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July 30, 2003

Go for it!

Today on NPR (audio archive will be available after 6 PM) there was a short interview with an economist who stated that "going for it" on 4th & 1 yard to go in a football game is the rational thing to do. And yet most fans know that coaches generally refuse to "go for it," even if it is "4th & inches"! Why? The economist stated "...we are quite perplexed, because we know that people tend to maximize their benefit...." This is a clear application of rational choice theory and its short-comings, the economist notes that coaches are probably carrying over decision making patterns from other areas of life without reflecting upon it. I believe that rational choice theory has a big role to play in social science, but it tends to put the emphasis on human rationality and choice, neglecting that our evolutionary background probably has a strong effect on our reactions to any given situation. Our software can react dynamically to many situations, but we also have many pre-built modules that simply initialize whenever a familiar context is recognized.

Update: Here is David Romer's paper that elaborates his argument. For a more sports-oriented take, here is a column on the topic by ESPN's Greg Garber.

Posted by razib at 01:04 PM

when seeing a blatant asymmetry between theory and reality, my first instinct is a misspecified theory. It could be a Khaneman-Tversky type behavioral quirk, but odds are it's the economist, not tradition, that is in error.

Posted by: eric at July 30, 2003 01:18 PM

The general idea makes sense. It's a good way of explaining why people by lottery tickets, too - human decision making heuristics are not well-suited to dealing with such tiny probabilities, so unless someone has both knowledge of and faith in mathematics they may feel that buying the ticket makes sense.
Of course in the specific example given the economist may not have hard information on why he thinks the football coach should make a different decision... second guessing is easy. Plus I've seen a lot of coaches take the gamble.

Posted by: bbartlog at July 30, 2003 01:28 PM

I would comment if I knew what 'going for it' meant. Unfortunately I am ignorant of this and all other sport ...

Posted by: Jason Soon at July 30, 2003 01:40 PM

I can comment on the lottery tickets. People's indifference curves need not be smooth curves - that is, they may be risk-averse in most areas of life, especially those that involve big losses, yet lottery tickets may convey utility that is additional to the risk of losing/chance of winning money enough to tip their balance. Also there is a big difference between losing a lot of implicit income by having a bad fall, by, say, being on a risky transportation and losing income from choosing to buy lottery tickets and knowing one will lose a certain predetermined amount of small magnitude

Posted by: Jason Soon at July 30, 2003 01:43 PM

Yes, you can shoehorn the lottery ticket purchase in under classical economics by ascribing additional utility to the purchased ticket that is somehow above and beyond the actual monetary value. I prefer theories that acknowledge the existence of irrational actors to those that ascribe utility to various nebulous perceptions, though.

Posted by: bbartlog at July 30, 2003 02:19 PM


'Nebulous perceptions' are indeed questionable, but irrationality is not much better. For all the behaviorist tools--anchoring effect, representativeness bias--they really don't explain much except anecdotes. At least the newer behavioralists add some structure to irrationality, but even so the payoff from should have arrived by now (Khaneman and Tversky did most of their seminal work in the 70's and 80's), but it hasn't.

To me the greatest problem with utility theory is that it generally ignores that after a base level of consumption is acquired, most utility is from relative status. This is why indices of 'happiness' from surveys show that we are no happier today than we were 50 years ago, in spite of massive increases in material wealth, leisure time, etc. Relative status makes sense to evolutionary biologists (get those genes in the next generation), but it's anathema to economists because it makes their assumption of utility maximizing agents go from amorally selfish to immorally selfish (at least before the assumption was people were indifferent to others but their desire to be rich would indirectly lead them to a happy endgame, with relative status as a goal strife is eternal).

Posted by: eric at July 30, 2003 03:19 PM

People who buy lottery tickets obviously derive pleasre from the feelings of hope and optimism that the ticket gives them.

If they truly understood how little of a chance they have of winning, then they wouldn't get the enjoyment out of it that they do.

I figure that I have a much better chance of becoming a millionaire by investing in the stock market than I do by buying lottery tickets.

