Counting stats, rate stats and the argument hidden between them

Two families of number, two different claims

A counting statistic adds up what a competitor produced, so it grows with every additional appearance and never falls back down again. A rate statistic divides that production by the opportunity taken to generate it, which removes the effect of playing more and isolates the level. The two therefore answer different questions, one about how much was contributed in total and the other about how good the contribution was per unit of chance.

Because both are labelled with the same vocabulary of goals, points or wickets, readers routinely treat them as competing versions of one measurement. They are not competing at all, and the argument only becomes tractable once each side states which of the two questions it is answering.

Opportunity as the hidden variable

Every counting total is really a product of level and opportunity, and the published figure gives no indication of how those two contributed. A competitor in a role that generates many chances will accumulate impressive totals at a modest level of efficiency without doing anything remarkable. A competitor in a restricted role can be far more effective per opportunity and still finish well down any table built on totals.

Opportunity is determined by selection, tactics, position and the strength of the surrounding side, none of which the competitor fully controls. Ranking on totals therefore ranks partly on circumstances, which is defensible only if the ranking explicitly claims to be measuring contribution rather than ability.

Why rates mislead in small samples

Rates are more informative per unit of evidence and considerably less stable, because dividing by a small denominator magnifies ordinary variation enormously. A competitor with a short spell of opportunity can post a rate that no sustained career would ever match, purely through a favourable run. Minimum thresholds are the usual defence, and they work by excluding anyone whose sample is too small to support a reliable estimate.

Those thresholds are arbitrary, and setting one slightly differently changes which names appear at the top of the resulting table. A more honest presentation shows the rate alongside the sample size, so a reader can discount an extreme figure built on very little.

Shrinkage and the middle path

Statistical practice offers a compromise in which an extreme rate from a small sample is pulled towards the population average before being reported. The size of that pull depends on how much evidence exists, so a long record barely moves while a short one moves a long way. This produces estimates that are less exciting and considerably more predictive, because it accepts that unusual figures are usually partly luck.

It is unpopular in public rankings because it removes the extremes that make a table interesting to read and to argue about. The trade between an engaging table and an accurate one is a genuine editorial decision rather than a technical detail.

Presenting both without hedging

The practical resolution is to publish the total, the rate and the opportunity together, and to say which the ranking treats as decisive. That format costs almost nothing and removes the majority of misreadings, because the reader can see immediately where a high placing came from. It also makes the ranking falsifiable, since anybody can check whether the stated criterion was applied consistently across every candidate.

Where the two measures disagree strongly about a competitor, that disagreement is itself worth a sentence rather than being smoothed away. A ranking that explains its own internal tensions is more persuasive than one that presents a single number with unearned confidence.