Every menu carries an implied average. Diners work one out before they walk in, from a review, a price band or a glance at the window. It is one number standing in for a whole list. Like most numbers that do that job, it is accurate and close to useless.
A large record of professional tennis makes the same point with harder edges, because the list underneath it has been kept and published.
One number, seven answers
Across 116,382 completed professional singles matches, a player who loses the opening set goes on to win 16.52% of the time. One in six. That is the figure you hear.
Now split those same matches by how the first set was lost:
– lost it 7-6: wins 21.92% of the time, from 14,265 matches
– lost it 6-4: 19.41%, from 25,546
– lost it 7-5: 18.89%, from 10,252
– lost it 6-3: 17.39%, from 25,970
– lost it 6-2: 13.30%, from 19,739
– lost it 6-1: 11.06%, from 14,269
– lost it 6-0: 7.18%, from 5,833
Three times the difference between the top and the bottom. The average sat in the middle and described nobody in particular.
Why the comparison holds
Two of those groups are almost exactly the same size. The 7-6 group holds 14,265 matches and the 6-1 group holds 14,269, four apart.
So nobody can wave the gap away as a small sample. One group comes back twice as often as the other, from samples of the same size, measured the same way. The only difference is how close the set was.
The ordering holds too. Every time the margin widens by a game, the recovery rate falls, across all seven scorelines with no exception. One reversal in a sequence is noise. Seven steps in the same direction is a mechanism.
Three questions that work on any average
**By how much?** A gap is a number. Whether a set was lost by one game or six carries almost all the information about what happens next, and the headline threw it away.
**Are the groups the same size?** Two buckets of fourteen thousand give an honest comparison. Four hundred against forty thousand does not, because the small one swings for reasons unrelated to what is being measured.
**Does the order hold?** If the groups line up and keep lining up as the dimension increases, the pattern is real. If they jump around, it is probably noise wearing a pattern’s clothes.
Back to the menu
The average main course tells you almost nothing, in the same way and for the same reason. What you want is the spread, and whether the cheap end is a real option or a token.
One restaurant prices everything between twelve and fourteen pounds, another between six and twenty. They can advertise the same average and offer completely different evenings. The number that would tell you which is which is the one neither of them prints.
The figures here come from the Live Tennis API, a JSON service for developers. It covers live scores and fixtures, with players, match events and point-by-point history behind them. They are published openly under CC BY 4.0, free to reuse with attribution.
Method: completed best-of-three professional singles matches, 1 January 2023 to 14 September 2026. Retirements and walkovers excluded. Counted from the point-by-point record.