Sample size calculator for an edge
You believe you have an edge of a given size. This is the number of bets or trades before it can be told from zero, exactly, and the sequential rule that lets you stop sooner without cheating.
Worked example — Bets needed to tell this edge from zero: 19,648. A 2% return on turnover at 2.00 decimal (even money): 18.9 years at 20 bets a week
A good, real edge: A genuinely good edge, better than most people who claim one actually have
Advanced options 3
A 2% return at 2.00 means a true win rate of 51.000% against a break-even rate of 50.000%. The exact design rejects the null at 9,962 wins or more, which delivers 80.0% power at a true false-positive rate of 2.49%.
The per-bet payoff is a two-point variable: 1.00 units on a win and -1 on a loss. Its variance is set by the price, not by the edge, which is why a generic mean-difference power calculator understates the sample badly at long prices. Every figure assumes the edge is constant, the bets are independent, and the price you enter is the price you get.
Run a score from zero. Add 0.01980 after a win and -0.02020 after a loss. Stop and accept the edge if the score passes +3.466; stop and reject it if the score falls below -1.584; between the two, the record does not say yet. That is Wald's sequential probability ratio test, and it holds the same 80% power and the same 2.50% upper-tail false positive budget the fixed design above spends, while being read after every single bet. Checking a fixed-sample p-value the same way does not: repeated peeking at a test designed to be read once drives the real false positive rate far above the one printed on it. The expected stopping times are Wald's approximation, which ignores boundary overshoot and reads a little low.
The price is the column worth staring at: the edge stays the same size in every row of the second table while the sample needed to prove it grows roughly with the price, because variance grows with the square of the payout and the edge does not.
Bets needed for common ROI edges, at even money
At decimal 2.00, even money, the exact binomial sample needed to prove a claimed edge falls fast as the edge itself grows.
| Return on turnover | Exact binomial | Years at 20 a week |
|---|---|---|
| 0.5% | 314,142 | 302.1 |
| 1.0% | 78,595 | 75.6 |
| 2.0% | 19,648 | 18.9 |
| 3.0% | 8,759 | 8.4 |
| 5.0% | 3,143 | 3.0 |
| 10.0% | 786 | 0.8 |
Same edge at different odds
A 2% claimed edge is held constant in every row here. The sample needed to prove it explodes with the price, because variance scales with the square of the payout while the edge does not.
| Decimal price | Exact binomial | Years at 20 a week |
|---|---|---|
| 1.50 | 9,743 | 9.4 |
| 2.00 | 19,648 | 18.9 |
| 3.00 | 39,458 | 37.9 |
| 5.00 | 79,019 | 76.0 |
| 11.00 | 197,753 | 190.1 |
| 21.00 | 396,622 | 381.4 |
How many bets does a 2% edge need?
19,648 bets, by the exact binomial design at 95% confidence and 80% power. At twenty bets a week that is 18.9 years. The normal approximation says 19,615, close enough here and not close enough everywhere, which is why both are printed above.
The price sets the sample, not the edge: take the same 2% return to a 21.00 shot and the sample needed rises to 396,622 bets instead of 19,648. A bet is not a symmetric measurement: the payoff takes one of two values, so its variance scales with the square of the price while the expected return does not, which is the reason longshot strategies feel unfalsifiable on any human timescale.
A strategy review after 200 trades, or a tipster record over one season, cannot distinguish this edge from nothing, and any verdict delivered on that evidence is a coin flip dressed as analysis. If you already have a record, run it through the track record significance calculator first, then come back here to find out how far you still have to go.
What this does not model
- Every figure assumes the edge is constant, the bets are independent, and you get the price you entered. Real edges decay as markets adapt, real records are correlated within a day or a sector, and real fills are worse than the quote, all of which make the true sample larger than the one here.
- The sequential expected stopping times are Wald's approximation and ignore how far past the boundary the score lands, so they read slightly low.
- A sample size is not a promise: reaching n does not mean you learn the answer, it means you have an 80% chance of detecting the edge if it is exactly the size you claimed.
The next question after this one
Track record significance calculatorCalculatorRun the test on the record you already have, rather than planning the sample you would need.Open nextOther questions
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