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Abstract Understanding the relationship between biodiversity and ecosystem stability is a central goal of ecologists. Recent studies have concluded that biodiversity increases community temporal stability by increasing the asynchrony between the dynamics of different species. Theoretically, this enhancement can occur through either increased between-species compensatory dynamics, a fundamentally biological mechanism; or through an averaging effect, primarily a statistical mechanism. Yet it remains unclear which mechanism is dominant in explaining the diversity-stability relationship. We address this issue by mathematically decomposing asynchrony into components separately quantifying the compensatory and statistical-averaging effects. We applied the new decomposition approach to plant survey and experimental data from North American grasslands. We show that statistical averaging, rather than compensatory dynamics, was the principal mediator of biodiversity effects on community stability. Our simple decomposition approach helps integrate concepts of stability, asynchrony, statistical averaging, and compensatory dynamics, and suggests that statistical averaging, rather than compensatory dynamics, is the primary means by which biodiversity confers ecological stability.