Sports & Gaming · Probability · Tennis
Tennis Tie Break Probability Calculator
Calculate the probability of winning a tennis tie-break given each player's probability of winning a single point on serve.
Calculator
Formula
The tie-break is modeled point by point. Player A serves points 1, then players alternate serving in pairs (2 each). Using p = probability A wins a point on their serve and q = probability A wins a point on opponent's serve, we sum over all paths to 7+ points with a 2-point lead, plus the probability of reaching 6-6 and winning the sudden-death or extended portion.
Source: Carter & Crews (1974), 'An analysis of the game of tennis', The American Statistician.
How it works
In a standard tie-break, Player A serves the first point, then players alternate serving in pairs of two points each. This creates a service sequence: A, BB, AA, BB, AA, ... The calculator tracks every possible score state (i points for A, j points for B) and computes the probability of reaching each state, then winning from it.
Two inputs drive the model: p (probability A wins a point when A is serving) and q (probability A wins a point when the opponent is serving). From any state, the probability of A winning the next point depends solely on who is serving at that point, determined by the total points played so far.
The recursion terminates when either player reaches the target score (7 or 10) with a lead of at least 2. Memoization ensures efficiency. For a match tie-break (super tie-break), the same logic applies but the target changes to 10 points.
Worked example
Example: Player A wins 65% of points on own serve (p = 0.65) and 35% on opponent serve (q = 0.35) in a standard 7-point tie-break.
The service pattern means A serves point 1, B serves points 2–3, A serves points 4–5, and so on. Starting from 0-0 with A serving: P(A wins) = 0.65 × P(win from 1-0, B serving) + 0.35 × P(win from 0-1, B serving). Recursing through all states yields approximately 0.5683, meaning Player A has a 56.83% chance of winning the tie-break — a meaningful advantage despite both players having symmetrical point-win probabilities from the opponent's serve.
Limitations & notes
This model assumes point outcomes are independent and identically distributed within each service situation, which ignores psychological momentum, fatigue, and situational pressure. The model also does not account for double faults, aces, or other serve-quality variation within a single server's points. Real tie-breaks may diverge from these probabilities, especially at high-pressure moments like 6-6.
Frequently asked questions
What is the service order in a tennis tie-break?
The player who was next to serve in the set serves the first point of the tie-break. After that, players alternate serving in pairs of two points, switching ends every six points. So the sequence is: 1 point for Player A, 2 for B, 2 for A, 2 for B, and so on.
What is a match tie-break or super tie-break?
A match tie-break (also called a super tie-break or championship tie-break) is played to 10 points instead of 7, still requiring a 2-point lead. It is often used instead of a deciding third set in doubles or mixed doubles, and at some ATP/WTA events in lieu of a final set.
How do I estimate p and q for a real match?
You can use historical match statistics. 'p' is the fraction of points won on first and second serve combined when Player A is serving. 'q' is the fraction of return points won by Player A. ATP and WTA match stats pages provide these figures per player per match or surface.
Why does the server of the first point have an advantage?
Serving generally gives a player a higher probability of winning that point. Since Player A serves the first point alone before B's pair begins, A gets a slight extra serving opportunity over the course of the tie-break, which is why first-server advantage exists even when both players have identical underlying stats.
Can I use this calculator for a third-set super tie-break at Grand Slams?
Yes. Wimbledon and the US Open use a standard 7-point tie-break at 6-6 in the final set, while Roland Garros now also uses a final-set tie-break at 6-6. Select the 7-point format for these. The Australian Open uses a 10-point super tie-break at 6-6 in the final set, so select the Match Tie-Break / Super Tie-Break option for that format.
Does this model account for nerves or pressure at key points?
No. The model assumes a constant point-win probability throughout the tie-break. In reality, players may perform differently on big points like 6-6, 6-7, or 9-9. For a more nuanced analysis, you would need an importance-weighted model that adjusts p and q based on the score situation.
Last updated: 2025-01-30 · Formula verified against primary sources.