THE LAW OF GENIUS AND HOME RUNS REFUTED

I. INTRODUCTION "Empirical regularities in biology, as in other fields, can be extremely interesting. In particular, such regularities may suggest the operation of fundamental laws. Unfortunately, apparent regularities sometimes cannot stand up under close scrutiny" (Solow, Costello, and Ward 2003). A lively, provocative article by DeVany (2007) in Economic Inquiry argues that: * "the statistical law of home run hitting is the same as the laws of human accomplishment developed by Lotka.... Pareto ..., Price ..., and Murray...." * "there is no evidence that steroid use has altered home run" hitting, * "the greatest accomplishments in [science, art, and music] all follow the same universal law of genius," and * "the stable Paretian model developed here will be of use to economists studying extreme accomplishments in other areas," which apparently follows from his claim that the size distribution of annual home run production has a finite mean but infinite variance and follows a "power law distribution." DeVany's argument is not unique: it is part of a large and growing literature where claims of the ubiquity of power laws are legion. (1) DeVany takes the additional step of connecting this statistical analysis to an argument about the effect of steroids on home run hitting by major league ballplayers: "steroid advocates have to argue that the new records are not consistent with the law of home runs and, that the law itself has changed as a result of steroid use." Our purpose of this article is to suggest that the above should be met with a fair amount of skepticism. First, we try to provide some background on previous attempts to identify the existence of universal laws and provide the intellectual context for DeVany's claims. Second, we show that DeVany's claims follow from a flawed statistical inference procedure. His procedure, with probability l, would find evidence consistent with "infinite variance" for virtually any nontrivial data set. To do so, we first analyze the size distribution of a quantity, which could not follow a power law distribution and show that using DeVany's inference procedure, we would be led to the same (incorrect) claim. We also discuss the important distinction--elided by DeVany and others writing in related literatures--between an unconditional distribution and a conditional distribution. Third, we observe that the size distribution of home runs cannot follow a power law distribution and show that the posited class of distributions provide an inadequate approximation to the data, at best. Fourth, while concurring with DeVany's implicit criticism that "steroid advocates" who rely on recent "trends" to substantiate their views have not made their case, we suggest that the problem is that the question is ill posed. The level and distribution of total home runs in any given year is minimally a function of hundreds of things: the quality of pitching, the weather, the introduction of new ball parks, the number of games played, the distribution of baseball talent across the teams, and so forth. To claim that only one "cause" is responsible for a trend involves some (possibly unstated) assumption about the myriad of other factors. Indeed, what is sauce for the goose is sauce for the gander: those seeking to support or deny the claim that increased use of steroids have led to increased home run hitting will have to employ considerably more "shoe leather" than mere statistical analysis of the unconditional distribution of home runs per player or time trends in home run hitting. We conclude by observing that neither examination of time trends in annual home run production nor examination of the unconditional distribution of home runs will settle the dispute between "steroid advocates" and "steroid opponents" and that more convincing evidence will have to be sought elsewhere. II. …