Success-volume relationships in funnel plots

Since their first use in the context of performance assessment, funnel plots have become an established means of comparing outcomes of entities (broadly defined) in a transparent way which helps the plots’ users both to account for natural variation and to avoid spurious ranking. In this work a method is described by which outcome-volume relationships can be incorporated into funnel plots. It uses a regression based on a double exponential relationship of the form [1-exp(-a(n^b))]. Illustrative examples of the use of this method to compare performance in research funding competitions, healthcare and baseball are given.