest that NHL coaches are too conservative. The current strategy is easily outperformed in terms of ANP with more aggressive decisions regarding pulling the goaltender. All of the papers mentioned in Section 1 similarly conclude that goalies should be pulled earlier. An important question concerns the benefit that a team realizes over the course of a full season of 82 games by using more aggressive strategies. We simulate 4 million games between average road and home teams under three general strategies. The objective is to compare the ANP using the current strategy with the ANP using more aggressive strategies. The results are given in Table 8 and are listed in increasing order of aggressiveness.
From Table 8, an average team can increase its expected number of points by 1 over the course of an 82-game season by simply pulling the goalie when trailing by any number of goals with less than 3 minutes left. A more aggressive approach results in an improvement over the current strategy by 1.5 points. Without providing all of the details, the more aggressive approach involves pulling the goaltender when shorthanded, even-strength and on power-plays with increasing time remaining and various goal deficits. Finding even better strategies is an obvious research question of interest. The gain in terms of expected number of points might turn out to be 2-3 points per season. While that may not seem to be a major improvement at first glance, note that the seeding of 13 teams (43% of all teams) would have been higher than their actual seeding had they obtained an extra 2.1 points during the 2007-2008 season.
Table 8 looks like this:
There’s something off about this, I think – the numbers seem to be too low to me. The average team in the NHL gets around 92 points a year and these numbers seem to low. I’ve emailed the authors to ask about it but it doesn’t really affect their analysis in terms of the optimal strategy in certain situations as far as I can tell.
If you’ve read this far, you can probably guess why I wrote this. We saw two aggressive goalie pulls from Dallas Eakins so far in the pre-season: one in Winnipeg where he pulled Dubnyk quite early and then tonight in Oklahoma City he pulled Dubnyk with eight minutes left in a 3-0 game. Regrettably, Dallas scored about thirty seconds later to make it 4-0 and send Dubnyk back into the nets.
This is going to be a talking point over the course of the season, I suspect. That being said, there’s not a shred of evidence that Eakins is wrong to be more aggressive in pulling the goalie – if anything, the evidence probably suggests that he won’t be aggressive enough, getting his goalie out earlier. Still though, what it appears that he’ll do comes closer than most to what is likely the optimal strategy. It’s probably not a huge gain – a point or two over the course of a season but, as the authors note, a point or two can change things significantly.Email Tyler Dellow at email@example.com