Game Theory and Sports and You

• Posted by Adam Warner
• on October 20th, 2009

In our never-ending quest to diss stats nuts every time they try to tackle sports, I bring you this from The Economist (hat tip Mutant Dog).

PASS, or slip the football to the running back? Fastball or curveball? Place the penalty kick to the goalkeeper’s left, or to his right? To those who play sport for a living, the choice can mean glory or ignominy; to fans, ecstasy or agony.

To economists, it is a test of the “minimax” theory of how two-person, zero-sum games should be played. A player should mix up his choices in such a way that the chance of success is the same: the probability of scoring a goal, say, should be the same whether he kicks to the left or the right. And his choice should not depend on what he did last time.

Do people who play games for a living behave as the theory predicts? Not according to a new paper* by Kenneth Kovash, of Mozilla, the organisation behind the Firefox web browser, and Steven (“Freakonomics”) Levitt, of the University of Chicago, who crunched the evidence from 3.1m pitches in Major League Baseball and 128,000 plays in the National Football League (NFL).

In baseball, fastballs were the most common type of pitch, making up 65% of the sample. However, batters enjoyed significantly more success against them, on average, than against other types. That implies pitchers sent down too many. Worse still for the theory, having thrown a fastball, a pitcher was less likely to throw another next time. Cutting down on fastballs and removing the correlation between pitches, the authors suggest, might be worth a couple of games a season—enough to help a team squeeze into the playoffs in a tight year.

Mr Kovash and Mr Levitt find similar flaws in the NFL. Teams tended to pass the ball too little and to run it too often, and were less likely to pass if they had passed on the previous play. Over a 16-game season, these choices might cost a team the equivalent of half a win.

I both think this has a lot of merit, and is ridiculous. Is that possible?

I’ve seen Game Theory pieces like this relating to poker. What if you used some sort of randomized bluff strategy. In other words,let’s say you want to bluff on 20% of all hands, but obviously dont want to just do it every 5th hand. What if you created some sort of randomizing program that will tell you which hands to bluff (having nothing to do with the actual hand in front of you). Would such a system outperform your judgement? In theory, would be much more difficult for another player to read what you are doing.

In the same vein, randomized play calling in football or pitch selection in baseball should outperform, as they say.

But in reality again, like last week, they play these games on an actual field. Perhaps pitchers throw more fastballs than anything else is because they actually throw them better? Maybe when you’re actually standing in the batters box, it’s hard to time a swing when a pitcher is changing speeds from pitch to pitch. Maybe, just maybe, pitchers feel that even if a batter suspects a curve or changeup coming after a fastball, he’ll still have trouble adjusting his bat speed. Maybe a pitcher (a good one) is planning out a whole sequence of pitches.Maybe a pitcher likes throwing one up and in, then painting the outside corner next. Even if everybody knows that’s the next pitch coming.

And in football, ever see a team set up a pass by running a couple times then using play action?

So yes, game theory sounds great, but I truly doubt random behavior will beat out a well thought out and executed strategy.

Again though, here’s my suggestion. Try all this math stuff at Duke. Hire a Freakonomics disciple as head coach. Have him announce he’s hiring Monte Carlo simulation whizzes as his playcallers. Would at least throw the opposition off as there won’t be much in the way of tendencies to shoot against.

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