Shootout Game Theory: Should Shooters Want Goalies Guessing?

Jack Han wrote a cool piece the other day about the shootout and game theory. He had a number of different ideas, but I want to address one in particular.

I believe his point was as follows.

“As a shooter in the shootout, if you are unpredictable, the goalie won’t know what is coming and will play you straight up. If, however, you have one prominent move and a lesser-used secondary option, the goalie is likely to know that and cheat, allowing you to score more often on your secondary option, which overall will increase your effectiveness.”

I want to look at this point within the unrealistic context of an NHL goalie having complete information on the shooter’s true shootout talent, ie their base rate, and the percentage of the time in which he uses a primary move relative to a secondary one.

So let’s say you’re a league average shootout performer with two moves (let’s say a backhand deke and a backhand-forehand deke). When the goalie plays reactionary, you score on 33% of your shots. You can, however, decide to adjust this rate by leading the goalie into guessing by using your primary move significantly more than your secondary move. The goalie, as I mentioned above, knows how much you use each move, just not in which cases you will use which.

In theory, this operates as an efficient market, which means that the goalie will do whatever it takes to maximize his odds of saving the puck, depending on what you do.

If we assume that every time the goalie guesses right, he makes the save, and every time he guesses wrong, you score, then if you use your primary move 80% of the time, the goalie will guess, and you will score on the other 20%. These numbers change depending on your tendencies, as the table below shows.

Screen Shot 2015-08-03 at 6.38.39 PM

In the goalie plays you efficiently, however, these percentages won’t hold up because once your success rate gets to the base rate, he will change to reading you, and the base rate will hold. This is shown in the table below.

Screen Shot 2015-08-03 at 6.38.50 PM

The point here is that as a league-average shootout performer, it doesn’t really matter how you vary your moves, because a smart goalie with the correct information will adapt based on the percentages.

Now the caveat is that we don’t operate in an efficient market, and this data is not available to goalies (or to anybody, because shootouts aren’t iterated/repeated games). There is variance worked into even the data we do have. So it is possible one could take advantage of a goalie in a one-time encounter, or a goalie that doesn’t understand this theory. I’m not sure over the long term that it can be that much of a help though.

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