How bad is it? Your chances from any score

A set down, a break down, someone just got broken and everyone at the table has an opinion. Pick the situation — or set the exact score — and this works out the chance of coming back, from that score alone.

Equal means the same strength on serve and on return — the question of what the scoreline says on its own.

What this number is, and what it is not

It is exact for two players who serve every point at a fixed strength. Real points are not quite like that. A study of 86,298 points at Wimbledon from 1992 to 1995 found the difference small, and concluded that for “predicting the winner of the match while the match is in progress” the assumption still works well — “if we correct for the quality of the players” (Klaassen and Magnus, Journal of the American Statistical Association, 2001).

That condition is the whole catch. With the players set equal, this page deliberately does not correct for quality: it answers what the scoreline says on its own. And a scoreline is itself evidence about quality. Falling behind is likelier to happen to the weaker player than to the stronger one, so a player who is behind is more likely than not to be the weaker of the two, and real comebacks are rarer than the equal-players figure says. That is reasoning rather than a measurement: by how much is a question for match records, not a scoring model, and this page quotes no measured comeback rate because none has been checked against its source.

Two sets down is exactly one in eight

Between equals the arithmetic is as clean as tennis gets. Every set is a coin flip — who serves first in a set does not change the chance of winning it — so from two sets down in a best-of-five you need three flips in a row: 12.5%, one in eight exactly. A set down in a best-of-three is 25.0%, one in four. Neither depends on how strong the serve is. Once a set is under way, it does. A break down in the deciding set, between equals, leaves 18.0% when both win 55% of points on serve and 8.1% at 70%: a break is harder to win back when holding is easy.

How much the next point is worth

Win the next point and the chance moves one way; lose it and it moves the other. The gap between the two is the point’s importance to the match, and from this score it is 2.5 percentage points. That is the literature’s definition of importance, which is not the same as importance to the game — the point importance page has both, and why they differ by so much.

Serve or return?

From this score, one more point in a hundred on your player’s serve is worth 5.05 points of match probability; one more on return is worth 5.10. Return buys slightly more here, with your player serving this game. Before a best-of-five match between equals serving at 65%, it is return, by 1.1% — a real difference and a small one. Which is easier to improve is the useful question, and not one a scoring model can answer.

What the model assumes

Every figure assumes each point is an independent trial at a fixed strength for the server. That is an assumption, not a fact about tennis. A study of 86,298 points at Wimbledon from 1992 to 1995 (Klaassen and Magnus, "Are Points in Tennis Independent and Identically Distributed?", Journal of the American Statistical Association, 2001) found that real points are not quite like this, and that the divergence is small. Read these figures as exact for players who serve every point at the same strength.

Worked out in your browser for the one score on the board, by the same engine the site’s other tennis figures are built and checked with. Serve order is carried from set to set rather than reset.