Advanced Theory
advanced10 min read
Variance, Standard Deviation, and Sample Size: When Can You Trust Your Results?
How many bets do you need before your results mean anything? The math behind confidence intervals in sports betting.
The Sample Size Problem
You've won 58% of your last 50 bets. Are you a sharp bettor or just lucky? The answer depends on understanding variance and sample size.
The Math of Variance
For a series of bets at -110 odds:
- Standard deviation per bet ≈ 1 unit
- Standard deviation over N bets ≈ √N units
- Expected profit per bet (at 55% win rate) ≈ 0.05 units
How Many Bets to Prove Skill?
To be 95% confident your results aren't due to luck:
| True Win Rate | Bets Needed for 95% Confidence |
|---|---|
| 52% | ~6,000 |
| 53% | ~2,500 |
| 54% | ~1,500 |
| 55% | ~1,000 |
| 56% | ~700 |
| 60% | ~250 |
At a 55% win rate, you need approximately 1,000 bets before you can be reasonably confident your edge is real.
Confidence Intervals
After 100 bets at -110 with a 55% win rate:
- Expected profit: +5 units
- Standard deviation: ~10 units
- 95% confidence interval: -15 to +25 units
You could be anywhere from down 15 units to up 25 units — and all of it would be within normal variance for a 55% bettor.
The Danger of Small Samples
| Scenario | 50 Bets | 500 Bets | 5,000 Bets |
|---|---|---|---|
| True 55% bettor shows 45% | 18% chance | 1.5% chance | ~0% chance |
| True 50% bettor shows 55% | 24% chance | 1.3% chance | ~0% chance |
| True 55% bettor shows 60% | 16% chance | 1.3% chance | ~0% chance |
Practical Takeaways
- Don't judge yourself on fewer than 500 bets — The variance is too high
- Track CLV instead — CLV stabilizes faster than win rate
- Expect losing months — Even a 55% bettor will have losing months ~30% of the time
- Don't change strategy based on short-term results — Trust the process over 1,000+ bets
- Beware of tipsters with small samples — 100 bets at 60% proves nothing