Tennis Serve Statistics Calculator: First-Serve %, Points Won and Hold Rate
First-serve percentage, points won on first and second serve, total service points won, double-fault and ace rates, break points saved, an ATP-style serve rating and the service-hold probability from match stats, with tables showing what a better first or second serve is worth.
How it works
1st % = first in ÷ attempts · won on 1st = 1st points won ÷ first in · won on 2nd = 2nd points won ÷ (attempts − first in) · p = all service points won ÷ attempts · hold = p⁴(1 + 4q + 10q²) + 20p³q³ · p²/(1 − 2pq), q = 1 − p · serve rating = 1st % + 1st won % + 2nd won % + games held % + aces/match − double faults/match
Every service point starts with a first serve, so first serves attempted equals service points. Three numbers describe a serve: how often the first serve lands, how many points it wins when it does, and how many points the second serve wins (double faults count as second-serve points lost). Points won on second serve is the best single sign of a player’s level; the men’s tour average is only just above 50%. Total service points won is the weighted mix of the two: p = first-serve % × won on first + (1 − first-serve %) × won on second. The hold estimate treats every point as independent with that same chance and applies the standard deuce-game formula: you win 4–0, 4–1 or 4–2, or reach deuce and then win two points in a row before losing two. Because hold probability rises steeply with p, a few extra points won on serve turn into many more holds: 60% of points won holds about 74% of the time, 65% about 83% and 70% about 90%. The tables show the trade-off: how the hold rate would change at other first-serve percentages if your win rates on each serve stayed the same, and the hold rate at any level of service points won. The serve rating adds up the same four percentages plus aces minus double faults per match, the way the ATP serve leaderboard ranks players; top servers score around 300.
Worked example
With the defaults: 42 of 68 first serves in = 61.8%. 32 of those 42 points won = 76%, and 14 of the 26 second-serve points won = 54%, so 46 of 68 service points = 67.6% overall. With p = 0.676 the deuce-game formula gives an 87% hold probability; in fact 10 of 11 games were held (90.9%). The 3 double faults are 11.5% of second serves, the 6 aces are 0.55 per game, and 3 of 4 break points were saved. Serve rating = 61.8 + 76.2 + 53.8 + 90.9 + 6 − 3 = 285.7. The 68 points over 11 games are 6.18 points per game against 6.00 expected.
Frequently asked questions
What is a good first-serve percentage?
Around 60–65% on the men’s and women’s tours, and 55–65% for strong club players. It only counts with a high win rate on it: landing 80% of first serves that win 60% is worse than landing 60% that win 78%.
How is service points won calculated?
Add points won on first serve and on second serve and divide by total service points. It equals first-serve % × first-serve win rate + second-serve % × second-serve win rate.
What double-fault rate is acceptable?
Under 10% of second serves for club players; tour players average around 8%.
How is the hold probability estimated?
From your service points won, assuming every point is independent with the same chance. The deuce-game formula sums the ways to win 4–0, 4–1 and 4–2 plus the chance of reaching deuce and then winning it.
What is the ATP serve rating?
A single score that adds first-serve %, first-serve points won %, second-serve points won % and service games won %, then adds aces per match and subtracts double faults per match. Higher is better; the best servers on tour reach about 300.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.