The Great Average Performance Debate: Geometric vs. Harmonic Mean

A long-standing debate in computer architecture centers around how to calculate average performance. Hennessey and Patterson's seminal work advocates for the geometric mean due to its desirable mathematical properties. However, a recent paper challenges the geometric mean's physical meaning, proposing the "Equal-Time Harmonic Speedup" as an alternative. The author argues that the harmonic mean better reflects real-world scenarios, equating to the total speedup when running workloads sequentially. However, this overlooks the uneven distribution of workload times in practice, rendering its physical meaning often irrelevant. The article concludes that unless the exact workload mix and weights are known, no single-number average perfectly compares machines, leaving the geometric mean as a reasonable choice due to its ease of comparison and widespread familiarity.
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