Modeling Law Review Impact Factors as an Exponential Distribution

Abstract:     
Legal scholars have already begun examining impact factors among law reviews as a measure of influence among these journals and the schools that publish them. John Doyle has compiled citation statistics for a wide range of English-language law journals, including total citations in law journals, total citations in judicial opinions, and journal impact factors. Ronen Perry has developed a measure of law school prestige based on the Doyle database. Bibliometrics is rapidly emerging as a preferred alternative to more subjective assessments of academic prestige and influence. Law should not be immune from this trend.

This paper evaluates the underlying mathematics of impact factors among law journals. Law journal impact factors follow the sort of stretched exponential distribution that characterizes many right-skewed distributions found in the natural and social sciences. Indeed, a simple exponential distribution - that is, a stretched exponential distribution with an exponent of 1 - generates a strikingly accurate, even beautiful, histogram of impact factors among law reviews. Mindful of physicist Hermann Weyl's admonition that any necessary choice between truth and beauty should favor beauty, I freely admit to sacrificing some marginal improvement in the descriptive accuracy of my model in order to develop the elegant mathematics of the simple exponential distribution.

Further elaboration of this model of law review impact factors as an exponential distribution yields the Gini coefficient of a stylized legal literature in which each journal's influence is expressed by its impact factor. The remarkable result of this inequality computation is that the Gini coefficient of the legal literature modeled according to a simple exponential distribution is exactly 1/2, an outcome that is determined analytically rather than empirically. I conclude that modeling law review impact factors according to an exponential distribution gives rise to a powerful mathematical tool for assessing influence among law journals and law schools.

Number of Pages in PDF File: 26

Keywords: impact factor, bibliometrics, rankings, Garfield, Doyle, Perry, Gini coefficient, Lorenz area, power law, stretched exponential, Bradford's law, Zipf's law, U.S. News, exponential distribution, empirical analysis, calculus

JEL Classification: C00, E25

working papers series