How can each brand’s buyer base buy the category at above the average rate?

Abstract

An apparent anomaly in brand metrics data is that the aggregated buyer base of each brand appears to buy the category at above the average rate. This seems arithmetically impossible. The effect is real, but it has a simple explanation. It is caused by the fact that heavy category buyers buy more brands than light buyers do. They therefore appear in the buyer base of multiple brands, and so inflate the category buying rate for each brand to above the overall average rate. This study shows what it calls the ‘category purchase rate anomaly’ in empirical data, as well as demonstrating how it occurs via a simulated dataset.