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November 15, 2007


Without reading the article, I can't tell whether they've taken into account the fact that a diving goalie has a higher chance of stopping a centrally-kicked ball than a non-diving goalie has of stopping one sent to the perimeter. But even that said, their explanation rings true.

I wonder whether the act-omission distinction is a special case of a wider set of "biases": that mean that it's often better to fail conventionally (dive and miss) than to fail unconventionally (stand still and miss and look like an idiot). In this case the losses aren't necessarily symmetric, and they're influenced by what other people (who may have less information than you) think about what you should do. That would seem to yield at least two types of distinct prediction from the action-bias hypothesis implied above:

(1) The default need not necessarily be to "do something". Sometimes it'll be one of a number of different somethings (e.g. Romer's finding that teams systematically make poor choices about whether to go for a field goal or a first down). Or it might be to do nothing (are there any actual examples of instances where "do nothing" is the norm?).

(2) It would also suggest that such biases are more likely to persist (despite personal expertise) in cases where (a) your outcomes depend partly on how other people judge you, and (b) the people judging you aren't very well informed.

I saw only the abstract, so I can't tell much about their methods.

Do they compare goalies who jump more versus jump less, and see that jumping more has a worse payoff? Do they persuade some goalies to jump less and then observe a better payoff?

If it's based on statistics about the directions the ball comes, there's room for error. It might seem reasonable that goalies should be able to catch some shots that they actually can't catch, and they know it but you don't.

Given the probability distribution of kick direction, the optimal strategy for goalkeepers is to stay in the goal's center

A goalkeeper who followed the strategy of staying still would very soon cease to encounter this distribution, of course. The current distribution of kick directions should be a function of what is known about goalkeeper behaviour combined with some analysis of the difficulty of the kick (per Mark Nau's comment above), whereas the analysis appears to make the naive assumption that the strategies of kickers and goalkeepers are largely independent.

Once a goalkeeper had established the reputation for doing nothing disproportionally (in comparison to other goalkeepers) wouldn't that make the job of the kickers easier? They could quit trying to guess or discern which way the goalie would dive or feint (beforehand or during the approach), simply pick one of the corners, and take a little pace off the ball or aim a foot or two more toward the center, with better odds of making a goal.

Seamus, strategies should be in a game theoretic equilibrium, where each side's choices are a best response to the other side's. This data suggests behavior is not in equilibrium here.

Didn't the other blog juggernaut Levitt have a paper on this a few years ago? His main point was that the mixed strategy of "dive left" vs. "dive right" and "kick left" vs. "kick right" worked pretty well in practice. Although I think that the result concurred that "not dive" and also "kick center" were underrepresented.

Another factor for the kicker is that a *perfectly executed* kick to the corner is unsavable, regardless of the goalie's action (if it's right in the corner he can't reach it even he dives the right way).

Obviously this is tricky and risky shot to pull off (might miss!) but has the advantage of not requiring the goalie to guess wrong.


I think that Seamus might be right because a goalie repeatedly plays the game and there is no definite last period. This means that in equilibrium the players might rationally base what they do on how they believe their current move will effect future moves of their opponents. The only way that Seamus would be wrong is if there is something special about repeatedly played zero sum games that precludes this from happening. But even then this game isn't strictly zero sum.


While you may be right that the data suggest the game is not in equilibrium and therefore the goalie should shift his behavior so that he stays in the center with greater frequency, the following quote is almost certainly not true: "the optimal strategy for goalkeepers is to stay in the goal's center." Such a predictable strategy is almost certainly not the optimal strategy because it would be terribly easy for the opposite side to adapt to such a predictable strategy. I think this one point is what's causing a lot of the comments to question the conclusion.

I suppose we could say that, if we hold the other side's strategy fixed, then the optimal strategy is to stay in the center. The writer may have meant it in that sense. But the conditional is important.

A goal-keeper is expected to miss a penalty kick most of the time. So there is no "penalty for failure": the goalies misses are forgotten, the few he saves are elevated to heroic status. And few goalies are chosen on the basis of their penalty stopping ability.

What about the kicker? If he misses a shot, or it is stopped, it's much more of a disaster for him - the penalty for failure is large indeed. Does he preform as game theory would expect, or does he also succumbing to social pressures? Could this be checked from the same data?

That reminds me of a Dilbert strip.

Dilbert goes to the boss with a problem.
The boss carefully considers the situation, and decides that there is nothing he can do about the problem. However, "doing nothing" would make him look bad to his own bosses.
The punch line is Dilbert telling his co-workers "He wants daily status reports until the situation improves."

Don't just do something, stand there!

Another piece of data that might be relevant: major league pitchers throw baseballs so fast that, in order to successfully hit the ball, a batter has to begin his swing before the ball leaves the pitcher's hand. I imagine that a goalie facing a penalty kick is may be in a similar situation: the decision of what segment of the net to guard probably has to be made before the goalie can see where the ball is going to go.

Robin Hanson wrote:

This data suggests behavior is not in equilibrium here.

This is interesting. Levitt et al wrote on the same topic (available here , pdf), and came to the conclusion that keeper/kicker strategies are indeed in equilibrium (mixed, of course). They also derive the fact that kickers choose middle much more often than keepers as part of the equilibrium of the game they set up (Proposition 3(i)). Now I don't have access to the JEP paper so I can't compare it to Levitt et al's - but someone has got to have their payoff matrix wrong. Maybe both.

So, optimal behavior as a goalie includes staying in the center of the goal every once in a while, just to keep everyone honest. This seems a lot like poker, now that I think about it.

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