Here is a problem that shows up whenever you work with numbers you did not collect yourself. You find a variable that clearly drives one series. You assume it drives the related series too, because both come from the same records. Often it does not, and nothing in the data warns you.

Professional tennis gives an unusually clean example, because the sport publishes two measures drawn from exactly the same matches.

The same six groups, measured twice

Professional tennis is organised in tiers, from the main ATP and WTA tours down through the Challenger level to the ITF circuit. Standard of play falls as you go down. That is the variable.

Measure one is how often a player holds serve. Across 2,294,737 service games:

ATP: 78.62%

Challenger M: 74.10%

ITF M: 70.26%

WTA: 64.36%

Challenger W: 60.40%

ITF W: 58.93%

That is a spread of 19.69 percentage points from top to bottom. The tier you are looking at tells you most of what you need to know.

Measure two is how often a player who loses the opening set goes on to win the match. Same tiers, same period, 116,382 matches:

ATP: 18.21%

Challenger M: 17.32%

Challenger W: 17.25%

WTA: 17.04%

ITF W: 15.97%

ITF M: 15.18%

That is a spread of 3.03 points. The same variable that moved the first measure by nearly twenty points moves this one by three.

Why this is the interesting part

Both numbers come from the same matches, counted the same way, over the same dates.

One of them is largely explained by the standard of play. The other is barely touched by it.

Seen the hold rates alone, you would conclude that tier is the dominant factor in this sport. You would then carry that assumption into the next question you asked. You would be wrong by a factor of six.

There is a second warning underneath the first. The two measures do not even rank the tiers in the same order. Men's ITF sits third on hold rate at 70.26%, above the WTA tour at 64.36%. On comeback rate the order reverses: WTA is fourth at 17.04% and men's ITF is last at 15.18%.

So the ordering is not stable either. A ranking built on one metric does not survive being asked a different question about the same population.

What is actually going on

Holding serve is a direct measure of one skill against another, repeated hundreds of times a match. Raise the standard of play and the server gains more than the returner does, so the number climbs steadily.

Winning from a set down is a different kind of quantity. It depends on how closely matched the two players happen to be. That is roughly similar at every level, because draws at every level put similar players against each other. The tier changes the quality of the tennis. It does not change how evenly matched the field is.

Put plainly, one measure is about level and the other is about spread, and a variable that moves level need not move spread at all.

Three things to take from it

Check whether your driver survives the next question. A variable that explains one series is a hypothesis about the next one, not a finding.

Compare the sizes of the effects, not only their directions. Both of these move the same way down the tiers. One moves six times as far, and direction alone would have hidden that.

Watch for rank order changing between metrics. When two measures of the same population disagree about ordering, at least one of them is answering a narrower question than it appears to.

None of this needs a model. It needs the same breakdown run twice, with the two results put side by side. That is a few minutes of work, and the step most often skipped.

Where the figures come from

All of the above comes from the Live Tennis API, a JSON service for developers. It covers live scores, fixtures and match events, with completed results and point-by-point history behind them. The figures are published openly at blog.livetennisapi.com/studies.json under CC BY 4.0, free to reuse with attribution.

Method: completed best-of-three professional singles matches on the ATP, WTA, Challenger and ITF circuits, 1 January 2023 to 14 September 2026. Retirements and walkovers excluded. Tiebreak games excluded from hold rates. Counted from the point-by-point record. The hold rate figures reproduce the widely published ATP and WTA rates on a method tuned to neither. That check is what makes the rest of the table worth reading.