*This post originally appeared on Hockey Graphs.*

The NHL is in the middle of a goalie pulling frenzy. While the year is still young, coaches of teams who are losing by a goal have been pulling their goalie roughly around the 1:40 mark of the 3rd period the last two years, about 40 seconds earlier than they were in previous years. This development, of course, is a long time coming – analysts have been arguing for years that teams should be more aggressive in removing their netminders.

The main reason that teams have been pulling their goalies earlier is the difference in the value of a goal for and against when teams are losing. If you’re down by 2 in the third period, allowing another goal hardly impacts the amount of points you expect to earn, while scoring a goal can be a major boost to your expected points.

This is something that Micah McCurdy has written about extensively, and his idea of leverage shows how the incentives to play offense or defense change as you approach the end of the game depending on the score. Leverage is simply the change in expected standings points due to a goal for (Offensive Leverage) or against (Defensive Leverage) at a given point in time for a given score differential. The plot below shows how leverage changes for both the home and away teams depending on the score and time left in the game.

This change in approach is exciting from an analytics perspective, as it represents a tangible way that numbers can be used to actively advocate for demonstrably better strategies. And the adoption of this more aggressive but technically sound approach leads almost naturally to a new question: should teams pull their goalie when they’re trailing late on the power play?

Answering this question obviously requires us to make a lot of assumptions – after all, no one is really doing this, so we’re going to have to guess how it’ll work in a real game to do the math on when it’s worthwhile and when it’s not.

The first assumption that we’ll make is that teams will play cautiously with this strategy, and that they’ll replace their goalie with 30 seconds left in the power play if they haven’t scored by that point in time. This may be difficult to do in practice, but in our simulation we’ll assume that teams are able to replace their sixth skater with a goalie instantaneously at the 1:30 mark and we’ll update the scoring rates we’re using accordingly at that point.

We’ll also assume that scoring rates for and against are consistent with what we’ve observed in the past. We’ll use 6v4 goals for and against per 60 for play in the last 2 minutes of the game as our baseline rate since 6v4 play earlier in the game is almost entirely delayed penalty calls which will obviously decrease the rate of goals against per 60. And we’ll use overall 5v4 scoring rates as our baseline scenario, and as the expected scoring rate for the last 30 seconds of play. We’ll assume that scoring rates are constant across the whole power play which is obviously false, but probably defensible for the purposes of this analysis.

With these assumptions we can start by digging into the scoring rates to see how much of an impact playing at 6v4 has on goal scoring.

Goals Per 60 |
5v4 |
6v4 |
1:30 6v4 + 0:30 5v4 |

For |
6.4 | 12.6 | 11.0 |

Against |
0.8 | 8.7 | 6.7 |

Looking at the numbers it’s clear that (as we’d expect) scoring both for and against goes way up when you pull your goalie. Goals For per 60 at 6v4 are nearly twice that of 5v4, while Goals Against per 60 are more than eight times higher when teams play with an extra attacker. Clearly this is a high risk strategy, but does the payoff justify the cost?

To get that answer we’ll have to look at the offensive and defensive leverage charts and apply the scoring rates above to calculate the impact on expected points we’d expect to see from using each strategy for a power play starting in a given minute. The formula for this is simple: for a strategy *S *(either 5v4 or 6v4 + 5v4) and a power play starting at minute *M,* take the offensive and defensive leverage at *M + 1 *(we’ll assume that goals will occur on average in the middle of the power play) and multiply those numbers by the probability of scoring or allowing a goal on a 2 minute power play using that strategy.

*xPts Value (S, M) = P(GF | S) * Off Leverage(M+1) – P(GA | S) * Def Leverage(M+1)*

When you do this for both 5v4 and the hybrid 6v4/6v4 strategy above, we can plot the expected power play value (in standings points) at any given point in time to see where the hybrid goalie pull strategy might be effective.

As you can see, the value of the hybrid strategy is highly dependent on the score, venue, and time remaining. When teams are down by 2, there’s a good argument for pulling the goalie on a power play at any point in the 3^{rd} period, with some small positive value appearing as early as the 15 minute mark in the 2^{nd} period (5 minutes remaining). On the other hand, when teams are down by only 1 goal, the model suggests more caution, with visiting teams seeing positive value in pulling the goalie on a power play when there are 15 minutes left in the 3^{rd}, while home teams see the break-even point closer to the half-way point of the 3^{rd}.

We can also look at the problem by plotting the difference between the 5v4 and hybrid-6v4 strategy to look at the net benefit of pulling the goalie on the power play. For teams down 2, that peaks out around 0.025 standings points for an away team (fairly consistent throughout the 3^{rd} period), and 0.0375 for a home team around the half-way point of the third. When teams are down by 1, obviously the value continues to increase as the game goes on, as there’s a strong argument to keep the goalie out even when playing at 5v5.

While an extra 0.025 standings points may not seem like a big deal, it does help to view that number it in context: a team down 2 at home with 15 minutes to play is expected to earn roughly 0.19 points anyways, so a boost of 0.025 is effectively increasing your expected points by ~13%. With 10 minutes left, that same team should expect to earn just 0.11 points, so the 0.039 extra points you earn are increasing your expected points by 35%.

You could also look at the value of this strategy it in terms of dollar value.- while assigning a dollar value to a standing point is tough, Patrick D of Fear the Fin put it at roughly $1.25M/point in 2013-14 which works out to ~$1.5M/point in 2018-19 dollars. Josh and Luke Younggren also put a rough estimate of the cost of a win last year at ~$4.8M/win, or $2.4M/point. If we split the middle on these two estimates and call it $2M/point we get the following estimates of the dollar value of executing this strategy at any given time.

These aren’t huge numbers, but even trying this strategy four-to-five times per year is worth ~~more than the cost of a well paid NHL analyst~~ nearly half the cost of a player on a league minimum deal. It’s not the same as adding a superstar to your team, but every marginal benefit can help in today’s NHL.

Of course, there are many reasons why this strategy might not work. The data we used at 6-on-4 was entirely from end-of-game scenarios where the defenders may be wary of pushing hard for a goal and may be more content to just get the puck out of their zone than they would be with more than 5 minutes left to play.

It’s also possible that the specific act of replacing the goalie on the fly may be more difficult than it sounds on paper. Teams will have to both designate a player to be responsible for leaving the zone around the 30 second mark, and will need to make sure they don’t errantly pass the puck to that player around the time they’re supposed to be leaving the ice (not an easy task in the middle of the flow of a power play).

Nevertheless, the math seems to show that this might be a strategy that could be worth trying out for teams. Do I expect teams to jump on board and take this up overnight? Not at all. But with the trend towards more aggressive coaching when teams are down late, it’s only a matter of time before someone ~~gets crazy enough to let me try my weird experiments on their AHL team~~ decides that the extra edge may be worth the odds looks they’ll get when they first try it.

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