Joint Distributions and the Slow Spread of Good Ideas

byDavid_J_Balan10y20th Jul 200918 comments


A few years ago a well-known economist named David Romer published a paper in a top economics journal* arguing that professional football teams don't "go for it" nearly often enough on fourth down. The question, of course, is how this can persist in equilibrium. If Romer is correct, wouldn't teams have a strong incentive to change their strategies? Of course it's possible that he is correct, but that no one ever knew it before the paper was published. But then would the fact that the recommendation has not been widely adopted** constitute strong evidence that he is not correct? The paper points out two possible reasons why not. First, the objective function of the decision-makers may not be to maximize the probability of winning the game. Second and more relevant for our purposes, there may be some biases at work. The key point is this quote from the article (page 362):

"Many skills are more important to running a football team than a command of mathematical and statistical tools. And it would hardly be obvious to someone without knowledge of those tools that they could have any significant value in football."

Romer's point is that what's relevant is the joint distribution of attributes in the pool of potential football coaches (or other decision-makers). Even in something like professional football where there is a very strong incentive to get better results, it may take a long time for coaches who are willing/able to adopt a good new idea to out-compete and displace those who continue to use the bad old idea if there are very few potential coaches who both have the conventional talents and understand the new idea.

I think Romer is right about this, and his point is the main take-away point of this post. But I don't think the main "joint distribution" problem is a paucity of would-be coaches who understand both conventional football stuff and math: math talent can be hired to work under a head coach who doesn't understand it, just like medical talent is. Rather, it needs to be the case that the joint distribution is unfavorable and that this can't be gotten around by just adding math talent as necessary. Maybe the problem is a paucity of potential coaches who have both conventional coaching skills and also the attitude that nerds are to be listened to rather than beaten up. This may explain why baseball seems to have been much more accepting of statistical analysis than has football.

The point is this: an unfavorable joint distribution of attributes in the pool of potential decision-makers can greatly retard the adoption of good ideas, even when incentives to adopt are very strong, which means that the fact of non-adoption is not decisive evidence that an idea is bad. But for this to be true, there must be some reason why the people with the principal attribute cannot simply seek and incorporate the advice of the people with the secondary attribute. This will often be because the very acculturation process that produced the people who have the principal attribute creates some barrier to them making use of the secondary one.

"Do Firms Maximize? Evidence from Professional Football." by David Romer, Journal of Political Economy (2006). It is a sad commentary on the state of the economics profession that some journal editor seems to have made him change the title from the much cooler: "It's Fourth Down and What Does the Bellman Equation Say? A Dynamic-Programming Analysis of Football Strategy."
**I think this is a true statement, but I could be wrong. Please correct me if I am.
***Another possibility is that the problem is not the coaches, but the fans. A coach who sticks with the conventional strategy is protected by a "nobody ever got fired for buying IBM" attitude, whereas a coach who does something unconventional (but probabilistically correct) runs the risk of getting fired if it doesn't work out. This just pushes the irrationality from the coaches to the fans, but that might be more plausible: they have access to less resources to figure out what is and is not a good idea, and have much less of an incentive to try to get it right. Then the problem would be a paucity of fans who have the attribute "really care about football" and "understand and are willing to support good ideas, even from nerds."