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Tennis win probability calculator: from points on serve to games, sets and matches

Tennis scoring nests points inside games, games inside sets and sets inside a match, and each layer magnifies a small edge. A player who wins 62% of points on serve against an opponent who wins 60% is only slightly better point by point, yet wins a best-of-five match about five times in eight.

Enter each player’s chance of winning a point on their own serve and choose the format. The calculator follows Newton and Keller’s published model, in which every point is independent and the two chances stay fixed all match, and works out each probability exactly.

By Reign Creative LLCPublished More in the Tennis hub

Calculate match win probability

Each player’s share of points won on their own serve, as a percentage.

Every other set has a seven-point tie-break at six games all. A 10-point match tie-break replaces the final set.

Player A wins the match62.6%

Player B wins the match
37.4%
A holds serve
77.6%
B holds serve
73.6%
A wins a tie-break
53.3%seven points
A wins a set
56.8%tie-break set

Most likely score in sets: 3–1 (23.7%), 3–2 (20.5%), 3–0 (18.3%). Scores are from player A’s side.

The model

Newton and Keller (2005) model a match from two numbers: pA, the chance that player A wins a point on A’s serve, and pB, the same for B. Every point is independent and the two chances never change. The chance of holding serve is their equation (5), with q = 1 − p:

Holding serve

G(p) = p4(1 + 4q + 10q2) + 20p3q3 · p2 ÷ (1 − 2pq)

The first part counts wins to love, 15 and 30; the second reaches deuce and then wins two points in a row before the receiver does. In a No-Ad game, deuce is one deciding point, so the server simply needs four points before the receiver gets four: p4(1 + 4q + 10q2 + 20q3).

Winning a tie-break from 6–6

pA(1 − pB) ÷ (pA(1 − pB) + (1 − pA)pB)

Tie-breaks, sets and matches are built up score by score, following the serve: in a tie-break one point, then two each, as the ITF’s Rule 5 sets out; in a set, alternate games, with the tie-break counted as the 13th. From 6–6 in a tie-break each further pair of points has one served by each player, which gives the closed form above, and an advantage set from five games all works the same way with games. Newton and Keller proved that in this model it makes no difference who serves first.

Worked example

Two illustrative players: A wins 62% of points on serve, B wins 60%. The two-point edge grows at every layer of the scoring:

62% against 60% on serve
MeasurePlayer APlayer B
Holds serve77.6%73.6%
Wins a tie-break53.3%46.7%
Wins a set56.8%43.2%
Wins a best-of-three match60.1%39.9%
Wins a best-of-five match62.6%37.4%

The final-set format matters too. In a best-of-three match between the same two players, A wins 60.1% with tie-break at 6–6, 60.3% with advantage set, 58.7% with 10-point match tie-break: the shorter the decider, the more room for the weaker server.

How an edge on serve compounds

Player B fixed at 60% of points on serve; player A at 60% plus the edge shown:

Player A’s chances as the edge grows
A on serveA holdsA wins a setBest of threeBest of five
60%73.6%50.0%50.0%50.0%
61%75.6%53.4%55.1%56.4%
62%77.6%56.8%60.1%62.6%
63%79.5%60.1%64.9%68.4%
65%83.0%66.3%73.7%78.5%

The calculator reproduces Newton and Keller’s equation (5) exactly and the match probabilities in their Tables 3 and 4 to within 0.003, most of them to four decimal places.

How to read it, and its limits

  • Points are not truly independent. Pressure, momentum, fatigue and tactics all move a player’s chances during a match, which the model leaves out.
  • A serving percentage depends on the opponent and the surface; a figure from one match-up does not carry over to another.
  • It covers singles scoring with the formats listed. Short sets and other alternatives in the ITF’s Appendix V are not included.
  • The results describe what the inputs imply. They are not a forecast of any match and not betting guidance.

For what decides the points this model treats as identical, read playing the big points in tennis and tennis scoring for beginners.

Tennis Career Simulator 2026 resolves its matches at the points that matter: you decide how to serve, return, defend and attack under pressure, with your attributes, style and preparation setting what is on the table.

Reign Creative LLC makes Tennis Career Simulator 2026, so we have a commercial interest in it. It is not affiliated with, or endorsed by, any league, team, players’ association or athlete.

Good to know

Frequently asked questions

How does a small edge on serve become a big edge in a match?
Each layer of the scoring compounds it. With 62% of points won on serve against 60%, the better server holds 77.6% of service games to 73.6%, wins 56.8% of sets and 62.6% of best-of-five matches. A longer match gives the better player more chances to show it.
What does the model assume?
That every point is independent and each player’s chance of winning a point on serve stays the same all match — Newton and Keller’s “iid” assumption. Real points are not quite like that: pressure, fatigue and tactics all matter. Newton and Keller cite an analysis of four years of Wimbledon data finding that the departure from this assumption is small for most purposes.
Does it matter who serves first?
Not in this model. Newton and Keller proved that the chance of winning a set, and so a match, is the same whoever serves first, and the calculator’s exact figures agree for every format it offers.
Which formats can it handle?
Best of three or best of five sets, with a seven-point tie-break at six games all. The final set can instead be an advantage set or a 10-point match tie-break, and games can be played with No-Ad scoring, where deuce is settled by one deciding point — the alternatives in the ITF Rules of Tennis.
Is the result a prediction?
No. It shows what two fixed serving percentages imply under a simple model, which is useful for understanding how tennis scoring works. It does not forecast any real match and is not betting guidance.

Sources

  1. Probability of Winning at Tennis I. Theory and Data (Studies in Applied Mathematics 114:241–269, 2005) (opens in a new tab)Paul K. Newton and Joseph B. Keller (copy hosted for a University of Pennsylvania course) — accessed
  2. ITF Rules of Tennis, 2021 edition — Rules 5 and 6 and Appendix V (No-Ad, match tie-break) (opens in a new tab)International Tennis Federation — accessed
  3. 1.3.6.6.18. Binomial Distribution — e-Handbook of Statistical Methods (opens in a new tab)NIST/SEMATECH — accessed

League, governing-body and team names appear here only to identify the formulas and rules being used. Reign Creative LLC's sports games and calculators are not affiliated with, endorsed by or licensed by any league, team, players' association or athlete, and all names and marks belong to their owners.

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