During a 1931 National Hockey League game between the Boston Bruins and the Montreal Canadiens, the Canadiens were up 1–0 with just a minute left to play. Art Ross, the Bruins coach at the time, pulled his goalie from the game and replaced him with a sixth attacker, hoping to tie the game and send it into overtime. It didn’t work; yet, ever since then, “pulling the goalie” has become a last-ditch, high-risk play when a team is behind and the end is nigh.
But Clifford S. Asness, founder of AQR Capital Management, and New York University’s Aaron Brown analyzed the practice over the years and conclude that pulling the goalie can be a “sound strategic move” that is often used too late. They offer some advice to hockey coaches but also find implications for investment managers.
Asness and Brown utilized a five-point model that sketches out a basic hockey game, which typically has five attackers trying to get a puck past a goalie and into the net. The model includes the probability of Team A scoring with five attackers, the probability of Team A scoring with a pulled goalie and six attackers, and the probability of Team A scoring when Team B pulls its goalie, as well as the goal differential (average difference in scoring) between five and six attackers, and the time remaining in the game.
When the researchers applied their model to all games played in the 2015–16 NHL season, they initially found that pulling the goalie seemed like a bad gamble. When a team opted for a sixth attacker, its probability of scoring went up 1.18 percent per 10 seconds of play—but because its goal was undefended, the team playing at regular strength got a 2.54 percent boost. “The team that pulls its goalie nearly quadruples the probability of its opponent scoring, while not even doubling its own chance to score,” write Asness and Brown.
But the debate doesn’t end here, because time matters—as does winning the game. Moreover, a loss in overtime still earns the team a point toward hockey rankings, while a loss in regulation play does not.
At a certain point in the game, Asness and Brown find, a losing team should take the gamble and try for the six-attacker with an empty net. A team losing by one goal should pull its goalie with 5:40 left to play. A team down two goals should pull with 11:40 left, and a team down three goals should pull at 17:40.
Yet fans will never see a coach down two points pull a goalie with more than 10 minutes left to play, the researchers observe. Instead, it’s standard to pull in the final minute or so. Asness and Brown surmise that the decision is guided by reputation: a coach who pulls early and wins will be seen as a lucky gambler rather than a skilled coach. “[W]inning ugly is undervalued versus losing elegantly; and losing ugly can be career suicide,” they write.
Herein lie the lessons for portfolio managers. It’s well established that cheap stocks outperform expensive ones, but owning cheap stocks, usually those of companies in some form of distress or dislocation, means going against the herd and suffering severe criticism if that decision results in losses. And a CIO “who chooses an alternative investment that disappoints will face sharp criticism, even if the portfolio now has a better expected long-term ratio of risk to return (and succeeds unconventionally.)”
The researchers’ advice to CIOs is to spend more time modeling risks and rewards in laboratory settings, since CIOs do not have the same benefit of experience that sports coaches get, playing game after game under the same conditions and starting from zero every time. And their advice to hockey coaches: “You’re not pulling your goalies nearly early enough; well, at least not yet.”