*at random*what you'll do at each encounter, where the appropriate probabilities can be calculated. (A sports example would be a pitcher choosing what sort of pitch to make, and a batter deciding whether to swing or not.) So why doesn't anybody (so far as we know) use a random number generator to call pitches?

Although this doesn't seem to be brought up in the comments there (at least not yet), I suspect that the reason for this is that sports people are for the most part resistant to change. But more importantly, they have to answer to the media. And when your closer throws a pitch down the middle of the plate and it gets hit out of the park, and you lose, do you really want to explain to the news people that a random number generator told you to do that? There is no other line of work I can think of where it would be quite so obvious

*which*decision led to the bad outcome; more importantly, there is no other line of work with call-in radio shows devoted to dissecting everything that happens.

## 4 comments:

my sense is that there's an intuituve understanding of randomized equilibria among the players. Namely, pitchers and batters (to take one example) know intuitively that they need to be unpredictable (not technically the same as random, but functionally equivalent) in order to get an edge.

Similarly for basketball players (should I drive left or right to the basket, etc).

This might not be codified at the level of strategy, which is what you're asking about I think, but it does play a role in mano-e-mano strategizing.

a pitcher has 3 pitches (curve, chageup,fastball), a batter comes up to the plate and can't hit sliders and changeups... guess which one you throw?

defensive line (in football) is weak on one side of the field (starter just got off injury list), what side do you put pressure on?

Randomness wouldn't make sense then. Every team has a weakness/strength that needs to be exploited/avoided. Randomness would be silly if the pitcher was told to throw a slider he can't throw.

In the long run randomness might work, but that's if everything the randomness is controlling is done perfectly. If you can't throw a slider, and the computer tells you to, it wont slide and it turns into a home run.

Math example:

I think winning at a game where you have a row of coins, an even number of coins, and you alternate picking one up with another person. the person starting can always win by choosing even or odd (whichever set is more valuable) and only picking those up.

Butyou can get a better score by alternating your strategy and picking up the most valuable coins along the way.I see that is what sports are doing...

It seems to me that players do use randomized strategies, but not in the simplistic sense of random (or quasi-random) number generation.

A better description of the players' strategy would be, as already implied in the previous comment, some sort of a highly-structured stochastic model (say, a Bayesian network) where there is substantial randomness but also significant bits of prior information that makes sure that a particular players weaknesses are suitably exploited and nonsensical maneuvers do not appear in crucial situations.

We're talking about "sports teams". People who refused statistical evidence that showed that there was no such thing as a hot hand.

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