The causal relationship between the biodiversity of natural and modified environments and their net primary production has been a topic of significant scientific controversy and scrutiny. Early theoretical and empirical results indicated that production was sometimes significantly correlated with species richness when species richness was directly manipulated in experimental systems. Possible mechanisms for this phenomenon include statistical sampling effects, complementary resource use and mutualistic interactions. However, the interpretation of experimental results has sometimes confounded species richness with species composition, and disentangling the effects of species diversity from species identity has proved a formidable challenge. Here, I present a statistical method that is based on simple probability models and does not rely on the species composition of individual plots to distinguish among three phenomena that occur in biodiversity-production experiments: underyielding, overyielding and (a new concept) superyielding. In some cases, distinguishing these phenomena will provide evidence for underlying mechanisms. As a proof-of-concept, I first applied this technique to a simulated dataset, indicating the strengths of the method with both clear and ambiguous cases. I then analysed data from the BIODEPTH experimental biodiversity manipulations. No evidence of either overyielding or superyielding was detected in the BIODEPTH experiment.