How to Calculate Expected Value for a Moneyline Bet—and Why It Only Pays Off Over the Long Run

Expected Value (EV) is the single number that tells you whether a bet is mathematically worth placing: the average amount you would win or lose per wager if you could repeat the exact same bet many times. The formula is simple—(win probability × potential win) minus (loss probability × wager)—and you can compute it by hand for any moneyline line. A positive result (+EV) implies profit over time; a negative result (-EV) implies a loss over time. The catch, as betting analysts consistently emphasize, is that the edge only becomes reliable across a large sample of bets, not on any single game.

Understanding Expected Value (EV) in Sports Betting

EV is a statistical measure that quantifies the average amount a bettor can expect to win or lose per bet if the same wager were repeated multiple times, as betting writer Benjamin Pilgrim explains in his guide to the calculation. Rather than predicting who wins a single game, it answers a different question: if you made this bet over and over, would you come out ahead?

Oddschecker's support documentation frames EV as a fundamental concept for determining whether a bet, made repeatedly, is likely to be profitable in the long run, because it quantifies both the potential for profit or loss and its magnitude. By regularly placing bets with positive EV, bettors increase their probability of making a profit over time. That reframing—from picking winners to pricing wagers—is what separates EV-based betting from ordinary handicapping.

The Expected Value Formula Explained

The formula, as Smarkets' betting education team presents it, is: (amount won per bet × probability of winning) − (amount lost per bet × probability of losing). SportsBetting3's lesson on the topic states the same structure for moneyline wagers: EV = (Win Probability × Potential Win) − (Loss Probability × Wager).

Each input has a precise meaning. The potential win is your profit if the bet wins, not the total return—for a $100 bet at +125 odds, that's $125 in profit. The wager is the amount you lose if the bet loses. The probabilities are the trickiest part: they should reflect the side's actual chance of winning, which means removing the sportsbook's built-in margin, known as the vigorish or vig, from the implied probabilities in the posted odds.

That margin matters. Smarkets illustrates it with a coin toss: a fair market prices heads and tails at 2.0, but a bookmaker would offer around 1.90 on both. Running the EV calculation on that price yields (9 × 0.50) − (10 × 0.50) = −0.5, meaning you would lose an average of 50p for every £10 staked—a bad value bet on an outcome you can predict exactly.

Worked Example: Calculating Expected Value for a Moneyline Bet

The following calculation, drawn from SportsBetting3's lesson, uses a hypothetical NFL matchup: the Chiefs at −150 against the Ravens at +125, with a $100 wager. You can replicate these steps for any moneyline price.

Step-by-step EV calculation for Chiefs −150 vs. Ravens +125 on a $100 wager
Step	Ravens (+125)	Chiefs (−150)
1. Potential win on a $100 wager	$125 profit	$100 profit (risking $150)
2. Implied probability from the odds	44.44%	60.00%
3. No-vig win probability	42.55%	57.45%
4. Loss probability	57.45%	42.55%
5. Apply EV = (Win Prob × Potential Win) − (Loss Prob × Wager)	(0.4255 × $125) − (0.5745 × $100)	(0.5745 × $100) − (0.4255 × $150)
6. Expected Value	−$4.26	−$6.38

Here is the reasoning path behind each row. The implied probabilities come straight from the American odds: +125 implies 44.44% and −150 implies 60.00%. But those two numbers sum to 104.44%—the overround, which is the sportsbook's margin baked into the line. Dividing each implied probability by that 104.44% total produces the "no vig" probabilities of 42.55% for the Ravens and 57.45% for the Chiefs, which sum to a clean 100%. SportsBetting3 uses these no-vig figures as the win probabilities precisely because they exclude the bookmaker's vigorish and sit closer to each side's actual probability of winning.

Plugging those into the formula gives the Ravens: (0.4255 × $125) − (0.5745 × $100) = −$4.26, and the Chiefs: (0.5745 × $100) − (0.4255 × $150) = −$6.38. Both sides are negative—which is exactly what you should expect, since the vig ensures most bets carry negative EV. The lesson's takeaway: most bets will have a negative expected value, so the goal is to find wagers with EV as close to zero as possible, and any bet with genuinely positive EV is better still.

Interpreting Your EV Results: +EV, -EV, and Neutral EV

The interpretation rule is straightforward, per Smarkets: positive expected value implies profit over time, while a negative value implies a loss over time. A neutral EV of exactly zero means you break even on average across repeated wagers—neither gaining nor losing to the book.

Two qualifications keep the interpretation honest. First, these readings apply when the wager is repeated consistently; EV describes an average, not the outcome of one game. Second, the EV figure is denominated in dollars per wager, so it also tells you the size of your edge or disadvantage: the Chiefs bet in the worked example loses an average of $6.38 per $100 staked, a worse price than the Ravens' −$4.26, even though Kansas City is the favorite. Being right about a team and getting a bad price are two different problems.

Utilizing EV for Long-Term Profitability: Strategy and Variance

The strategic value of EV lies in repetition. As TheOver's formula guide puts it, not every bet will win, but consistently placing bets with a positive expected value will yield profits over time, because those wagers statistically favor you. Smarkets agrees: if you constantly find value bets, you will be a profitable bettor in the long run—while acknowledging that bookmakers build a margin into their odds and exchanges charge commission, which is precisely what turns otherwise fair prices into −EV wagers.

Variance is the reason a +EV bettor can still lose money in the short term. BettingPros' Mike Maher notes that variance is a significant factor in any probabilistic activity. He explains that a bettor with a genuine mathematical edge can still experience losing streaks of 50 or 100 bets, and for this edge to become reliable, a much larger sample, generally several hundred bets or more, is required. A single +EV bet that loses is not evidence the calculation failed; it is one draw from a distribution whose average the EV describes.

This is also why EV is a screening tool rather than a prediction tool. The calculation cannot tell you who wins tonight. It tells you whether the price you're being offered compensates you for the risk, once the vig is stripped out. Bettors who chase the biggest names or favorites without checking EV are, in the worked example's terms, paying $6.38 per $100 for the privilege.

Making Informed Decisions: Your Long-Term EV Betting Strategy

The decision framework is to consistently identify and place bets with a positive Expected Value (+EV) to achieve long-term profitability in sports betting, understanding that short-term results will vary. That means computing the no-vig probabilities for every price you consider, applying the formula, and passing on wagers with deeply negative EV even when you like the team.

The measurable indicator is to monitor your betting results over a large sample size to observe if your overall profit/loss aligns with the cumulative Expected Value of your placed bets. If your running total tracks the sum of your calculated EVs across several hundred wagers, the method is working; if it diverges persistently, the win probabilities feeding your formula—not your luck—are the first thing to re-examine.