What "expected value" actually means
Expected value (EV) is the average amount you'd win or lose per bet if you could place the exact same wager thousands of times. It's the single number that separates a mathematically good bet from a bad one. A bet with positive expected value (+EV) is one where the price you're getting is better than the true probability of the outcome. A bet with negative EV (−EV) is one the book has priced in its favor — which, thanks to the vig, is most bets on most days.
The key word is average. EV says nothing about what happens on your next ticket. It describes the long run — and the long run is the only arena where a disciplined bettor can actually come out ahead.
The EV formula, in plain terms
For a single bet, the formula is:
EV = (probability of winning × profit if you win) − (probability of losing × amount staked)
You need three inputs: your estimate of the true win probability, the payout at the odds you're offered, and your stake. The odds give you the payout; your model (or a de-vigged market price) gives you the probability. Let's put real numbers to it.
Worked example 1: a +150 underdog
You stake $100 on a team at +150. American +150 means a $100 win pays $150 profit. In decimal terms that's 2.50, and the break-even probability is 1 ÷ 2.50 = 40%. In other words, this bet is only worth making if the team wins more than 40% of the time.
Suppose your assessment says the true probability is 45%. Then:
EV = (0.45 × $150) − (0.55 × $100) = $67.50 − $55.00 = +$12.50
That's +12.5% EV per dollar risked. You will still lose this bet 55% of the time — but each time you place it, you gain $12.50 on average. Repeat it enough and the math surfaces.
Worked example 2: a −110 pick
Standard −110 juice means risking $110 to win $100, or risking $100 to win $90.91. The decimal is 1.909, and the break-even probability is 52.38% — not 50%. That extra 2.38 points is the book's cut. If you truly win this bet 55% of the time:
EV = (0.55 × $90.91) − (0.45 × $100) = $50.00 − $45.00 = +$5.00 per $100
Why win rate is a trap
Here is the idea that trips up most bettors: a high win rate does not mean a good bet, and a low win rate does not mean a bad one. What matters is win rate relative to the price.
Consider a heavy favorite at −400. Decimal 1.25, so a $100 bet wins just $25, and the break-even probability is 80%. Say you cash it 78% of the time — a gaudy win rate:
EV = (0.78 × $25) − (0.22 × $100) = $19.50 − $22.00 = −$2.50
You win nearly four out of five bets and still bleed money. Now flip it. An underdog at +200 (decimal 3.00, break-even 33.3%) that you win only 38% of the time:
EV = (0.38 × $200) − (0.62 × $100) = $76.00 − $62.00 = +$14.00
You lose 62% of these and still profit. Win rate is a vanity metric. EV is the scoreboard.
Where the probability comes from: de-vigging
The hard part isn't the formula — it's getting an honest probability. The market itself is the best available estimate, but book prices are inflated by the vig, so you have to strip it out first. This is called de-vigging, or finding the "no-vig" fair price.
Take a two-way market where one side is −110 (implied 52.38%) and the other is +100 (implied 50.0%). The two implied probabilities sum to 102.38% — that overround is the hold. To get a fair estimate for the favorite, normalize: 52.38 ÷ 102.38 = 51.16%.
Now line-shop. If a different book offers that same side at +100 — implied 50.0% — you're paying for a 50% shot on something worth 51.16%. That's +EV:
EV = (0.5116 × $100) − (0.4884 × $100) = +$2.32 per $100 (about +2.3%)
Edges this size are what a scanner is built to catch. Doing it by hand across 40+ books, every market, all day, isn't realistic. EdgeFinder pulls live odds, de-vigs each market to a fair price, and flags the +EV gaps automatically — you can see the current free list on today's edges.
CLV: the check on whether your EV was real
You estimated a probability. Were you right? You often can't know from one game, but closing-line value (CLV) is the best available proxy. The closing line — the final price before kickoff — is the sharpest number the market produces, because it has absorbed all the money and information. If you consistently bet prices better than the close, you were probably beating a fair estimate, and positive EV should follow over time.
Example: you take a team at +150 and it closes at +120. You locked in a longer price than the market's final word. That's positive CLV — a durable signal that your +EV was genuine, not luck. It's also why a credible tool publishes a verifiable, timestamped record of pregame picks graded on both results and CLV, rather than a cherry-picked win streak.
From EV to stake size: a word on Kelly
Knowing a bet is +EV doesn't tell you how much to risk. The Kelly criterion links edge to bankroll: for the +150 example (true 45%, decimal 2.50), full Kelly suggests about 8.3% of bankroll. Most disciplined bettors use a fraction of that — quarter-Kelly here would be roughly 2% — because probability estimates are uncertain and full Kelly swings hard. Sizing down protects you when your model is slightly off, which it always is to some degree.
The bottom line
A good bet is not one that wins. It's one where the price beat the true probability at the moment you placed it. Any single result is noise; only the long-run average of your EV means anything. Chase +EV, measure yourself with CLV, size sensibly, and let variance do what it does. If you want the de-vigging, line-shopping, and +EV detection handled for you, sign up for EdgeFinder — the free tier shows the top edges each day.
For education and analysis only. No bet is a guaranteed winner, and positive EV does not promise profit over any given stretch. 21+ where legal; know your jurisdiction and bet responsibly.