Expected value: the only number that matters

EV = (true_prob × win_payout) − ((1 − true_prob) × stake). The win_payout uses decimal odds minus 1 — at -110 the win_payout per $100 stake is $90.91. A 55% true probability at -110 yields EV = 0.55 × 90.91 − 0.45 × 100 = +$5.00 per $100, or a 5% return. Notice that hit rate alone does not capture this: 70% at -300 yields EV = 0.70 × 33.33 − 0.30 × 100 = −$6.67. Pros optimize for EV, not win rate.

Edge: the gap between your probability and the market's

Edge in percentage-point form is edge = (true_prob − implied_prob) × 100. A -110 line implies 52.38%; a true probability of 55% gives 55.00 − 52.38 = 2.62 percentage points of edge. Important nuance: edge against the raw implied probability overstates your real edge because the implied includes the bookmaker's vig. To measure edge net of vig, devig the market first (see the No-Vig calculator), then compare your true probability against the fair probability.

Worked example: 55% true probability at -110

Implied probability of -110 = 52.38%. Raw edge = 55.00 − 52.38 = 2.62 pp. Fair price at 0.55 implied = decimal 1 / 0.55 = 1.818, American ≈ -122. The market is offering -110 when fair price is -122 — a real edge worth taking. EV per $100 stake = 0.55 × $90.91 − 0.45 × $100 = +$5.00. At quarter Kelly with $10k bankroll, the optimal stake is roughly $73.

FAQ

What is expected value (EV) in sports betting? +

EV is the average dollar return per wager if you placed the same bet at the same price thousands of times. The formula is EV = (true_prob × win_payout) − ((1 − true_prob) × stake). A bet with positive EV makes money in the long run; a bet with negative EV loses money in the long run. Win rate alone is misleading — a 70% hit rate at -300 odds is still −EV, while a 53% hit rate at -110 is +EV. Pros chase EV, not hit rate.

How is edge calculated and what counts as a "good" edge? +

Edge is the gap between your true probability and the market's implied probability, expressed in percentage points: edge = (true_prob − implied_prob) × 100. A 2% edge on a heavily-bet market (NFL spreads, NBA totals) is considered strong. Anything above 4% is suspiciously good and usually means a stale line, an error, or a misestimated true probability. Below 1%, the bet is rarely worth the variance — the slop in your probability estimate likely swamps the edge.

Why does the calculator show a "fair price"? +

The fair price is the American odds equivalent of your true probability. If your model says a bet is 55% to win, the fair price is roughly -122 (decimal 1.82). If the book is offering -110 (decimal 1.91), you are getting a better price than your fair value — that gap is your edge in odds form. Fair-price thinking matches how pros line-shop: they know what a bet is worth and only place it when a book is offering meaningfully more.

What's the minimum edge a serious bettor should require? +

Common practice is at least 1-2% edge AFTER devigging the book, on markets with reasonable liquidity. Higher juice markets (player props, alt lines, longshots) demand 3%+ to be worth the variance and the higher modelling uncertainty. The cushion exists because your probability estimate has its own error bars — if you require a 1% edge and your model is off by a percentage point, every bet you place is actually breakeven or worse. Fractional Kelly stakes (quarter Kelly) help survive that estimation error.

How is this different from the Kelly calculator? +

EV tells you WHETHER to bet. Kelly tells you HOW MUCH. The EV/Edge calculator answers "is this bet profitable at all" — if EV is ≤ 0, do not place it. Kelly takes the same probability + odds inputs and tells you the optimal stake size given your bankroll, maximizing long-run logarithmic growth. Use this calculator first to confirm +EV; if positive, push the same inputs into Kelly for stake sizing. Both numbers matter; ignoring Kelly leads to over-betting and ignoring EV leads to confidently betting losers.

EV and Edge Calculator