Live Tennis APITennis match win probability calculator
Enter the share of points each player wins on their own serve. You get each player's chance of holding serve, winning a tie-break, winning a set and winning the match.
Chance of winning the match
- Player A
- 59.9%
- Player B
- 40.1%
Player A wins 64% of points on serve and Player B 62%. Best of three sets, with a tie-break to seven at six games all in every set.
| Chance to | Player A | Player B |
|---|---|---|
| Hold a service game | 81.3% | 77.6% |
| Win a tie-break to 7 | 53.3% | 46.7% |
| Win a set | 56.7% | 43.3% |
| Win a tie-break to 10 | 53.9% | 46.1% |
| Win the final set | 56.7% | 43.3% |
| Win the match | 59.9% | 40.1% |
This is a teaching calculator. It does not reproduce the win probability the Live Tennis API returns in win_probability_p1. The page address holds your numbers, so you can bookmark a result or send it to someone.
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How much does a small edge on serve change a match?
In this model, take a player who wins 64% of points on serve against one who wins 62%. The first holds serve 81.3% of the time and the second 77.6%. That small edge on each point becomes 56.7% for a set and 59.9% for a best of three match. Over best of five it is 62.4%.
How does the calculator work?
It builds the match from the point up. Each step uses only the step below it.
- Game. The server wins to love, to 15 or to 30, or the game reaches deuce. From deuce the server needs two points in a row before the receiver gets them. The formula under this list gives the chance of holding.
- Tie-break. The calculator follows every score from 0-0. The first point has one server, and after that each player serves two points in turn. A tie-break to seven runs on from 6-6 until one player leads by two points. A tie-break to ten does the same from 9-9.
- Set. It follows every game score from 0-0 with the serve changing each game. A set ends at six games with a two-game lead or at 7-5. At six games all the tie-break decides it.
- Match. Sets are independent. Best of three needs two sets and best of five needs three.
In the formula, p is the chance the server wins a point and q is the chance the server loses it.
hold = p^4 * (15 - 4p - 10p^2 / (1 - 2pq))What does the model assume?
Every point is independent of the ones before it. Each player wins a point on their own serve with one fixed probability for the whole match. There is no momentum, no fatigue and no extra weight on a break point. First and second serves are one number.
Player A serves first in the calculator. That choice does not change a set or a match. Newton and Keller prove it for sets with a tie-break to seven. Our tests check it on the code for both tie-breaks.
What does the model leave out?
Real players do not win points at a fixed rate. The share changes with the opponent, the surface, the day and the score. Newton and Keller discuss the evidence that real points are not independent.
The inputs matter more than the arithmetic. A season average is measured against many opponents. The model wants each player's share against this opponent, which nobody knows before the match. Treat the result as an illustration of how tennis scoring turns points into matches, and nothing more.
Where do the serve numbers come from?
Service points won is the points a player wins while serving, as a share of the points they serve. The Live Tennis API reports it for a match as service_points_won_pct. You can also type any two numbers to see how the result moves.
Which matches use which format?
The ITF Rules of Tennis 2026 allow best of three or best of five sets (Rule 7). In a tie-break set, a tie-break to seven is played at six games all (Rules 5 and 6).
The Grand Slam Rule Book 2026 sets best of five for men's singles main draw matches. Other matches are best of three unless a tournament decides otherwise. The final set tie-break there goes to ten points (Article I.L).
The ATP Official Rulebook 2026 and the WTA Official Rulebook 2026 both set standard tour singles as the best of three tie-break sets. An event with its own format, such as short sets, is outside this calculator.
Sources
- Paul K. Newton and Joseph B. Keller (2005). Probability of Winning at Tennis I. Theory and Data. Studies in Applied Mathematics, volume 114, issue 3, pages 241 to 269.
- A. James O'Malley (2008). Probability Formulas and Statistical Analysis in Tennis. Journal of Quantitative Analysis in Sports, volume 4, issue 2.
- Tristan Barnett and Stephen R. Clarke (2005). Combining player statistics to predict outcomes of tennis matches. IMA Journal of Management Mathematics, volume 16, issue 2, pages 113 to 120.
Rule books and papers opened on 11 November 2026.