Monday, March 26, 2012

"We're better than those guys

Statisticians rarely make good members of sports teams.

I found this out the hard way when I used to be on a frisbee team. Most people run on overconfidence. I've had numerous arguments with people over whether this makes sense or not. The general view is that if I psych myself up that we're going to win, I'm going to try harder to make it happen. If I believe I'll fail, I'll be demoralised and not try hard.

The idea is thus that belief in success and failure has a self-fulfilling component. Only a component, mind you - if I really truly believe I can beat Kobe Bryant to the net in a game of one-on-one, I will fail. But I'll still have a better chance than if I don't believe in myself.

Frankly, I was always a bit skeptical of this argument, as it reeks of a second-best solution. In other words, if you're being rational, better answers are unlikely to come from deliberately feeding in faulty inputs. Including your chances of victory. This only works if it's the workaround to some other faulty process - one bias (inability to try hard in the face of failure) is offset by another bias (convincing yourself that you won't fail).

But I remain committed to the belief that the first-best solution is always to eliminate the biases - in this case, figure out how to try hard even if you do think you'll lose.

Since this is what I aim at, I want to know the true probability, and work from there. It's a fair bet that most other team members (if they're non-economists or non-statisticians) won't feel that way. They'll view you as a negative nancy.

I remember this came to its zenith when we were down at half time. The captain of the team was trying to get us fired up. He said 'hands up who thinks we're going to win this game'. About half the team put up their hands. He responded, 'Right, you guys are on the field'. Personally, I thought this was absurd, but that's probably part of the reason I never got made captain.

The net effect of all this is that you end up with the absurd result that on any given sports field, at least 70% of the players think they're going to win. They think that they're better than the other team. Talk about the Lake Wobegon Soccer team effect.

It also leads to a hilarious misconception of what it means to be 'better' than the other team. For most people, if they lose on a knife-edge, they'll be bitterly disappointed.

But the statistician sees it differently.

If we play against a really rubbish team, we'll win about 95% of the time. Then we'll advance higher, and play a better team, that we'll beat 70% of the time. We'll advance higher still, until we're playing a team that we have an edge over, but it's tough - we might win 60% of the time. 

And eventually, we'll get to a point where we're playing against a team that's very evenly matched. We'll have a 50% chance of winning. And we might just end up in a 16-16 game to 17. And someone drops the disc, and the other team scores. And we lose.

The non-statistician weeps.

The statistician is sanguine. In expectation, we got exactly where we should have. We bet on a fair coin, and it  came up tails. This time we lost. Next time we'll win.

But there's no disappointment just because the coin landed on tails.

Funnily enough, that might make for a reasonable consolation speech afterwards. It would certainly have a better likely effect relative to the 'we're probably not going to win, but I plan to try jolly hard anyway' speech.

On the other hand, I'd would be much more inspired by the speech that talked about the true probabilities.

After all, not everybody who's willing to face up to true probabilities is necessarily a coward. The best response to likely defeat is to stare the truth in the face, and give it the finger.

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