In ice hockey, if you’re down by one goal and the clock is ticking down, should you take the chance of pulling your goalie to get a sixth attacker on the ice and increase your chances of scoring? And if you decide to go for it, when is the optimal time to pull the goalie? Is it with a minute left to play? Two minutes? Or three?
Well, hockey coaches and fans, the answers can be found in a recent paper by Clifford Asness of investment firm AQR Capital Management and Aaron Brown, formerly of AQR and now an instructor at NYU’s Courant Institute of Mathematical Sciences. After examining a lot of data and doing a little math, the authors found that if you are down by one goal against an evenly matched team and want to go for at least a tie, the optimal time to pull your goalie is with 5:40 of play left in the game.
Five minutes and forty seconds may seem awfully early, since coaches typically don’t pull their goalie until the last minute or so – if they decide to do so at all. Perhaps even more surprising is that if you’re down by two goals, you should pull your goalie at 11:40 minutes remaining – or less than half way through the third period. Then if you end up scoring, you should put your goalie back in and pull again at 5:40 if you’re still behind.
Before going further, let’s note a few important things. First, the authors only looked at the objective of maximizing a team’s regular season standing points where a loss is worth zero points, a tie is worth 1.5 points, and a win is worth two. That means they focus on tying up the game from behind. If you end up losing, they do not care if it’s by a single goal or four. Whether it’s a narrow loss or an absolute trouncing, a loss is never worse than zero points.
Second, pulling your goalie does increase your chances of getting trounced. That’s because at the same time goalie-pulling raises your chance of scoring, it also raises the other team’s chance of scoring by almost twice as much.
Third, Messrs. Asness and Brown aren’t offering advice on specific game situations, where you would consider other factors like what players you have, which team is better, etc. They are only saying what to do on average over the long term – and on average, hockey coaches are not pulling their goalies nearly early enough.
The interesting question is, why? The data is out there, and coaches get the benefit of hundreds or thousands of repetitions of game situations -- so why do they keep making a sub-optimal decision?
We’re not just picking on hockey coaches here either. Other researchers have shown that football coaches don’t go for it on fourth down as much as they should. Basketball coaches resisted taking a lot of three-point shots for far too long. And years ago, Eric wrote in this newsletter that soccer goalies facing a penalty kicker typically dive dramatically to the left or right in their save attempts when statistics clearly show the highest rate of success comes from staying in the middle.
Why we ignore the evidence on the best course of action is a fascinating question. On the one hand, it could be that we think we are different and better than everyone else and don’t have to follow the evidence. On the other hand, it might be that we’re just afraid of looking bad. Asness and Brown note that “sins of commission are far more obvious than sins of omission” -- so if you pull your goalie and end up losing spectacularly, it could be career suicide. That recalls John Maynard Keynes’ famous line that “it is better for reputation to fail conventionally than to succeed unconventionally.”
For Asness and Brown, the parallels between goalie-pulling and investing are just too good to ignore because surely there are times when we should embrace unconventional risk but do not. As an example, they point out that cheap stocks have been shown to outperform expensive ones, but also look like “worse” companies. That can make investors who buy expensive stocks look “prudent” while those who buy cheap ones look “rash.” But is that right? “Nope,” they say, “the data say otherwise.”