Statistically testing your performance

"I'm winning" is a claim. This module gives you the tools to test it.

Testing ROI

Null hypothesis: your true ROI is zero (or equal to −margin). With $n$ flat-staked bets, an average ROI $\bar{r}$ and a per-bet standard deviation $s$ :

t = \frac{\bar{r}}{s / \sqrt{n}}

If $|t| > 1.96$ , the result is significant at the 5% level.

The multiple testing trap

If you test 20 strategies (leagues, markets, filters), on average one of them will look significant at 5% purely by chance. This is p-hacking.

Apply a correction (for example Bonferroni: divide the threshold by the number of tests).
Validate any strategy you find on fresh data before putting money on it.

Risk of ruin

The probability of losing a given share of your bankroll depends on your edge, your variance and your stake size. For a Kelly strategy (fraction $c$ of Kelly), a classic approximation is:

P(\text{bankroll falls to } x \text{ times its value}) \approx x^{(2/c) - 1}

Strategy	P(losing 50% at some point)	P(losing 80%)
Full Kelly ( $c$ = 1)	50%	20%
½ Kelly	12.5%	0.8%
¼ Kelly	0.8%	≈ 0%

(These figures assume your estimated probability is exact. With estimation errors, reality is worse.)

The distribution of maximum drawdown

Rather than a formula, the most reliable method is Monte Carlo simulation:

Take your actual betting history (odds, estimated probabilities, stakes).
Replay it thousands of times, drawing the results at random according to your probabilities (or resample your history: bootstrap).
Look at the distribution of the maximum drawdown: the median, the 95th percentile.

If the 95th percentile of the drawdown exceeds what you can handle, reduce your stakes.

Interactive tool

Bankroll

Number of bets

Odds

Estimated probability

Observed frequency (p)

Number of simulations

Probability estimation error0.0 pts

Strategy

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

The multiple testing trap

If you test 20 strategies (leagues, markets, filters), on average one of them will look significant at 5% purely by chance. This is p-hacking.

Apply a correction (for example Bonferroni: divide the threshold by the number of tests).

Validate any strategy you find on fresh data before putting money on it.

Risk of ruin

The probability of losing a given share of your bankroll depends on your edge, your variance and your stake size. For a Kelly strategy (fraction

c

of Kelly), a classic approximation is:

P(\text{bankroll falls to } x \text{ times its value}) \approx x^{(2/c) - 1}

Strategy	P(losing 50% at some point)	P(losing 80%)
Full Kelly ( $c$ = 1)	50%	20%
½ Kelly	12.5%	0.8%
¼ Kelly	0.8%	≈ 0%

(These figures assume your estimated probability is exact. With estimation errors, reality is worse.)

The distribution of maximum drawdown

Rather than a formula, the most reliable method is Monte Carlo simulation:

Take your actual betting history (odds, estimated probabilities, stakes).

Replay it thousands of times, drawing the results at random according to your probabilities (or resample your history: bootstrap).

Look at the distribution of the maximum drawdown: the median, the 95th percentile.

If the 95th percentile of the drawdown exceeds what you can handle, reduce your stakes.