The question
"I'm up 5% over 1,000 bets. Am I good, or just lucky?"
Asking whether your betting edge is real is the most important question you can ask, and most people answer it with their gut. This lesson gives you the number that answers it properly.
The idea in one sentence
Imagine a bettor with no edge at all: the bell curve shows every result they could get by luck, and the p-value tells you how often luck alone would produce results as good as yours.
The picture
Flip a coin 1,000 times and you won't get exactly 500 heads. You'll get 489, or 512, or 497. Repeat that thousands of times and plot the results, and you get a hill: most results bunch near 500 and extreme ones are rare. That hill is the bell curve, which statisticians call the normal distribution.
Betting works the same way. Take a bettor with zero edge and let them place 1,000 bets. Their ROI won't be exactly 0%. It lands somewhere on a bell curve centred on 0%, and some of these no-edge bettors will be up 8% by pure luck.
The key question is how far out on that curve your result sits.
The bell curve is described by two numbers:
- The mean (the centre). For a no-edge bettor, 0% ROI.
- The standard deviation (the width). How much results naturally swing. Longer odds mean a wider curve, because results are lumpier.
One rule of thumb is worth memorising. About 68% of results fall within 1 standard deviation of the centre, 95% within 2, and 99.7% within 3.
Worked Betfair example
You've backed 1,000 selections in Match Odds and Over/Under markets at average odds of 3.0 and you're showing +5% ROI. (Illustrative figures.)
- What win rate does +5% imply? At odds of 3.0, a 5% ROI means you win 1.05 ÷ 3.0 = 35% of bets.
- How much does one bet swing? Each £1 bet either wins £2 or loses £1. The standard deviation of one bet is 3.0 × √(0.35 × 0.65) ≈ £1.43 per £1 staked. That's very noisy.
- Standard error over 1,000 bets. 1.431 ÷ √1,000 = 1.431 ÷ 31.6 ≈ 0.045, or 4.5%.
- t-statistic. 5% ÷ 4.5% ≈ 1.10.
- p-value. The tail beyond t = 1.10 is p ≈ 0.135. That's about a 13.5% chance, or 1 in 7, that a no-edge bettor matches you.
Verdict: +5% over 1,000 bets at these odds is not yet evidence of an edge. It might be real, but luck explains it comfortably.
How the same +5% looks as your sample grows
| Bets | Standard error | t-statistic | p-value (one-sided) | Verdict |
|---|---|---|---|---|
| 100 | 14.3% | 0.35 | 0.36 | Meaningless |
| 500 | 6.4% | 0.78 | 0.22 | Meaningless |
| 1,000 | 4.5% | 1.10 | 0.135 | Not yet |
| 3,000 | 2.6% | 1.91 | 0.028 | Promising |
| 5,000 | 2.0% | 2.47 | 0.007 | Strong evidence |
You need roughly 3,300 bets at average odds of 3.0 before a 5% edge reaches t = 2. Longer odds need even more. Shorter odds need fewer, because each bet is less noisy.
The formula
The standard error: the width of the curve for your ROI
- σ (sigma) is the standard deviation of a single bet's profit, per £1 staked.
- n is the number of bets.
In plain English: the swing in your ROI shrinks with the square root of the number of bets. To halve the noise you need four times as many bets, which is why small samples tell you almost nothing.
The t-statistic: where you sit on the curve
- ROI is your profit divided by total staked.
- SE is the standard error from above.
In plain English: t counts how many standard errors your ROI sits above zero. A t of 1 is common (about 1 in 6 no-edge bettors do this well), 2 is interesting (about 1 in 40), and 3 is strong evidence (about 1 in 700).
The swing of one bet
- O is the average decimal odds.
- p is your win rate.
In plain English: the longer the odds, the lumpier each result, and the wider the curve.
The p-value: the shaded tail
Draw a line on the bell curve at your result. The area beyond that line is the p-value: the probability that a bettor with no edge would do at least as well as you by luck.
- Small p-value (e.g. 0.01): luck rarely produces a result like yours. That's evidence of an edge.
- Large p-value (e.g. 0.30): plenty of no-edge bettors get results like yours. There's no evidence yet.
The traditional cut-off is p below 0.05 (1 in 20). For betting, be stricter, about p below 0.01, because most people have tested more than one idea before arriving at the one they're checking.
Normal vs t-distribution: with a small sample you only have an estimate of the true swing. The t-distribution allows for that: the same bell shape with fatter tails, so it's more cautious. Past about 100 bets the two curves are almost identical.
Try it
Set 1,000 bets, odds 3.0, ROI 5% and commission 0%, and check you get t ≈ 1.10 and p ≈ 0.135. Put commission back to 2% and see how much weaker the same result gets. Then drag the number of bets up and watch the curve narrow until your line sits out in the tail.
Common mistakes
- "p = 0.03, so there's a 97% chance my edge is real." Wrong. The p-value is the chance of results this good if you had no edge. It isn't the chance your edge is real.
- Testing lots of systems and reporting the best one. Test 20 worthless systems and one will probably hit p below 0.05. Correct for it (Lesson 7.4).
- Checking every day and stopping when it looks significant. Peeking and stopping at a good moment inflates your false positives. Decide the sample size up front, or use sequential testing (Lesson 7.3).
- Testing before commission. Test your ROI after Betfair's 2%. At average odds of 3.0, a 5% gross ROI becomes about 3.6% net.
- Treating linked bets as independent. Five bets on the same match aren't five pieces of evidence. The maths assumes independent bets.
- Confusing significant with big. With enough bets a 0.5% edge can be "significant" and still not worth your time.
Why this matters so much: why good models still lose money.