Definition
Standard deviation measures how spread out results are from the average result. In betting, it shows how much actual outcomes can swing around an expected value.
For a full set of outcomes, the formula is:
σ = sqrt(Σ(x - μ)^2 / N)
x is each result, μ is the average result, and N is the number of results.
A low standard deviation means results cluster close to the average. A high standard deviation means results swing farther away from the average.
Worked Example
A bettor makes five $110 bets at -110 odds. Each win profits $100, and each loss loses $110.
Results:
+$100, -$110, +$100, -$110, +$100
Average result:
($100 - $110 + $100 - $110 + $100) / 5 = $16
Each result is compared with the $16 average, squared, averaged, then square-rooted:
σ = sqrt(((84^2 + -126^2 + 84^2 + -126^2 + 84^2) / 5))
σ = sqrt(10,584) = $102.88
Why It Matters
Standard deviation helps a bettor understand bankroll swings, not just average return. It is most useful when comparing strategies with similar expected value but different levels of volatility.