Sunday, July 04, 2010

Poor play can be caused by bad luck

Why hasn't England won a World Cup since 1966? Who knows? The sample size is too small to draw any real conclusions. It could just be luck. In an excellent column in Thursday's Ottawa Citizen, Dan Gardner explains:

"Unfortunately, this habit of dismissing luck as a factor is not limited to sports. It's human nature. We fabricate explanatory stories automatically and effortlessly, but luck is routinely excluded from those stories because we have no intuitive feel for randomness. We often struggle merely to see luck.

"Consider England's 40 years of disappointment at the World Cup. The very fact that it has lasted four decades is often the foundation of claims that it reflects national character or whatever, but in those 40 years there have only been 10 World Cups and England has only been a serious contender in -- I'll pick a fairly arbitrary number -- six or seven. And what disasters befell England in those six or seven events? One year it was Diego Maradona's "hand of God" goal. Several times, England was ousted by penalty kicks, which are only a little more dependent on skill than coin tosses: The keeper guesses left, the ball goes right, and another chapter in the history of English misery is written."

Gardner goes on to talk about luck in other sports, and also in world events. (I also enjoyed his book about risk, which came out a couple of years ago.)

One thing I wish had been emphasized more is what you might think of as "micro luck." Gardner mostly talks about "macro luck," the big events that were obvious and obviously out of their control -- Maradona's hand of God, the goal against the Germans the referee didn't see, and so on. But most of the luck affecting sports is the smaller things, the outcomes that don't look like they involve luck at all because they appear to be entirely within the player's control. The pass that goes right to the teammate so he has an extra split-second to shoot, or the challenge that manages to get the ball from the other team at midfield.

A perfect pass is seen as a sign of skill -- which it is. But not every pass, even by the best player, will be perfect. If there were a way to make the same player attempt the same pass a thousand times or so, you'd probably see a normal distribution of where the pass would go. Some of the time the pass would be perfect; some of the time the pass would be a little off; and, rarely, the pass would be mis-hit and be completely off, perhaps a giveaway to the other team.

The difference between a good passer and a weak passer is not that the good passer is *always* good and the weak passer is *always* weak -- it's that the good passer has a tighter distribution of where the passes go, so that his passes are more often closer to the target.

Previously, I used basketball free throws as an example. An NBA player has shot thousands and thousands of foul shots in his life. All of them came in exactly the same circumstances -- same distance from the hoop, same height, same regulation size basketball, no opposing player to worry about. What happens? Even in those perfectly-controlled conditions, they can only hit 80% or so. Why? It's just a limitation of the human body. If you're even the slightest bit off in trajectory or velocity, the shot won't go. It's just a limitation of human physiology that we can't control our arms and legs precisely enough to hit the target 100% of the time. We're just not built for that level of precision.

In soccer, whether a particular player successfully makes a particular pass is about how good the player is, but it's also about whether he was lucky on the attempt. We can't control the movements of our bodies perfectly. With practice, we can be more and more consistent, but not perfect. Even 95% isn't good enough. Suppose that it takes 12 consecutive passes to move the ball from down the field to the opponent's penalty area. The probability of winning twelve consecutive 95% bets is 54%. Almost half the time, our attack will fail, and it'll be because a 95% pass, an almost sure thing, failed. It doesn't look like luck -- it looks like a gross error on the part of a certain midfielder. But that error is still luck if 95% is typical for players of that caliber.

Furthermore, what if, on a given day, the team only completes 92% of passes instead of 95%, just by random chance? Now the probability of getting the ball down the field is only 37%. That's only about 2/3 as many scoring chances as before.

If that happens to a team, and it loses the game, the narrative will be about how ineffective it was -- they couldn't get an attack together, and their passing wasn't crisp. And that's absolutely legitimate. The team did play poorly, and a lot of passes did indeed go bad.

The point is that poor play, too, can be caused by simple bad luck.

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At Monday, July 05, 2010 9:01:00 AM, Blogger Jeff J said...

Great column and great post.

It almost bubbles to the surface in Gardner's column, but not quite: he's talking about the just-world fallacy, which seems to be a regular theme in many of the numbers-based sports blogs out there.


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