What each tennis format does to the better player

Every argument about a scoring rule — the 10-point tiebreak, no-ad, best of five — is really an argument about two things: how often the better player wins, and how long it takes. Those are exactly the two things a scoring model can measure, so this page measures them, rule by rule, with nothing else changed.

That is the total-points figure on any match-stats page. Under the hood it is an edge of 2 points in every hundred on serve and 2 on return, which is what takes the better player to about 52% overall.

Best of five favours the better player

The better player’s margin over a coin flip is 22% larger over five sets than over three at these settings: 73.7% against 69.4%. That is real, and it is why the longer format is said to protect the favourite. Two extra sets widen the margin; they do not decide the match.

A match tiebreak trades edge for time

Replacing a full third set with a 10-point match tiebreak gives away 13% of the better player’s margin and saves 14% of the points. Add no-ad scoring on top and the margin given away rises to 19%, for a match 23% shorter. Whether that is a good trade is a question about schedules and courts, not probability — but it is a trade, and both sides of it are on the table above.

The 10-point final-set tiebreak barely changes who wins

Over five sets, the three ways of finishing a deciding set — a 7-point tiebreak, a 10-point one, or playing on until someone is two games clear — give the better player chances within 0.3 percentage points of each other. Measured by who wins, the rule change is close to invisible, and so is the length of the average match: across the three it differs by under 1%.

The average is the wrong number to look at for this rule, though: what it changes is the tail. Between two players who hold 90% of their service games — what winning 70% of points on serve works out to — an advantage final set that reaches 6-6 is still level at 20-20 6.3% of the time. Between players who hold 78% (62% of points on serve), it is 0.25% — about 25 times less often. The rule barely changes who wins. What it removes is a marathon, and the marathon is a big server’s problem. These figures are for two equal players, whatever edge is selected above.

Is a tiebreak a coin flip?

Closer to one than a set is, but no. At these settings the better player wins 56.5% of 7-point tiebreaks against 63.3% of whole sets. A tiebreak keeps 49% of the better player’s margin over a coin flip: it is a short contest, and short contests leave more to chance. That is the part of the complaint that is true. The part that is not is “coin flip” — the edge is smaller, not gone.

A stronger serve does not amplify a small edge

You might expect that when serve dominates, small differences become decisive. In this model the same points edge is worth slightly less when the server wins 70% of points than at 62%: best of three, a +2 player wins 68.0% against 69.4%. This holds for an edge spread evenly across serve and return; a player whose whole advantage is a bigger serve is a different question, and not one this page models.

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.

Each side has a single serve strength for the whole match. That fits singles. In doubles, partners take turns to serve, and a pair whose partners win 55% and 70% of their service points is not the same as one player at 62.5%: holding serve does not scale in a straight line with points won, so the two service games do not average out. Whether that makes these figures too kind or too harsh to a doubles pair has not been worked out here. Formats are described by their rules, not by which events use them. Every figure is exact under the model — serve order is carried from set to set rather than reset, and every loop in the scoring closes in a formula — so nothing here is simulated.

See also: how these figures are computed.