Expected Value (EV)

Expected value tells you whether a bet is mathematically worth making — not whether it will win, but whether making it over and over would leave you ahead or behind. It’s the single number that separates “good bets” from “bets that happened to win.” A parlay can cash and still be a terrible-EV play; a bet can lose and still have been the correct decision. EV is how you tell the difference.

The math is simple in structure even though the inputs are hard to pin down. You need three things: your stake, the payout the sportsbook is offering (converted from American odds into a dollar profit), and your own honest estimate of how often the bet actually wins. Multiply your estimated win probability by the profit if it hits, multiply your estimated loss probability by the amount you’d lose, and add the two together. If that sum is positive, the bet is +EV — profitable in the long run at that price. If it’s negative, you’re paying for entertainment, not investing.

The part bettors skip is supplying their own win probability. The sportsbook’s odds already imply one (that’s what “implied probability” means), but that number is the book’s opinion, padded with vig. EV only exists as a useful concept when you have a probability estimate that’s independent of the book’s line — from a model, from injury news the market hasn’t priced in yet, from a discrepancy between two books. Without that independent view, you’re just restating the odds back to yourself and calling it analysis.

Example

Say the Jacksonville Jaguars are +240 moneyline underdogs on the road, and you’ve built a small model — factoring in the opposing quarterback’s ankle injury that you think the market is underrating — that puts Jacksonville’s true win probability at 35%, not the market’s implied 29.4% (100 ÷ (240+100)).

You bet $50 on the Jaguars.

• If they win: +240 odds pay $2.40 in profit per dollar staked, so profit = $50 × 2.40 = $120.
• If they lose: you lose the $50 stake.

Now weight each outcome by your estimated probability:

• Win branch: 0.35 × $120 = $42.00
• Loss branch: 0.65 × (–$50) = –$32.50

EV = $42.00 – $32.50 = +$9.50

That $9.50 is your expected profit per $50 bet, or an edge of about 19% of your stake. It doesn’t mean you’ll make $9.50 this Sunday — you’ll actually win $120 or lose $50, nothing in between. What it means is that if you found this exact 35%-true/29.4%-implied mismatch a hundred times and bet $50 each time, your average result would land near +$9.50 per bet, roughly $950 across the hundred bets, even though most individual weekends would look nothing like that average.

Flip the model slightly and the whole trade collapses: if your real win probability were only 27% instead of 35%, EV becomes 0.27 × $120 – 0.73 × $50 = $32.40 – $36.50 = –$4.10. Same odds, same stake, worse bet — because EV lives or dies on the accuracy of your probability estimate, not on the price alone.

Key Points

• EV is only as good as your probability estimate: The odds are fixed and public; your win-probability input is the only variable you control, and it’s usually a guess dressed up as a number. Be honest about your model’s error bars before trusting a thin edge.
• A single win or loss tells you nothing about whether the bet was correct: A +EV bet loses plenty of the time (in the example above, 65% of the time), and a –EV parlay cashes occasionally anyway. Judge the decision by the math at the time you made it, not by the final score.
• Compare EV, not just win probability, across bets: A 60% chance to win $20 can have worse EV than a 35% chance to win $120, depending on stake and payout. Always run the full calculation rather than ranking bets by “most likely to hit.”
• Vig makes most bets slightly negative by default: On a standard -110/-110 side, the implied probabilities sum to about 52.4%, not 100%, which is the book’s built-in edge. You need a real information or modeling advantage just to climb back to breakeven, let alone positive EV.
• Small, consistent edges compound; one-off “locks” usually don’t: A steady +3% to +5% EV edge across a large volume of bets is how long-term profit actually gets made. Chasing a single bet you’ve talked yourself into as “can’t lose” is usually a sign the probability estimate was reverse-engineered from the desired conclusion.
• Line shopping is free EV: Finding the same bet at +240 instead of +220 changes nothing about your win probability but directly increases the profit side of the equation, so comparing prices across books before betting is one of the few completely riskless ways to raise your EV.