tennis
Best of Five vs. Best of Three: Why Slam Favorites Win More
More sets, less room for luck
A tennis match is a sequence of sets, and the better player has to win only slightly more than half of them to be a clear favorite over a longer distance. The more sets there are, the more often the stronger player’s edge survives the bad stretches. That is why men’s Grand Slam matches, played over five sets, produce fewer upsets than the best-of-three matches on the rest of the tour.
This is not a vague tendency. It follows from arithmetic, and the arithmetic is simple enough to do yourself.
The formula
Say a player wins any single set with probability s, and sets are independent. Then the chance of winning a best-of-three match is s² × (3 − 2s), and the chance of winning best-of-five is s³ × (6s² − 15s + 10). We checked both formulas against a direct count of every way a match can end.
| Set win probability | Best of 3 | Best of 5 | Difference (pp) |
|---|---|---|---|
| 0.52 | 53.0% | 53.7% | +0.7 |
| 0.55 | 57.5% | 59.3% | +1.8 |
| 0.60 | 64.8% | 68.3% | +3.5 |
| 0.65 | 71.8% | 76.5% | +4.7 |
| 0.70 | 78.4% | 83.7% | +5.3 |
| 0.75 | 84.4% | 89.6% | +5.3 |
The extra two potential sets add the most for players who are clear but not overwhelming favorites. At 50% nothing changes, and for very lopsided matchups both formats approach certainty.
From a rating gap to a Slam price
Rating systems like Elo usually express strength as a win probability for a normal, best-of-three match. To price a best-of-five match you work backwards to the set probability, then forward again. Using the standard Elo scale of 400 points, this is what the same rating gap means in both formats:
| Elo gap | Best of 3 | Best of 5 | Difference (pp) | Fair odds Bo3 | Fair odds Bo5 |
|---|---|---|---|---|---|
| 50 | 57.1% | 58.9% | +1.8 | 1.75 | 1.70 |
| 100 | 64.0% | 67.3% | +3.3 | 1.56 | 1.49 |
| 150 | 70.3% | 74.8% | +4.4 | 1.42 | 1.34 |
| 200 | 76.0% | 81.1% | +5.1 | 1.32 | 1.23 |
| 300 | 84.9% | 90.1% | +5.2 | 1.18 | 1.11 |
A 100-point gap is a 64.0% favorite in three sets and a 67.3% favorite in five. You can try your own gaps in the Elo probability calculator, and the current ratings are on the Elo rankings page.
What this means for pricing a Slam match
Take a favorite who is 70% to win a best-of-three match. Over five sets the same player is 74.4% to win. The break-even price moves from 1.429 to 1.344. A model calibrated only on best-of-three matches would therefore understate the favorite at a men’s Slam, and an analyst who forgets the conversion would see a phantom edge on the underdog.
Our model applies this conversion for best-of-five matches. The conversion does not tell you which side is mispriced. The market knows about the format too, so the value question stays the same: is your estimate, after the conversion, different from the no-vig price by more than the margin?
Where the simple math stops
The formulas assume every set is an independent coin flip with the same probability. Real matches are not like that. Fatigue accumulates over five sets, players adjust after losing a set, a surface can change with the weather, and a specialist’s serve can make some sets far more predictable than others. Treat the numbers as the baseline that a rating gap implies under neutral assumptions, not as a forecast for a specific match.
Surface matters on top of format: why ratings need to be surface-specific covers that side of the picture.
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Frequently asked questions
- Why do favorites win more often in best-of-five matches?
- Each additional set is another chance for the better player's edge to show up. With a 60% chance per set, a player wins 64.8% of best-of-three matches but 68.3% of best-of-five matches.
- Which tennis matches are played over five sets?
- Men's matches at the four Grand Slams. Women's Grand Slam matches and almost all other matches on both tours are best of three.
- How much does the format change the odds of a big favorite?
- Less than for a moderate favorite. A 300-point Elo gap is 84.9% over three sets and 90.1% over five, a difference of 5.2 points, while a 100-point gap moves from 64.0% to 67.3%.