You are playing in you local club golf tournament, getting ready to tee off and there is last-minute addition to the field… Tiger Woods.  Will you play better or worse?

The theory of tournaments is an application of game theory used to study how workers respond when you make them compete with one another.  Professional sports are ideal natural laboratories where tournament theory can be tested.  An intuitive idea is that if two contestants are unequal in ability but the tournament treats them equally, then both contestants should perform poorly (relative to the case when each is competing with a similarly-abled opponent.)  The stronger player is very likely to win so the weaker player conserves his effort which in turn enables the stronger player to conserve his effort and still win.

There is a paper by Kellogg professor Jennifer Brown that examines this effect in professional golf tournaments.  She compares how the average competitor performs when Tiger Woods is in the tournament relative to when he is not.  Controlling for a variety of factors, Tiger Woods’ presence increases (i.e. worsens, remember this is golf) the score of the average golfer, even in the first round of the tournament.

There are actually two reasons why this should be true.  First is the direct incentive effect mentioned above.  The other is that lesser golfers should take more risks when they are facing tougher competition.  Surprisingly, this is not evident in the data.  (I take this to be bad news for the theory, but the paper doesn’t draw this conclusion.)

Also, since golf is a competition among many players and there are prizes for second, third etc., the theory does not necessarily imply a Tiger Woods effect.  For example, consider the second-best player.  For her, what matters is the drop-off in rewards as a player falls from first to second relative to second to third.  If the latter is the steeper fall, then Tiger Woods’ presence makes her work harder.  Since the paper looks at the average player, then what should matter is something like concavity vs. convexity of the prize schedule.

Also, remember the hypothesis is that both players phone it in.  Unfortunately we don’t have a good control for this because we can’t make Tiger Woods play against himself.  Perhaps the implied empirical hypothesis says something about the relative variance in the level of play.  When Tiger Woods is having a bad season, competition is tighter and that makes him work harder, blunting the effect of the downturn.  When he is having a good season, he slacks off again blunting the effect of the boom.  By contrast, for the weaker player the incentive effects make his effort pro-cyclical, amplifying temporal variations in ability.

Jonah Lehrer (to whom my fedora is flipped) prefers a psychological explanation.