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Maths · the arithmetic behind a price

Maths

How many bets before a record means anything

Distinguishing a 55 per cent bettor from a 50 per cent one with reasonable confidence takes several hundred bets. At a hundred bets, a 55 per cent result has a confidence interval that comfortably contains 50.

The signal grows with the number of bets while the noise grows with its square root, so the ratio between them improves slowly. Four times as many bets gives roughly twice the clarity, not four times.

What a hundred bets proves Fifty-five wins from a hundred looks convincing and is consistent with a true rate anywhere from about 45 to 65 per cent. Both a strong edge and no edge at all fit inside that record comfortably.

This cuts against pessimism too. A hundred bets at 45 per cent is equally uninformative, and abandoning a process on that evidence is as unjustified as celebrating one.

Which is where it goes wrong. Almost every published record is shorter than the length at which it would begin to be evidence, and the shorter it is the more confidently it tends to be presented.

What to do with it. Ask for the count before the percentage. If the count is under a few hundred, the percentage is not yet a fact about anybody's skill.

Check one. The tipster record checker takes a claimed record and its usual price, and shows the break-even rate and how often luck alone would produce that record.

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