Why NHL Teams Should Pull The Goalie More Often – Game Theory Tuesdays
http://mindyourdecisions.com/blog/2015/05/05/why-nhl-teams-should-pull-the-goalie-more-often-game-theory-tuesdays/#.Vf36M6PD-pp
There is some interesting strategy at the end of ice hockey games. Teams that are down by a goal or two get desperate to tie up the score. Aggressive teams will substitute an extra attacker by removing their own goalie, leaving an empty net. So long as the team can retain possession they have a better shot of scoring. But if they lose the puck, the other team can score on an unguarded goal. I always thought this was a great part of NHL games. The shame is it doesn’t happen enough. Teams only pull the goalie for the last couple of minutes in close games. It got me thinking about the game theory. Is it possible teams are too conservative? Should they pull the goalie for a longer amount of time? Are there other advantageous situations to use the strategy? Surprisingly, the answer to all of these questions is yes! I did a bit of searching and statistical research suggests teams are too conservative in pulling the goalie. Just like NFL coaches often erroneously punt on 4th down, or NBA coaches mistakenly rest players in foul trouble, NHL coaches mistakenly leave the goaltender and fail to use an extra attacker. Here is the reason why they should be more aggressive in pulling the goalie. Should you remove the goaltender? One school of thought holds “always leave the goaltender in the game.” In the 1980 Olympics, the Russian team never opted for an extra attacker, a move that surprised US players who pulled off the miracle on ice. supposedly teams in Europe are less likely to pull their goalie. In the US, the extra attacker is a time-tested strategy, dating back to the Boston Bruins in 1931. The strategy makes intuitive sense. If you are going to lose the game if you fail to score, you should sacrifice some defense for extra offense. The interesting question is how long you should employ the strategy. Setting the optimal time is difficult as there is a slippery slope paradox. If you would be willing to have an empty net for x seconds, you would be indifferent, or even favor, an empty set for x + 1 seconds. But extending the logic means you would be fine pulling the goalie for the entire game–and that clearly doesn’t make sense! Intuition and logic may be poor guides, so let us consider the statistics. Thinking Statistically In 2007, the conventional strategy was to pull the goalie with 1 minute left when trailing by one goal and with 1:30 left when trailing by two goals. Were coaches doing the right thing? David Beaudoin, a statistics professor at the University Laval, wondered this question while watching an NHL game. He wrote a paper, co-authored by Simon Fraser University’s Tim Swartz, that suggests teams should pull the goalie more frequently. (Here is a link to the paper (pdf): Strategies for Pulling the Goalie in Hockey. David Beaudoin and Tim B. Swartz.) The paper develops a simulation to analyze the correct decision. At any given time, there are some major events that can happen in a game: one of the teams can score a goal, be called for a penalty, or have a penalty expire. If a penalty is called, then that will affect the number of players on the ice and determine a matchup (5 on 5, 6 on 5, etc.) A hockey game can then be thought of as a sequence of trials where these events might occur given the matchup. Pulling a goalie can be modeled as another type of matchup that affects the probability of scoring or getting a penalty. In statistical terms, the authors modeled the hockey game as a Markov chain of these states, and then they used Monte Carlo methods to estimate the parameters under different circumstances. The paper indicates the model was able to mimic the results of actual NHL games pretty well, so the model seemed like a reasonable tool. Pull The Goalie More Often! The authors used season-long data averages and simulated millions of games to estimate how different strategies would affect the chance of winning a game. A number of different situations were analyzed. For example, what should you do as the road team when your team is trailing by 1 goal with 3 minutes left? The conventional strategy is to pull the goalie at the 1 minute mark. Sometimes this works; other times it does not. A strategy was judged according to the outcome of the game and its associated points. In the NHL, a team gets 0 points for a loss, 1 point for a draw/loss in overtime, and 2 points for a win. A team that is down by a goal is very likely to lose and get 0 points. Occasionally the team will tie it up (to get 1 point) or even win it (to get 2 points). On average, the conventional strategy results in the team earning 0.2045 points. This makes sense as the team mostly loses the game, but it occasionally wins it. What if the team did the same thing, but also pulled the goalie when they had a power-play? This more aggressive strategy slightly raises their expected number of points to 0.2116. The team can further increase the expected points to 0.2527 by pulling the goalie for the entire 3 minutes until the score is tied. The higher average point totals mean that pulling the goalie tends to lead to more wins on average and therefore this is a good strategy. The critical part is a team gets 0 points if they lose by 1 goal or 2 goals. A team that pulls its goalie may give up a goal here and there, but it will not be penalized as it still gets 0 points. The key is that pulling the goalie can help a team score and thereby get a tie or even a win. The paper suggests home teams should pull the goalie when trailing by 2 with up to 6 minutes left. And they should even do this with about 2 minutes left and they are playing shorthanded (one player down). Pulling A Goalie Can Help A Team Make The Playoffs Increasing a team’s expected point total by fractions of a point might sound meaningless. But over a large enough sample, the better strategy can make a meaningful impact. If a team adopted all of these more aggressive strategies over an entire season, they would earn an average of 1 to 2 more points. This is significant because 1 or 2 points is often the difference between a team that qualifies for the playoffs versus one that gets eliminated from the post-season. One of the interesting parts of being aggressive, uncovered by the statistics, is the extra attacker increases the probability the other team commits a penalty, enhancing the offensive advantage even more. For more details on the model and the statistics, check out the full paper (pdf): Strategies for Pulling the Goalie in Hockey. David Beaudoin and Tim B. Swartz. Why Aren’t Coaches Doing This Already? The paper did make its way to St. Louis coach Andy Murray who did employ an aggressive strategy, according to The Globe And Mail. But most teams stuck to conventional wisdom. In 2014, Denver Avalanche coach Patrick Roy surprised people by often aggressively pulling his goalie. And it worked. But when asked if analytics had persuaded him, Roy replied “No. I never look at statistics, to be quite honest.” Why aren’t coaches adopting the more aggressive strategy, if it could mean the team would have a better playoff shot or seeding? There’s some game theory here too! Game Theory Implications As fans we think teams are always looking to improve the chance of winning. But individuals in teams often have slightly different incentives. One issue is each coach wants to protect his job. He wants to make decisions that resonate with a team’s players, fans, and owners. A coach that loses on an unconventional strategy is more likely to be blamed and fired. A second issue is that if pulling the goalie works, then it is an advantage only so along as other teams are not doing it. If all teams pulled their goalies optimally, then every team would increase its scoring over the season. But raising the point total of every team by 1 or 2 points does not change the relative ranking of the teams, and so pulling the goalie early would not give a competitive advantage to any individual team! These dual forces enhance the resistance to pulling the goalie. No individual coach wants to take the risk of proving the strategy works, for fear of losing a job. And if the coach proves the strategy works, then everyone can copy it and free-ride on the risk the coach took. A similar phenomenon has happened in baseball, for example. At first teams only relied on scouting and basic statistics. Very few teams took the risk to use advanced metrics to gain an advantage. Once the Oakland A’s proved sabermetrics were successful, then every team copied the “Moneyball” strategy. Now all teams care about pitch count, on-base percentage, and defensive shifts. The net effect is that baseball is a different product, but no team gets a competitive advantage since all teams are using analytics. In spite of inertia, I think NHL teams will adopt analytics and eventually start pulling the goalie more often. It is the smart choice and makes for more exciting play. This should be reason enough because the NHL should always be looking to improve its product and ratings.