Why NHL Coaches Should Pull Their Goalies Much Sooner – Game Theory
This discussion is based upon an article that discussed the benefits of “pulling the goalie” in order to get an extra skater out on the ice. At any point in the hockey game, a coach may take his goalie off the ice to put another skate on the ice. This obviously has the penalty of having an empty net, making it easier for the other team to score if they gain possession of the puck. The obvious benefit is that your team now (potentially) outnumbers the other team by 1 or more skaters. This strategy is almost always reserved for the last 1-2 minutes of the game by the losing team. The idea of the strategy is this: if a team is losing and fails to tie/overtake the lead, they always get 0 points. So if a team pulls their goalie and gets scored on (and thus loses), the payoff is the same even if they had kept their goalie in and lost, say 2-3 instead of 2-4. In hockey, the points are distributed as follows: Loss = 0, Overtime Loss =1, Win = 2. The hope is that the extra skater will, more often than not, lead to more tied**/won games than if they had played conservatively. This strategy is ubiquitous in hockey, but the author uses game theory to show that coaches are still far too conservative when it comes to pulling their goalie (Just like how in American Football, coaches punt on fourth down way more than they should). When down by one goal, teams often wait until one minute remaining to pull their goalie; if down by two they may pull the goalie at the 1:30 mark. The author argues that optimally, these figures should be closer to 3 minutes and 6 minutes respectively.
The article clearly correlates with our class discussions on game theory. We have different events, strategies, and payoffs in ice hockey. The model is much more complicated, as the payoff differs according to several variables. The variables include, but are not limited to: home vs. away, power-play (5v4) vs. even-strength (5v5) vs. short-handed (4v5), and a multitude of other things. The primary link to game theory is comparing pay-offs. For example, a home team that is down by 1 goal with 3 minutes left could either decide to play the conservative strategy (wait until 1 minute left), or pull the goalie at that moment. After statistical analysis, the expected point payoff for the first scenario is 0.2045, and 0.2527 for the latter. It’s clear that there is a dominant strategy here, even if it differs by just .05 points per game. Over a season of 82 games, a team who pulls their goalie more aggressively would likely add 1-2 points to their total, which is often the difference between the playoffs or the golf links for bubble teams. The fact that there is a dominant strategy begs a question: why aren’t coaches doing this already? While hockey has recently been making huge steps towards advanced statistics, many “old school” coaches prefer conventional wisdom. A coach also has to take into account the payoff of being the first to try out this aggressive strategy. He wants to keep his job, and coaches that lose with an unconventional strategy is more likely to be fired. Fans will remember the few times they lose by two goals due to pulling the goalie more than they will remember the many many times they have lost in the past due to conventional wisdom. Maybe it’s time to give fans and General Managers a crash course on the “Law of Large Numbers”. What’s interesting is that when coaches finally make the switch, the rest will surely follow. This will obviously result in a Moneyball-esque situation where no one sees the benefit of the payoff because everyone else is getting the same edge. Nevertheless, as coaches start embracing advanced statistics, I believe we’ll be seeing a lot less of the goalie (and a lot more confused first-time hockey-game-goers) at the end of close games.
Article: http://mindyourdecisions.com/blog/2015/05/05/why-nhl-teams-should-pull-the-goalie-more-often-game-theory-tuesdays/#.VfmI4_kUWhc
**tied games at the end regulation go to a sudden death overtime. Losing in OT leads to 1 point, winning leads to 2 points.