Stephen Curry and mixed strategies

Ever since I learnt recently about the rise of Stephen Curry, and Golden State Warriors’ rise using a three-point strategy, my interest in basketball and the NBA has gone up. I still can’t watch a game – the randomly spaced ad-breaks are too mindfucking for that. But I’ve been reading a lot more about Curry and Golden State Warriors and Joe Lacob of KPCB.

There are two ways in which you can attack in basketball – you can either keep tiki-takaing and drive in to get close to the basket to layup/dunk or you can go for a three-pointer. We can think of each basketball attack as a “game”, where the offensive team decides to go for either the three-point or the tiki-taka, and the defensive team decides how to defend against it.

I won’t bother with drawing the payoff table here, but given research on similar “games” in sports (such as penalty kicks in football), it wouldn’t be hard to guess that the dominant strategy here is the “mixed strategy”, where a team chooses at random whether to tiki-taka or long range.

Over time, this would have led to a certain proportion of the time when the team would have decided to take long shots, and defences would have adapted accordingly (defence against a mixed strategy is also a mixed strategy).

What Curry’s extraordinary three-point shooting skills have done is that they’ve completely changed the payoffs for his team, but significantly increasing the payoff of the three-point strategy. So the Warriors have adapted their strategy accordingly, by going for the three-point game more often than the tiki taka game.

And my sense is that Curry’s shooting statistics are so much better than others’ that the proportion with which the Warriors go with the three-point strategy (as the game theoretic solution suggests) is significantly higher than the proportion with which other teams adopt such a strategy in attack.

Consequently, defences have failed to anticipate this change in the payoff matrix and defend like they do against other teams (whose mixed strategy hasnt changed). In other words, the Warriors’ opponents haven’t been playing the optimal strategy while playing against them. And this is what has led to their unprecedented 73-win NBA season.

With time, other teams are likely to adjust and adapt more optimal strategies. It’ll be interesting to see how the Warriors perform next season!

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