Investigating the quantity–quality relationship in scientific creativity: an empirical examination of expected residual variance and the tilted funnel hypothesis

Among scientists who study scientific production, the relationship between the quantity of a scientist’s production and the quality of their work has long been a topic of empirical research and theoretical debate. One principal theoretical perspective on the quantity–quality relationship has been the equal odds baseline, which posits that a scientist’s number of high-quality products increases linearly with their total number of products, and that there is a zero correlation between a scientist’s total number of products and the average quality of those products. While these central tenets of the equal odds baseline are well known, it also posits a number of more specific and less discussed aspects of the quality–quantity relation, including the expected residual variance and heteroscedastic errors when quality is regressed on quantity. After a careful examination of the expected variance by means of a non-parametric bootstrap approach, we forward a further prediction based on the heteroscedasticity implied by the equal-odds baseline that we term the tilted funnel hypothesis, that describes the shape of a bivariate scatterplot when quality is regressed on quantity, as well as the change in the strength of slope coefficients at different conditional quantiles of the quality distribution. In this study, we empirically test the expected residual variance and the tilted funnel hypothesis across three large datasets (including approximately 1.5 million inventors, 1800 psychologists, and 20,000 multidisciplinary scientists). Across all of the data sets, the results empirically supported the tilted funnel hypothesis, and therefore the results provided further evidence of the utility of the equal odds baseline.