Expected Value: The Only Number That Matters Long Term

Expected value is the sum, across every possible outcome of a wager, of the probability of that outcome multiplied by its payoff. Written compactly: EV = Σ p(x) · payoff(x).

Consider a $100 wager at +150 on an outcome you believe has a true 45% chance. The bet pays $150 on a win and loses $100 on a loss. Expected value equals (0.45 × $150) + (0.55 × -$100), or $12.50. Over many repetitions, this bet yields an average profit of $12.50 per $100 staked.

A bettor who lost the wager above lost real money. The bet was still correct. A bettor who took +150 on an outcome with a true 30% probability would have a negative EV bet even if they happened to win. Treating individual outcomes as evidence of skill is the single most expensive mistake in amateur betting.

Professionals evaluate decisions on inputs: pricing, probability estimate, and execution. They evaluate results only across large samples, where the noise of individual outcomes averages out.

Every EV calculation rests on a probability estimate. Markets price probabilities reasonably well, especially in liquid US sports. Beating the market requires either better information, better models, or pricing inefficiency. Without one of these, your probability estimates are likely worse than the market's.

A practical discipline: write down your estimated probability before checking the market price. If you systematically beat the closing line, you have an edge. If you do not, the EV you assigned was wishful thinking.

Positive EV does not guarantee profit. Variance and bankroll size determine whether you can survive long enough to realize your edge. A bet with positive EV but excessive size relative to bankroll has a high risk of ruin. EV tells you the direction; bet sizing tells you the speed; bankroll tells you how long you can travel.