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

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.

Introduction

The purpose of this paper is to investigate and explain an apparent anomaly that occurs in brand performance data derived from consumer purchase panels. The anomaly is that each brand's buyer base appears to buy the category at above the average rate. At face value this seems arithmetically impossible, but is shown to be due to (a) the distribution of category purchase frequency is highly skewed (many infrequent, very few frequent buyers) and (b) those frequent buyers buy more brands than the infrequent ones do, thereby they appear in the buyer base of each brand and so inflate the...

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