Posted by: Gordon Gekko at July 30, 2003 04:40 PM

Those of you who would never buy a lottery ticket are ill qualified to comment on those of us who do. As a lotto buyer, I can tell you the calculus involved, at least for me: There is no loss contemplated or possible, as the amount tendered is negligible, therefore the numerical odds are superfluous. The fact is that someone will win, and the winner is someone who holds a ticket. Thus, the calculation is, zero money in, and a tiny possiblity that there will be a huge return + the entertainment value provided by checking the number in the morning paper. For me, that represents a very good value... and I do statistics for a living!

Posted by: Michael Gersh at July 30, 2003 06:07 PM

Bbartlog - the economic explanation for lottery tickets is perfectly intuitive and plausible and Michael Gersh has just confirmed it (though of course its strength is not reliant on any introspective confirmation). People do obviously get pleasure from taking the occasional *controlled* gamble and it's not clear to me that most of the time they even bother to find out what the odds of winning are and multiply them by prize to get the expected reward. Obviously there is a heuristic involved here rather than expected utility maximising - however you misunderstand the status of the rationality assumption. A theory that assumes irrationality is simply useless at this stage unless you're the mathematical genius who's going to come along and redesign economics. People have been carping on for years about rationality but rationality is no more a strong assumption than is 'reproduction maximisation' in evolutionary biology. Organisms don't consciously have a replication function yet it's useful to model them as if they do. The map is not the territory. Without the rationality assumption, or at least some constrained rationality assumption (where the calculus involves some rational amount of rationality because of imperfect information, costs of collecting information, etc) you are no longer in the realm of analysis but pure description.
Same problems at this stage plague relative status issues - I don't think economists care particularly whether they would have to assume amoral or immoral behaviour - what works is what is adopted - it's just that interpersonal utilities (which is what you're talking about) are hard to model too and the issue is whether the additional detail of interpersonal utilities is so important to the final equilibrium that it's worth adding in to recalibrate the results slightly

Posted by: Jason Soon at July 31, 2003 12:33 AM

Jason -

I've heard this line of argument before, and I must confess I don't get it. It seems to be saying, "We economists know that the models we use are useless, but we don't have anything better, and we'd rather continue to crunch numbers than just describe things - because then people might confuse us with sociologists."

Posted by: jimbo at July 31, 2003 06:15 AM

Jason -
Interesting explanation. Ok, you've convinced me, at least as regards useful economic modeling. I still regard Michael Gersh's explanation somewhat skeptically, since he seems willing to disregard or treat as negligible one quantity (the monetary cost of the ticket) while counting another smaller quantity (the expected winnings) on some level. But since he includes the entertainment value of the process I can't argue with his overall conclusion.

Posted by: bbartlog at July 31, 2003 08:21 AM

I didn't read the article, but certainly as you've expressed it here, that's much too simplistic. There is no one right answer whether or not to go for it on fourth and short, because it depends on many factors (field position, relative strength of lines, score, etc.). For instance, it would generally be insane to go for it on your own ten yard line.

Posted by: Rand Simberg at July 31, 2003 08:55 AM

I didn't read the article, but certainly as you've expressed it here, that's much too simplistic. There is no one right answer whether or not to go for it on fourth and short, because it depends on many factors (field position, relative strength of lines, score, etc.). For instance, it would generally be insane to go for it on your own ten yard line.

yep-that's a big point, it is rational within certain parameters. i just wanted to get across the major idea that coaches go for about 10% of the time they "should" go for it....

Posted by: razib at July 31, 2003 10:18 AM

I have read a similar analysis of the odds of having the strongest batter bat from the "cleanup" position, or fourth. It seems that there might be a numerical advantage to having the strongest batter go from the third position. Years later, I have detected no movement amongst baseball managers to change their traditional lineups.

Tradition and emotion are important factors; maybe as strong as numerical analysis. The expectations of fans and bosses may factor in as well. A coach might get less criticism from failing to go on fourth down than he would from going for it. Something like the old saw about buying from IBM. Taking the traditional approach and failing to be preferred to doing something untraditional and failing.

Posted by: Michael Gersh at August 1, 2003 07:05 PM