Any figure that summarises a mixed group will sit between its parts. If the parts are far enough apart, the summary stops describing anyone. A tennis dataset makes the problem easy to see, because the groups are labelled and the counts are published.
The measure is the service hold rate: how often the player serving a game goes on to win it. The corpus holds 2,239,440 service games with a known court surface, played between January 2023 and September 2026. Split by surface, the rate sits in a narrow band. Grass returns 74.43% over 74,673 games, hard courts 69.95% over 1,222,994, and clay 65.98% over 941,773.
Under nine points separate the three surfaces. A reader could reasonably conclude that hold rate is a fairly stable quantity.
The cut that breaks it open
Split the same games by competition tier instead and the picture changes completely.
The men’s ATP tour holds serve 78.62% of the time across 230,715 games. The men’s Challenger tier returns 74.1% over 622,018 games and the men’s ITF circuit 70.26% over 529,948. The women’s WTA tour returns 64.36% over 266,503 games. The women’s Challenger tier gives 60.4% and the women’s ITF circuit 58.93% over 553,157 games.
That is a spread of 19.69 percentage points between the top and bottom groups. One number had made the same measure look stable.
Why the first cut looked calm
Surface is a property of the court. Tier is a property of who is playing and under what format. The second one varies far more, so splitting by it exposes far more.
This is the general shape of the problem. The cut that produces a flat result is often the cut that has nothing to do with the mechanism. A flat result is not evidence that the underlying quantity is uniform. It is evidence that you divided along a line the quantity does not care about.
Two things worth taking from it
First, a headline rate across mixed groups should always come with the group sizes. Here the largest tier by volume is the men’s Challenger circuit at 622,018 games, while the ATP tour contributes 230,715. A simple average of the six tier rates would not equal the headline figure, because the groups are nothing like the same size.
Second, the denominators have to be checked before the percentages are compared. The surface breakdown covers 2,239,440 games and sums to that figure exactly. The tier breakdown covers the full corpus of 2,294,737 games. The 55,297 difference is matches whose surface the data feed never stated. The source documents that gap instead of leaving a reader to find it.
A check that makes the rest believable
The method here can be tested against figures published elsewhere. The widely cited hold rates are roughly 79% for the men’s top tour and roughly 64% for the women’s. This measurement returns 78.62% and 64.36% on a method tuned to neither, with tiebreak games excluded throughout.
That is the useful kind of validation. The method was not fitted to reproduce those numbers and it reproduces them anyway. That makes the twenty point spread harder to dismiss as a counting artefact.
What to ask of any summary figure
Ask which groups it averages over, how big each one is, and what the widest gap between them looks like. If the answer to the last question is twenty points, the summary is a starting point and not a finding.
All of the above comes from the Live Tennis API, a JSON service for developers. It covers live scores, fixtures, players and match events, with point-by-point history behind them. The figures are published at blog.livetennisapi.com/studies.json under CC BY 4.0, free to reuse with attribution.
Retirements and walkovers are excluded, and the counting is done from the point-by-point tape instead of estimated.
