Comparing the minimum of repeated runs flags benchmark regressions on shared CI runners with fewer false alarms than comparing means

Hypothesis

The Python timeit documentation advises that the minimum of the repeated timings is probably the only number of interest, because higher values come from other processes interfering rather than from variability in the code. The hypothesis extends this to automated regression checks on shared continuous-integration runners, where interference is stronger and unpredictable: for CPU-bound microbenchmarks, a check that compares the minimum of N runs on the candidate commit with the minimum of N runs on the base commit, using a fixed relative threshold, produces fewer false alarms on unchanged code and misses fewer injected slowdowns than the same check applied to the mean or the median. The reasoning is that interference on a shared machine only ever adds time, so the minimum estimates an interference-free run while the mean carries the noise. The advantage is predicted to disappear or reverse for I/O-bound benchmarks, where the minimum reflects a warm cache rather than the code.

Prediction

Across many CI runs of the same commit, the minimum will vary less between runs than the mean. With slowdowns of a few percent injected into the code, the minimum-based check will detect them at a threshold where the mean-based check either misses them or, at a lower threshold, flags unchanged commits. hyperfine's statistical outlier detection will flag runs on CI more often than on a quiet machine, which quantifies the noise the hypothesis is about.

Proposed test

1. Select a set of benchmarks: several CPU-bound (parsing, hashing, sorting), several allocation-heavy and several I/O-bound.
2. Create variants with known slowdowns of about 3%, 10% and 30% by adding proportional extra work, and keep the unchanged version as the control.
3. Run every variant on shared CI runners many times per day for at least two weeks, with N repetitions per run and interleaved order, recording all individual timings.
4. For each statistic (minimum, median, mean, trimmed mean) and each threshold, count false alarms on the control and misses on the slowed variants.
5. Compare the detection-versus-false-alarm curves per benchmark class and report the run-to-run variability of each statistic.

Status

No result is claimed. Possible confounds: CPU frequency scaling and heterogeneous runner hardware make even the minimum bimodal; a small N makes the minimum itself noisy; benchmarks with warm-up effects can make the minimum represent a state the production code never reaches.