There isn't really a shortage of writers or TV analysts who suggest that, when it comes to selecting goaltenders at the IIHF U20 world championship, coaches are better off going with the 'hot hand.' The deployment of Canadian goaltenders at the world junior championship is always heavily scrutinized, particularly in the last few years when there hasn't been a clear-cut No. 1, and also several much better goalies playing for other nations.
So how do you solve the riddle of whether to go with Malcolm Subban or Jordan Binnington? Which of the two should Spott start, on Boxing Day against Germany, and then farther along into the tournament? My suggestion would be that, rather than going by some illusory "hot hand," Spott ought to create a schedule and stick to it, barring injury. Subban has the higher save percentage in his OHL career and is used to the big ice surface and regardless of how he played in camp, he ought to be the No. 1. Play him in the opener against Germany, and then against the United States and Russia, as well as the semi-final and final. Binnington ought to see the start in the round robin against Slovakia, and then in the quarter-final, if necessary.
Why not just go with the hot hand? Because the data doesn't show that either Subban or Binnington are better coming off of a win than coming off of a loss.
What is the "hot hand effect"? Here's a brief introduction:
Gilovich, Vallone and Tversky (1985) demonstrated that individuals believe in the hot hand in basketball shooting, and that these beliefs are not correct (i.e., basketball shooters' probability of success is indeed serially uncorrelated). Other evidence from the lab shows that subjects in a simulated blackjack game bet more after a series of wins than they do after a series of losses, both when betting on their own play and on the play of others (Chau & Phillips, 1995). Further evidence of the hot hand in a laboratory experiment comes from Ayton and Fischer (2004). Participants exhibit more confident in their guesses of what color will next appear after a string of correct guesses than after a string of incorrect guesses.
It's common in basketball games and even in hockey. Coaches will give favour to players who are on scoring streaks, giving them ample power-play time or shifts in overtime. Players given more offensive opportunities tend to score more, so the "hot hand effect" becomes somewhat of a self-fulfilling prophecy. In this video clip, the Edmonton Oilers' management sits down with its analytics panel and one of them is attempting to explain to Kevin Lowe that a player that scores during regulation is not more likely to score during the shootout.
Hockey, like baseball, is a game of sequences, each with its own odds of success. A Ryan Strome shot from the circle carries a certain expected goal value, a point shot from Dylan DeMelo carries another, just as shots against Malcolm Subban or Jordan Binnington carry their own set of odds. Like coin flips, these odds are not affected by previous outcomes. You often hear the cliché about goaltenders needing to have short memories: if a goaltender dwelled too much on a loss or on a bad goal, they probably wouldn't have made a junior hockey team.
OHL's game-by-game stats pages are particularly useful, so I used them to check how either goalie did coming off a certain number of wins versus a certain number of losses. I started out by looking at coming off a loss, coming off a win, or coming off of two wins, or more than three. This is each players' OHL career as a whole, excluding games to start seasons, but including playoffs, along with Binnington's 2011 Memorial Cup appearance.
|After 1 Win||29||0.464||0.914||2.83|
|After 2 Wins||11||0.455||0.92||2.64|
|After 3+ Wins||11||0.545||0.934||2.24|
And here's Binnington:
|After 1 Win||37||0.514||0.897||3.34|
|After 2 Wins||18||0.667||0.913||2.88|
|After 3+ Wins||21||0.45||0.917||2.69|
"But wait a minute, Cam, didn't you say that the hot hand effect is an illusion? How come both Binnington and Subban appear to play way better after winning three games than after losing?" Well, I don't particularly have an answer for that. I didn't total up every OHL goaltender due to time constraints, but given how you're dealing with fewer games after 3+ wins than you are after a loss, there's a chance it could be simply random.
What is funny is that while Binnington has a .934 save percentage after his team is on a 3-game-or-longer winning streak, his team is below .500, unlike any other state.
Where I think you have similar amounts of games is if you simply total up the statistics after a loss, or after a win. Binnington has stopped 1,839 of 2028 shots when coming off a loss and 1,005 of 1,120 when coming off a win. Plug those numbers into your pocket calculator and I'm sure you'll find the save percentages are remarkably similar:
Ditto for Subban, 1,481 of 1,612 off a loss, and 1,506 of 1,638 coming off a win:
The major differences are in winning percentage and goals against average, which are affected by the teams in front of both players. The numbers would be better after a loss than a win, which I think is either due to randomness, or coaching adjustments being more likely to be made after a loss than a win.
The point of this, however, is that simply playing a goaltender because he played well in his previous game does not make him more likely to keep up that performance in his next game. Likewise, if you'd flipped a coin twice and it landed on "heads" both times, it doesn't mean that the third flip will make a "heads" call the more likely. Hockey players are people, but sometimes they act a little like weighted coins.