I am always writing about athletics from the strategic point of view:  focusing on the tradeoffs.  One tradeoff in sports that lends itself to strategic analysis is effort vs performance.  When do you spend the effort to raise your level of play and rise to the occasion?

My posts on those subjects attract a lot of skeptics.  They doubt that professional athletes do anything less than giving 100% effort.  And if they are always giving 100% effort, then the outcome of a contest is just determined by gourd-given talent and random factors. Game theory would have nothing to say.

We can settle this debate.  I can think of a number of smoking guns to be found in data that would prove that, even at the highest levels, athletes vary their level of performance to conserve effort; sometimes trying hard and sometimes trying less hard.

Here is a simple model that would generate empirical predictions.  Its a model of a race. The contestants continuously adjust how much effort to spend to run, swim, bike, etc. to the finish line. They want to maximize their chance of winning the race, but they also want to spend as little effort as necessary.  So far, straightforward.  But here is the key ingredient in the model: the contestants are looking forward when they race.

What that means is at any moment in the race, the strategic situation is different for the guy who is currently leading compared to the trailers.  The trailer can see how much ground he needs to make up but the leader can’t see the size of his lead.

If my skeptics are right and the racers are always exerting maximal effort, then there will be no systematic difference in a given racer’s time when he is in the lead versus when he is trailing.  Any differences would be due only to random factors like the racing conditions, what he had for breakfast that day, etc.

But if racers are trading off effort and performance, then we would have some simple implications that, if it were born out in data, would reject the skeptics’ hypothesis.  The most basic prediction follows from the fact that the trailer will adjust his effort according to the information he has that the leader does not have.  The trailer will speed up when he is close and he will slack off when he has no chance.

In terms of data the simplest implication is that the variance of times for a racer when he is trailing will be greater than when he is in the lead.  And more sophisticated predictions would follow.  For example the speed of a trailer would vary systematically with the size of the gap while the speed of a leader would not.

The results from time trials (isolated performance where the only thing that matters is time) would be different from results in head-to-head competitions. The results in sequenced competitions, like downhill skiing, would vary depending on whether the racer went first (in ignorance of the times to beat) or last.

And here’s my favorite:  swimming races are unique because there is a brief moment when the leader gets to see the competition:  at the turn.  This would mean that there would be a systematic difference in effort spent on the return lap compared to the first lap, and this would vary depending on whether the swimmer is leading or trailing and with the size of the lead.

And all of that would be different for freestyle races compared to backstroke (where the leader can see behind him.)

Finally, it might even be possible to formulate a structural model of an effort/performance race and estimate it with data.  (I am still on a quest to find an empirically oriented co-author who will take my ideas seriously enough to partner with me on a project like this.)

Drawing:  Because Its There from www.f1me.net

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