Break points are a sample size, not a skill

Conversion rates get treated as evidence of temperament when almost all of the variation is noise on a handful of points.

A player loses in four sets and the graphic goes up. Two break points converted from eleven. The narrative writes itself, and it is nearly always the same narrative, about nerve and big moments and a player who cannot finish.

Eleven points. That is the entire evidence base for a claim about somebody's character.

Run the arithmetic on what eleven attempts can tell you. If a player's true conversion rate is forty per cent, then getting two or fewer from eleven happens often enough to be unremarkable, and it happens to everybody several times a season. The same player, the same week, with the same nerves, will convert six from eleven in the next round and be described as ruthless. Nothing about him changed. The coin came up differently.

There is a second problem that makes the statistic worse than merely noisy. Break points are not randomly assigned. A player who is being outplayed on serve reaches more of them against weaker servers and fewer against better ones, so the denominator is contaminated by the quality of the opponent in a way that raw conversion never shows. A low conversion rate can mean somebody generated a lot of chances against a huge server, which is a compliment.

And the third thing, which almost nobody says. On a break point, the server is allowed to take more risk than usual, because losing the point loses the game anyway and there is nothing further to protect. Big servers go bigger. That is not the returner failing under pressure. That is the returner facing a harder delivery than he faced on any other point in the game.

So what would I use instead? Return points won, across the whole match, against that server. It has a sample size in the dozens rather than the low tens, it is not contaminated by scoreline effects, and it correlates with actually breaking serve over a season in a way that conversion rate does not.

None of which will stop the graphic appearing, because two from eleven is a story and thirty-one per cent of return points won is a number.

I have made my peace with that. I would just like commentators to stop diagnosing personalities from it.