What Is Variance?
A positive edge means the price you take is better than the true probability behind it. Over time, that should produce a positive average result. Variance is the short-run noise around that edge — the reason a profitable strategy can still have losing stretches, flat periods, and drawdowns before the long-run advantage shows up.
Example: Take a coin toss.
A fair coin lands heads 50% of the time, so the fair decimal price is 2.00. If a bookmaker offers 2.10, that bet is positive EV.
You can see the edge by comparing the bookmaker price to fair odds:
So you are being paid 5.0% above fair value, which is the same as an expected profit of $0.05 per $1 staked, or +5.0% EV.
But that 5% edge is not guaranteed to show up smoothly in the short run. Even with a real advantage, results can still be negative over a finite sample. Read on to see how often that can still happen in practice.
Using the same coin toss example above:
- true win probability = 50%
- bookmaker odds = 2.10
- flat $1 stakes
- each toss is independent
the chance of being overall negative after a run of bets is approximately:
| Coin tosses | Chance of being negative | 95% CI lower total profit | 95% CI upper total profit |
|---|---|---|---|
| 1 | 50.0% | -$1.00 | $1.10 |
| 10 | 37.7% | -$6.01 | $7.01 |
| 100 | 30.9% | -$15.58 | $25.58 |
| 500 | 15.2% | -$21.02 | $71.02 |
| 1,000 | 6.9% | -$15.08 | $115.08 |
| 10,000 | 0.00009% | $294.20 | $705.80 |
Even with a genuine +5% edge, there is still a meaningful chance of being down after 100, 200, or even 500 bets. That is variance in practice.
Variance is the gap between expected results and lived results in the short run. Even when a bet has positive expected value, outcomes can still be volatile over dozens or hundreds of bets. That is why good betting strategies need both a real edge and enough time for that edge to play out.