Computer Architects Can't Find the Average

Computer architects can’t agree on a way to find the average. For years, academic practitioners in this field have been arguing about the appropriate way to summarize the average performance of their designs. That is: given \(n\) workloads, if system \(A\) outperforms system \(B\) by \(S_1, S_2, \ldots, S_n\) on each, how much faster should you say system \(A\) is, on average? I think this argument is kind of pointless through. For the most part, people tend to use the arithmetic mean \(\left(\frac{1}{n} \sum_{i=1}^n S_i\right)\) or the geometric mean \(\left(\sqrt[n]{\prod_{i=1}^n S_i}\right)\). Henessey and Patterson’s famous Computer Architecture: A Quantitative Approach advocates for the latter: Using the geometric mean ensures two important properties: The geometric mean of the ratios is the same as the ratio of the geometric means. The ratio of the geometric means is equal to the geometric mean of the performance ratios, which implies that the choice of the reference computer ... Read full article.