Friday, January 22, 2010

What tennis players maximize

Nikolay Davydenko recently remarked that he cares less about tennis than Nadal and Federer:
"I have a good life. It's not only about tennis for me. Maybe I am not a champion like Nadal or Federer [demonstrating a pose to indicate single-mindedness]. For them, it's only about winning a trophy, winning a grand slam, maybe dreaming every day about it. I am not that guy, I am different. I don't cry like Federer at winning a grand slam. He holds it in all two weeks and then explodes. I am different."
This type reasoning is common among those who have ever put forth an effort to compete against others on some quantifiable scale and have fallen short of the number one spot (even though from our perspective it seems ridiculous that Davydenko would need to console himself for being only the fourth best tennis player on the planet). I suspect nearly everyone (including myself, almost daily) has at some point said to himself or herself "I must admit that this person [is more popular/is more wealthy/gets better grades/is a better worker/is more intelligent/is more attractive/weighs less/weighs more/has nicer things/has a cleaner house/is a better driver/plays the banjo better/is more articulate/gives more to charity/is more righteous/is more fun/has a deeper knowledge of alchemy] than me, but that’s ok because I care about things other than this one activity and this superior person lives an incomplete life for spending so much energy on this one thing."
When we say this, we are implying that the only dimension that matters is how good people are at maximizing their total well-being. Once we have done this, it is simple to assume that our definition of well-being is what everyone should be trying to maximize, and since other people appear to be pursuing something other than their own well-being (as defined by us), their lives are shallow and incomplete, despite how happy they may appear to be. As soon as we feel we are losing, we change the game into one in which we actually are the winner.
The question of what people are trying to maximize and how they go about doing so is key to field of economics at the moment. Traditional economics is driven by the assumption that people and firms rational maximize "utility," which can really be defined to be whatever you want it to be. Behavioral economics questions the assumption that people rationally maximize anything.
The recent financial crises struck a blow to economics because most economists were surprised and confused by it. On a large scale and for an extended period of time, banks appear not to have been rationally maximizing the present value of their expected profit stream. There was clearly a housing price "bubble," in which prices of houses were out of line with what would be expected in an efficient market for a long period of time. That economists have not yet developed a good model for bubbles is a serious problem if they hope to understand and explain the economy.
The reaction of traditional economists to examples of people that appear to be acting irrationally is that people are indeed rational maximizers, but sometimes people are maximizing something strange (this sentiment, ironically, seems a bit like they are trying to change the game into something in which they are still the winner). Behavioral economists suggest that people irrationally attempt to maximize their well-being.
I used to think that this distinction was unimportant. Whether people are rationally maximizing something totally crazy or irrationally maximizing something sensible seemed like two sides of the same coin to me. When I was watching the Roddick match the other night, and thinking about his strange serving habits, it occurred to me that this distinction is absolutely huge.
If you missed my previous post on the topic (The Behavioral Economics of the 2nd Serve), my basic thesis was this: When Roddick steps up to the line for a 1st serve, he wins the point 58.2% (71%*82%) of the time. If he misses his first serve, why would he bother hitting a conservative second serve if he has less than a 52% chance of winning the point with it? If he's trying to win points, he should just be hitting bombs for both his first and second serves.
A traditional economist would say that Roddick, like Davydenko, cares about more than maximizing the probability of winning the match. He is willing to lose a few matches if he loses with dignity and avoids criticism for foolishly being so aggressive and hitting so many double faults.
A behavioral economist might say that Roddick is attempting to maximize his chances of winning the match, but is for some reason irrationally avoiding double faults.
The traditional economist, therefore, is optimistic about Andy’s ability to pursue his own happiness. There is no problem if Roddick has decided he wants to be a mediocre top-ten tennis player who plays with style and is doing everything he can to achieve that.
The behavioral economist would say that someone needs to regulate Andy’s serving and prevent him front sabotaging his goal of winning tennis matches.
Even in this relatively simple example, it is a very deep and complicated problem to examine a tennis player’s motivations for playing a certain way.