A CappersUnite guide
Expected value, or EV, is the average profit or loss a bet produces per dollar wagered if you could somehow place that exact same bet thousands of times. A bet can win this one time and still be a bad bet, or lose this one time and still have been the right call — EV is what tells the difference. It's the single number that separates gambling on vibes from betting on edge.
EV = (Win probability × Amount won) − (Loss probability × Amount risked)
Everything in that formula is knowable before the bet except one thing: your true win probability. The odds tell you what the sportsbook implies your win probability to be. Whether you actually have an edge comes down to whether you believe the real probability is higher than that implied number.
Say a game is priced at -110, a standard two-sided line. Risking $100 at -110 wins $90.91 if correct. The odds imply a win probability of 52.38% (that's the break-even rate — below it you lose money long-run, above it you profit, before even looking at your own opinion of the game).
Now say your own model, research, or line shopping tells you this side actually wins 55% of the time, not 52.38%. Plug that into the formula:
EV = (0.55 × $90.91) − (0.45 × $100)
EV = $50.00 − $45.00
EV = +$5.00
That's a +5% edge — for every $100 you risk on bets like this, you'd expect to net about $5 over the long run. Drop your estimate to 50%, and the same bet becomes EV = (0.50 × $90.91) − (0.50 × $100) = −$4.55 — a bet you should never make, even though nothing about the odds changed.
EV describes an average over many repetitions, not a guarantee on any single one. A +5% edge bet still loses 45% of the time in this example — it just wins often enough, and by enough, that the wins outweigh the losses across a large enough sample. One loss on a +EV bet means nothing on its own; it's only a mistake if the probability estimate behind it was wrong, not because the coin came up tails this time.
This is the part no formula can do for you — EV is only as good as the win probability you plug into it. That number usually comes from comparing a book's line against the market consensus (shopping multiple books for the best price on the same bet), your own statistical model, or situational research the market hasn't fully priced in yet. If your probability estimate is just a guess, the EV calculation is just dressing up a guess in math — the edge has to come from somewhere real.
FairLine strips the vig out of a market to show you the break-even probability a line actually implies, EdgeSize turns an EV estimate into a bet size using the Kelly Criterion, and our Kelly Criterion guide covers exactly how much of your bankroll a given edge is worth risking.