Favourites who lose the first set win 31% of the time — and almost all of that number depends on how big a favourite they were

Every commentator has a version of the line: the favourite dropped the first set, so the match is anyone's. We wanted the actual number, so we went to 63,123 matches in our database that carry a closing price from Pinnacle, and asked a narrow question — when the player the market made favourite loses the opening set, how often do they still win?

The answer, over 19,515 best-of-three matches: 31.3%. Roughly one in three. That is the headline figure, and on its own it is close to useless, because it averages two very different situations.

Split those matches by how big a favourite the player actually was, and the number moves in a straight line. A marginal favourite — one the market priced between 50% and 55% — comes back 22.3% of the time, over 3,691 matches. Between 60% and 65%, it is 28.6%. Between 70% and 75%, 36.1%. Between 80% and 85%, 45.8%. And a favourite priced above 90%, the kind of mismatch you see in the first round of a Masters, still wins 69.6% of the time after dropping the opening set — on 204 matches, the smallest sample here and the one to treat with most caution.

There is no exception anywhere in that ladder. Every band is higher than the one below it.

The more interesting number is what losing the set costs. A 70-75% favourite normally wins 73.0% of their matches; after losing the first set, 36.1%. That is a fall of 37 points. But the punishment is not uniform: for a 90-95% favourite the fall is only 25 points, and for a coin-flip favourite it is 30. The heaviest damage lands in the middle of the range.

That shape makes sense once you stop thinking of the first set as a scoreline and start thinking of it as evidence. An overwhelming favourite who loses a set has mostly had an accident, and remains overwhelming. A moderate favourite who loses a set has told you something new about the match — that the gap you thought existed may not.

Split the comeback into its two halves and you can see where it is actually lost. To come back in best-of-three you have to win the second set and then the third. Our favourites force a decider 49.8% of the time — near enough a coin flip — and once level they win it 62.8%. Those two multiply back to the 31.3% we started with, which is a useful check that nothing has been double-counted. The hard part is the second set. The deciding set, the one usually described as a lottery, is not one: the favourite is still clearly the favourite in it.

Both halves scale with the price. A marginal favourite forces a third set 42.5% of the time and then wins it 55.4%. A favourite above 90% forces it 80.2% of the time and wins it 85.4%. So the very best players do not survive by being unusually good in deciders — they survive mostly by not needing one, and then by still being better when they do.

The format matters more than anything a player does. In best-of-five, where our sample is the men's Grand Slam draws, the same favourites come back 47.1% of the time rather than 31.3%. Two extra sets are worth roughly sixteen percentage points of insurance.

Two things people expect to matter, and do not. The first is the circuit: ATP favourites come back 32.2% of the time and WTA favourites 30.5%, on samples of 9,317 and 10,198. Whatever the reputation of the women's tour for volatility, it does not appear in this measurement.

The second is the size of the tournament, and this one is a trap worth explaining. Raw, it looks like a clean ladder: 30.8% at ATP and WTA 250 and 500 level, 32.0% at the Masters, 32.6% at the Grand Slams. Except that the average favourite at a Grand Slam is priced at 71.4% and at the smaller events at 66.7% — the big tournaments have bigger mismatches. Hold the favourite's strength constant and the ladder collapses: inside each band the three levels sit within one to three points of each other, and which one leads changes from band to band. The difference was never the tournament. It was who was playing in it.

A note on method, because it decides whether any of this means anything. The favourite is defined by the market price, not by our own ratings. Our Elo table holds today's numbers, so using it to classify a match from 2015 would be reading the future into the past. A closing price cannot do that: it existed before the match started. Probabilities are taken vig-free, retirements and walkovers are excluded because a match that did not finish cannot be come back from, and best-of-three and best-of-five are never mixed.