The question
"I've placed 150 bets and I'm up. How many more before I know it's real?"
How many bets to prove an edge is the question every bettor should answer before placing the first one. The answer depends on your odds and the size of edge you're hoping for, and it's usually far bigger than people guess.
The idea in one sentence
The number of bets you need grows with the square of how noisy each bet is, divided by how big your edge is, so small edges at long odds take a very long time to prove.
The picture
Think of the bell curve from Lesson 1.1 again. There are really two curves: one for a bettor with no edge, centred on 0%, and one for a bettor with your edge, centred on, say, +3%. With a small sample both curves are wide and they overlap almost completely. You can't tell which one your result came from.
Every extra bet narrows both curves. Eventually they pull apart, and a result from the edge curve rarely looks like a result from the no-edge curve. Sample size is the number of bets it takes for the two curves to separate.
Two settings decide how far apart they must be:
- Significance. How rarely you're willing to be fooled by a no-edge bettor. A one-sided 5% test is the usual minimum; 1% is safer.
- Power. How often you want to spot an edge that's really there. 80% is standard: you accept a 1 in 5 chance of missing a real edge.
| Odds | 2% | 3% | 5% | 10% |
|---|---|---|---|---|
| 1.5 | 4,794 | 2,106 | 739 | 172 |
| 2.0 | 9,792 | 4,349 | 1,562 | 387 |
| 3.0 | 19,788 | 8,835 | 3,209 | 818 |
| 5.0 | 39,780 | 17,808 | 6,502 | 1,681 |
| 10.0 | 89,760 | 40,239 | 14,734 | 3,837 |
Worked Betfair example
You back Over 2.5 goals at an average price of 1.95, and you believe your true edge is +3% ROI after Betfair's 2% commission. You place about 20 bets a week. (Illustrative figures.)
- Net odds. A winner at 1.95 pays £0.95 per £1, less 2%, so £0.931. Net odds are 1.931.
- Win rate your edge implies. 1.03 ÷ 1.931 = 53.3%.
- Swing of one bet. σ = 1.931 × √(0.533 × 0.467) ≈ 0.963 per £1 staked.
- Bets for your result to reach t = 2. (2 × 0.9633 ÷ 0.03)² ≈ 4,125 bets. That's the point where a true 3% edge would, on average, sit two standard errors above zero.
- Bets for 80% power at the 5% level. You want an 80% chance of passing a one-sided 5% test if the edge is real. The multipliers are 1.6449 and 0.8416, which add to 2.4865. (2.4865 × 0.9633 ÷ 0.03)² ≈ 6,376 bets (rounded up).
- In weeks. 6,376 ÷ 20 per week ≈ 319 weeks, a little over six years.
Verdict: a genuine 3% edge on Over 2.5 goals would take about six years to prove on results alone at 20 bets a week. Your 150 bets tell you almost nothing, whether you're up or down.
Bets needed to reach t = 2, by odds and edge
ROI after 2% commission. Longer odds and smaller edges push the number up fast:
| Average odds | 2% edge | 3% edge | 5% edge | 10% edge |
|---|---|---|---|---|
| 1.5 | 4,794 | 2,106 | 739 | 172 |
| 2.0 | 9,792 | 4,349 | 1,562 | 387 |
| 3.0 | 19,788 | 8,835 | 3,209 | 818 |
| 5.0 | 39,780 | 17,808 | 6,502 | 1,681 |
| 10.0 | 89,760 | 40,239 | 14,734 | 3,837 |
A 3% edge in Correct Score at around 10.0 needs about 40,000 bets just to reach t = 2. Nobody proves that on results.
The faster route: closing line value
Results are slow because each bet either wins or loses, which is a huge swing. Closing line value compares your price with the final price for every bet, win or lose. Its swing per bet is far smaller, so it can show an edge in a few hundred bets rather than several thousand. Keep measuring results, but judge the strategy early on CLV.
The formula
Bets needed to reach a target t
- n is the number of bets.
- t is the t-statistic you want to reach, usually 2.
- σ is the standard deviation of one bet per £1 staked.
- edge is your expected ROI after commission, as a decimal (3% = 0.03).
In plain English: divide how noisy a bet is by how big your edge is, multiply by the target, and square it. The squaring is what hurts.
Bets needed with power
- z_α is the multiplier for your significance level: 1.645 for one-sided 5%, 2.326 for one-sided 1%.
- z_β is the multiplier for your power: 0.842 for 80%, 1.282 for 90%.
In plain English: this is how many bets give you a good chance (the power) of passing the test if your edge is real. Planning to reach exactly t = 2 only gives you about a 50% chance.
The swing of one bet
- O_net is your average odds after commission: 1 + (odds − 1) × 0.98.
- p is the win rate your edge implies.
In plain English: the same swing formula as Lesson 1.2, which is why longer odds need so many more bets.
Try it
Set odds 1.95, edge 3%, 5% significance, 80% power and 20 bets a week, and check you get about 6,376 bets and 319 weeks. Then change the odds to 1.5 and to 5.0 and see how the answer moves.
Common mistakes
- Deciding the sample size after you've started. If you stop the moment things look good, you've let luck pick the stopping point. Fix the number up front, or use a proper sequential test (sequential testing).
- Planning for your hoped-for edge. Real edges are usually smaller than first estimates. Plan the sample for the edge you'd still bet on, not the one in your best backtest.
- Counting linked bets as separate. Home win, Over 2.5 and both teams to score on the same match move together. They add less evidence than three separate matches.
- Giving up on a real edge too early. Being down after 500 bets at 3.0 is not evidence your edge has gone. It's what the maths says will happen to lots of genuine edges (Lesson 7.3).
- Relying on P&L alone. Results are the slowest judge available. Track CLV alongside them from day one.
Why a small sample has sunk so many models: why good models still lose money.