Thursday, June 24, 2010

A Lesson in Psychic Reward to Winning

The economic model of an athletic tournament (and similarly job promotions, or anything with a prize) generally relies on a few simple things. First, the prize must be big enough to incent effort from all parties and structured so that players are not highly rewarded for mediocre performance. Second, the competitors in the tournament should be of relatively equal playing strength so that they do not perceive there to be too large a gap between them and their competitors, and therefore give less effort. Full effort in a tournament like Wimbeldon is paramount in keeping interest. If Nadal finds it too easy to win, he won't give a full effort and fans lose out as they don't see his amazing athleticism. If Mahut thinks there's no way he'll win no matter what, he might show up and stand there while Nadal aces him out of the tourney. Some players should be better and some worse, but in the end each person must gain positive or net zero expected value from competing in the tournament. In other words, the toll the tournament takes on the competitor (training costs, travel costs, the effect on future competitions, etc.) should not be negative with respect to the expected prize and expected chances of winning. But that's assuming a single match doesn't significantly reduce the expected value of other matches in the tournament and other tournaments!

Now, that's a very simple and brief generalization, but it makes the point of what we expect to incent players in a Tennis tournament: winning a big prize. But looking at the incredibly long matchup between Isner and Mahut, it makes us realize that in a sporting contest (and perhaps in a promotion competition at a job) there is utility gained from the prestige of winning even part of the tournament, irrespective of expected prize.

Isner is currently ranked #19 in the WTP Men's Singles Rankings, while Mahut isn't even in the Top 100. This article gives an idea of the toll it takes on one's body. That's not to mention Isner is playing in a 6 foot 9 inch frame...hardly conducive to running around for 10 hours straight. I would have expected one of the two to slightly miss and end the match at some point so they would not have to play on anymore. Woopsy! Not necessarily fix the match, but come to the conclusion that the reward is not worth the effort.

With respect to Mahut, he's not expected to cash big to begin with (Ranked #148). With respect to Isner, he has significant stake in future tournaments as well. Given the toll this could take on his body, it could cost him financial gains in the future (and actually gains in utility he may get from being a winner). At the very least, whoever wins the match is almost certainly going to be too tired to compete in the next one against a better opponent. So what's the point?

This is Wimbeldon. Other tournaments are not.


Apparently both of these guys have exorbidant pride. Some may call the behavior irrational at this point in the match...but those people would underestimate the power of winning a match at Wimbeldon. I'd say it's more worthwhile for Mahut to keep going than Isner. I don't think Isner could compete with anyone in the next round after this (and neither could Mahut), but Mahut may not get another chance at beating a Top 20 player for the rest of his career. And he's got a lot less going for him in future tournaments, where he's probably going to lose whether he's worn out or not. It should be interesting to see what happens today. Does someone give up? Will it end? Will either player be able to move tomorrow?

Time will tell--well, maybe--but no matter who wins (or even if they win any more matches for the rest of their respective careers), they'll be in the history books

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