Checking whether the ratio means anything

This is the part of the package that does not exist elsewhere, and it is the reason the package exists at all.

The acute:chronic workload ratio has a substantial literature arguing it does not predict injury. Rather than take a side, acwr ships the tests that argument rests on, so you can run them on your own athletes.

Without any injury data

print(acwr.rescaling_check(load))
# ACWR vs acute load alone, n=1172: Spearman 0.512 [0.461, 0.559], Pearson 0.390

That figure is from three years of one runner's log, 1,018 runs. For a version you can run yourself, see the worked example, whose every number is reproducible from the page.

The ratio is acute load divided by chronic load. When the denominator varies little next to the numerator, dividing barely changes the ordering of days and the ratio becomes a rescaled copy of the acute load. This reports how far down that road your data sits. In the limit it is exact: with a constant denominator the Spearman correlation is 1.0 and the ratio is the numerator in different units.

With injury data

result = acwr.compare_to_null(load, injured, kind="shuffle")
print(result)

This is the test from Impellizzeri et al. (2021). Compute the association between injury and the real ratio, then recompute it many times against ratios whose chronic denominator has been replaced by a contrivance, and compare. If a denominator can be swapped for noise without hurting the result, it was not doing any work.

Three contrivances are available. "shuffle" permutes the real chronic series, keeping its exact distribution and destroying its timing. "normal" draws from a distribution matched to the real chronic mean and spread. "constant" uses the mean, which is the fixed-value version of the original test.

Two properties, deliberately different

real_beats_null is one sided and true only when the real statistic exceeds the null interval. real_outside_null is two sided. A ratio that falls below its null has not beaten anything, and conflating those two was a bug in this package's own first draft.

How much do the window lengths decide the answer?

print(acwr.window_sensitivity(load))

Window sensitivity at threshold 1.5 (rac, 16 window pairs)
  reference 7/28 flags 16.0% of days
  flagged fraction across pairs: 1.6% to 20.7%
  agreement with the reference: 0.02 to 0.71 (Jaccard)

Seven and twenty-eight days are conventional. They are not derived from anything, and papers that use them rarely say why. This sweeps a grid of window pairs and reports the Jaccard agreement between the days each pair flags and the days the conventional pair flags.

The output above is from the same three years of one runner's log. No alternative pair agreed with 7/28 on more than 71 percent of flagged days, and the fraction of days flagged ranged over an order of magnitude. The window lengths moved the output more than the training did.

What none of this proves

The diagnostics are descriptive. They are not hypothesis tests, and a result on one dataset is a result on one dataset. A low agreement does not prove the metric is worthless, and a high one does not validate it. What they do is put numbers on choices that usually go unexamined.