Sample size · Formation

You have an ROI of +8% over 150 bets. Are you a good bettor? There's no way to tell. This module explains why, and how many bets you really need.

The intuition

Your observed ROI = your true edge + noise. The noise shrinks with the number of bets $n$ , but slowly: it's only halved when $n$ is multiplied by 4.

The standard deviation of the ROI after $n$ flat-staked bets is approximately:

\sigma_{ROI} \approx \frac{\sigma_{\text{bet}}}{\sqrt{n}} \quad \text{with} \quad \sigma_{\text{bet}} = \text{odds}\sqrt{p(1-p)}

Confidence interval on the ROI

A 95% confidence interval is approximately:

ROI \pm 1.96 \times \sigma_{ROI}

How many bets to detect an edge?

For the 95% interval to exclude zero with a true edge $E$ :

n \approx \left(\frac{1.96 \times \sigma_{\text{bet}}}{E}\right)^2

Average odds	True edge of +5%	True edge of +2%
2.00	≈ 1,500 bets	≈ 9,600 bets
4.00	≈ 4,800 bets	≈ 29,000 bets

And that's only a minimum threshold: with that many bets, a genuine +5% bettor has only about a one in two chance of statistically "proving" their edge.

Interactive tool

Bets needed

Odds

Edge (EV)

Educational tool. Results are theoretical estimates, not betting advice.

The intuition

Your observed ROI = your true edge + noise. The noise shrinks with the number of bets

n

, but slowly: it's only halved when

n

is multiplied by 4.

The standard deviation of the ROI after

n

flat-staked bets is approximately:

\sigma_{ROI} \approx \frac{\sigma_{\text{bet}}}{\sqrt{n}} \quad \text{with} \quad \sigma_{\text{bet}} = \text{odds}\sqrt{p(1-p)}

How many bets to detect an edge?

For the 95% interval to exclude zero with a true edge

E

n \approx \left(\frac{1.96 \times \sigma_{\text{bet}}}{E}\right)^2

Average odds	True edge of +5%	True edge of +2%
2.00	≈ 1,500 bets	≈ 9,600 bets
4.00	≈ 4,800 bets	≈ 29,000 bets

And that's only a minimum threshold: with that many bets, a genuine +5% bettor has only about a one in two chance of statistically "proving" their edge.