Variance Calculator
Quantify how wildly your bankroll can move when you repeat the same kind of sports bet. You supply win probability, decimal odds, stake, and how many bets—you get per-bet variance and the standard deviation of total profit over the sample.
The math assumes each bet is independent with the same stake and price. Parlays, teasers with shared legs, or steam-chasing correlated lines break that assumption—use the output as a baseline for uncorrelated flat betting.
Betting Variance & Standard Deviation
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Table of Contents
How to Use This Calculator
Enter win probability, decimal odds, stake per bet, and sample size n. The tool reports per-bet variance and the standard deviation of total P&L over n independent identical bets.
Win probability
Your model’s chance the bet wins at settlement—often derived from fair odds vs posted price.
Decimal odds
Posted price for the side you bet; profit on win is stake × (odds − 1).
Stake and n
Flat stake per trial and how many bets you want to summarize.
Read σ
Standard deviation scales with √n—volume narrows relative volatility but never removes it.
Binary Bet Variance
Let win profit = stake × (decimal − 1), loss = −stake. Per-bet variance uses the two-outcome distribution around the mean μ = p·win − (1−p)·stake.
Vartotal = n × Varone → σtotal = √(n × Varone)
Worked Examples
Example 1 — Coin-flip even money
p = 0.5, decimal 2.00, stake $100, n = 100. Mean P&L per bet is 0; per-bet variance is 10,000; σ over 100 bets ≈ $1,000—matches the calculator.
Example 2 — Favorite side
p = 0.6, decimal 1.67, stake $50, n = 200. σ grows with √(n)—compare to your bankroll for risk of drawdown.
Example 3 — Underdog
Higher odds widen the per-bet spread of outcomes; σ per dollar of stake can jump even with positive EV.
Interpreting σ
If total σ after 100 bets is $800, a normal-style rule of thumb puts about two-thirds of outcomes within ±$800 of the mean (discrete P&L is not truly normal, but the intuition helps).
Pair with ROI for yield, Kelly for sizing, and session loss for short trips.
Frequently Asked Questions
Variance measures how spread out profit is around the mean. For sports bets with two outcomes, it depends on win probability, stake, and payout odds.
Independent bets add variance linearly with n, so standard deviation of total P&L grows with the square root of n.
No—you can have edge and still face large swings. EV shifts the mean, not the width of the distribution by itself.
Convert to decimal before entering—this form expects decimal odds.
This model assumes independence—parlays and same-game multis break that assumption.
