Antonin Panenka converted probably the best penalty ever taken, coolly chipping the ball into the middle of the goal while goalkeeper Sepp Maier leapt to his left. Had Maier stood still, the ball would have gone into his arms, but no one had previously taken such a penalty the way Panenka did.

Took me a while to find the money quote - emphasis added. The article doesn’t claim that no-one ever took a penalty kick straight to the middle of the goal before - just a penalty of whatever kind Panenka was taking.

The problem with game theory is that the human mind doesn’t always make the game theory-correct decision.

Like someone already said, the reason players don’t kick for the middle more often is more than likely an (irrational) fear of having the goalie stay put and save it, making them look like a retard.

Penalty saves are so rare anyway that most players seem content to just aim for the corner. By far more penalties are missed than are saved.

The fear is so strong that nobody even TRIED to kick a penalty in the middle of the goal until about 1976, despite penalty kicks being around for a fair while previously to that (reference here: http://www.independent.co.uk/sport/football/news-and-comment/the-cruelty-of-the-penalty-what-becomes-of-footballs-brokenhearted-832777.html)

- tripping over the ball
- missing the goal completely both high and wide
- missing wide
- missing high
- kicking it straight and having the keeper stay still and save it
- kicking it left or right and having the keeper save it

All of these have an influence on the mixed strategy the penalty taker employs. Sure, you know that the goalie is more likely to pick a side and dive to it, compared to staying centred. But if you go straight and kick it straight to the keeper, you’ll look like a bigger goose than if you go right, the keeper goes to his left, and just gets enough on it.

As the designated penalty-taker for my old team, I can say for sure that missing a penalty is the worst outcome by far for the ego. This pretty much scotches your theory.

(And high more often, rather than low, as this article suggests.)

But I think Andrew actually identifies why penalty-takers don’t aim straight more often: the embarrassment factor if the keeper makes a save! Much better to take a punt on left or right and if the keeper gets to it, it’s a great save rather than a poorly taken penalty …

And I’m surpised Romer’s NFL paper wasn’t mentioned http://elsa.berkeley.edu/~dromer/papers/JPE_April06.pdf . Especially since it carries implications beyond sport…and is applicable to Rugby League. I wanted to do some research for Honours by getting stats out of David Middleton (on an repeated game theory model), but I chose another topic.

http://pricetheory.uchicago.edu/levitt/Papers/LevittTestingTheEconomicModel2002.pdf And here’s another bit by Levitt in sport, which was unsuccessful, so I understand why Leigh avoided it.

Exactly. You wouldn’t kick very many penalties if the goalie knew exactly where you were going to aim the ball. Success requires creating uncertainty for the goalie which requires that at least sometiems the kicker aims for one side or the other, despite the fact that (obviously) but for the goalie’s presence it would make sense always to shoot for the centre of the goals. Mind you, I haven’t actually read the paper so it’s possible they considered that point. For example, if shooters nearly always aim for the sides that wouldn’t make sense. They only need to do so enough of the time to create uncertainty. But that must surely still be a fair precentage of the time, otherwise the goalie would be best advised always to assume the kicker was going to aim for the centre.

Oh wait, maybe PROFESSIONAL FUCKING SOCCER PLAYERS have already figured out the most sucessful approach.

When I played field soccer, our coach said something like “you taking penault, you donna do same each time. Make heem deeferent, make keeper theenk too much”. And what Gilberto didn’t know was not worth knowing.

Andrew Leigh blogs on the economics of sport. The paragraph on why soccer players don’t always aim for the middle of the goal on a penalty rather suggests that either Andrew or the authors of the paper he’s summarising have quite a bit to learn about the game.

When I read that description, Ken, I presumed that Andrew must not have realised that the defending team is allowed to have a goalkeeper positioned between the posts. But, no, Andrew’s paper does recognise that, and ideed, as both an economist and a former football … errr … soccer player (and in fact a goalkeeper), I am having difficulty seeing anything particular wrong in Andrew’s blog. But feel free to point it out if you’d like…

it’s high time the NSW Labor government was unceremoniously booted out ASAP almost irrespective of the the other mob (and O’Barrell doesn’t look too bad).

I’m actually leaning towards some sort of Mad Max-ian dystopic anarchy. Seems the sanest choice.