A Player Impact Model for On the Fly Changes
Introduction
Plus-minus models like RAPM are a crucial tool for separating out a player’s impact on a team’s on-ice results at 5 on 5. In theory, we can adjust for all the recorded context of a shift – the strength of the opposition and teammates, the faceoff location, and the score of the game. Simple on-ice shot counts of an individual or combination of players can be misleading if they face particularly favorable or unfavorable situations.
On the other hand, these models make some simplifying mathematical assumptions. For instance, they assume that a player’s impact is constant while he’s on the ice and immediately stops the second when he changes. While this is a reasonable assumption about changes at a stoppage in play, on-the-fly changes are another matter. A player who steps onto the ice and faces a shot against two seconds later should not be held equally responsible for that shot as their teammate who has been on the ice for 30 seconds, while the player who changed behind the play two seconds before the shot is not held responsible at all. If certain players routinely change more irresponsibly than others, our plus-minus model will portray them more favorably than they deserve. If certain players tend to be switched on by their coaches when the puck is already in the offensive zone and a shot attempt is imminent, this model would do a better job of accounting for this deployment.
So how do we even begin to adjust our plus-minus model for this? We can visualize how a traditional model usually depicts the immediate change in responsibility to one where the change in responsibility is quick but not instantaneous:
While the design matrix of the traditional model uses a 1 or a 0 to indicate whether a player is on the ice for a given shift, each player on the ice is now assigned a value according to the output of the function depicted above, while the player who has changed off is given a value of one minus the value of the player on the ice. For instance, a player who changes onto the ice and faces a shot for or against 2 seconds into his shift, he would only get a value of around 0.1 in the new model, while the player who just changed off would get a value of around 0.9.
The motivation here is that individual shot rates in the first 5 seconds of an on the fly shift are very low but rise rapidly:
If a player has not had time to get in position to take a shot he has very likely had minimal opportunity to affect the play, and even from 5-10 seconds into a shift is benefiting from the situation created before he came on the ice, although the majority of the credit is now given to him relative to the player who switched off. After this, the player who switched off is given negligible credit.
On the other hand, on-ice shot rates for (the blue line in the chart on the right) are already near the shift average 1-2 seconds into an on the fly shift, suggesting that there are a large number of shots being credited to a player who has done almost nothing to create them, and justifying the need for a new model. On-ice shots against are low but rising the first 10 seconds of an on the fly shift: obviously players try to change when there is little threat of an imminent shot against.
We will first fit the traditional model and then compare it to the model where on the fly changes are treated as a rapid but continuous shift in responsibility from the player going off to the player coming on.
Results
All numerical values are in expected goals impact per 60 minutes. For simplicity, only median samples are displayed. For defensive columns, negative values are better. For offensive columns, positive values are better. The columns sumChange, offChange, and defChange represent the combined, offensive, and defensive changes to a player’s impact with a new model from the old model. “sumNew”,” offNew”, and “defNew” represent the combined, offensive, and defensive impact with the new model, and “sumOld” is just the combined impact with the traditional RAPM model.
Look up an individual player:
Biggest movers
Players who improved the most in our new model lean heavily toward big “shutdown” defensemen like Simon Benoit, Vladislav Gavrikov, Esa Lindell, and Colton Parayko and top pairing all-around defensemen like Devon Toews, Cale Makar, and Jake Sanderson. These players’ offensive coefficients grow far more than their defensive coefficients, implying that they are especially inclined to wait to get off the ice once their team is in a clearly advantageous position. This trend makes sense: defensemen are much more likely to be changing behind the play as their forwards carry the puck up the ice for a shot, and so there is a lot more potential for them to benefit from or be hurt by changing just before a shot for in a traditional RAPM model. Many of the forwards who improve the most offensively are known for playing defense-first roles as well.
Players whose impact on expected goals declined the most tend to be defensemen with favorable offensive deployment like Jamie Drysdale, Olen Zellweger, Morgan Rielly, and Philip Broberg or top offensive forwards who declined offensively like Nathan Mackinnon, Nazem Kadri, and Sidney Crosby – players whom a coach might like to put on the ice when the opposing team is tired and pinned in their own end – and top forwards who fall off defensively – Matthew Tkachuk, Alexander Ovechkin, Tim Stützle, Macklin Celebrini, and Nikita Kucherov – whom one could imagine might be in the habit of changing behind the play as the puck is being rushed the other way. Some of these top forwards still grade out on the high end of the new model despite being among the largest fallers in total impact.
Trophy Implications
Expected goals impact may make up a minor part of award trophy voting, but the new model brings to light some considerable contrasts between the top favorites for the major awards. Makar is one of the biggest growers in the new model thanks to his surprisingly defense-first deployment, while Norris Trophy favorite Zach Werenski is among those who decline the most with some of the kindest offensive deployment in the league. This much more favorable offensive deployment could also means better chances to compile more points at 5 on 5, where Werenski makes a big gap in production to Makar.
Of the main Selke candidates, Nick Suzuki falls into the category of the forwards whose results are somewhat inflated by favorable patterns of on the fly changes rather than a defensive workhorse, while Nico Hischier has some of the most responsible defensive shift patterns in the league, and is comparable to Suzuki in two-way impact at 5 on 5. Sam Reinhart grades out by far the best among forwards the apparent leaders in defensive impact, but doesn’t do nearly as much on the offensive end.
Takeaways
The fact that the types of players who benefit and decline with the new model tend to fit into rough categories and are not random from team-to-team should prompt hockey analysts and fans interested in hockey stats to rethink how popular xg impact models are biased by how coaches choose to deploy players and how responsible players themselves are in making changes.