Expected Value

In short: The average amount a bet wins or loses per dollar wagered over many repetitions. A bet has positive expected value (+EV) when the offered odds imply a lower probability than the true probability of the outcome.

Every bet has an expected value, whether the person placing it has calculated it or not. EV is the average return per dollar wagered if the same bet were placed thousands of times, sometimes winning, sometimes losing, but always with a long-run trajectory determined by the relationship between the offered odds and the true probability. Most retail bets have negative EV by design. That’s how sportsbooks make money.

The math

Expected value is calculated by weighting each possible outcome by its probability:

EV = (P_win × profit) - (P_loss × stake)

For a $100 bet on a coin flip at fair odds of +100 (even money):

EV = (0.50 × $100) - (0.50 × $100) = $0

A fair bet. Break-even over time.

But sportsbooks don’t offer fair odds. A typical NFL spread is priced at -110 on both sides. That same coin flip at -110 looks like this:

EV = (0.50 × $91) - (0.50 × $100) = -$4.50

You lose $4.50 per $100 wagered on average. Over a thousand bets, that’s $4,500 of expected loss, which is exactly the vig the book has built into the pricing. The math doesn’t care whether you win or lose any individual game. It tracks the long-run trajectory.

What -EV looks like in normal betting

Most retail bets are -EV. The 4-6% vig that retail sportsbooks bake into their lines means the average bet at a typical book is losing money in expectation, even when the bettor’s pick is reasonable.

Common -EV patterns:

• Standard -110 game lines. Every bet at -110/-110 pricing carries about 4.5% vig. A bettor who picks 50% of games correctly loses 4.5% of stakes long-term.
• Parlays. The vig compounds with each leg. A two-leg parlay at -110 each leg has effectively 9.5% vig, roughly double a single bet. Ten-leg parlays are nearly guaranteed losses.
• Player props. Retail prop markets often carry 6-10% vig because the lines are thinner and books need a wider margin. Betting props at most retail books is significantly -EV unless you’re systematically finding mispriced lines.
• Same-game parlays. Hold percentages of 15-25% are typical. Entertainment-priced, not investment-priced.

A casual bettor who hits 52% of -110 game bets is still losing money. The break-even point at -110 is 52.4%, not 50%. The gap is the vig, and the vig is the EV penalty.

What changes EV

Three things determine whether a bet’s EV is positive, negative, or zero:

The vig. Lower vig is better for the bettor. Sharp books like Pinnacle charge 2-3% vig; exchanges like Novig charge effectively zero vig (with a small commission on winnings instead). Lower vig moves the break-even point closer to 50%, making +EV easier to find.

The true probability vs. implied probability gap. When a book’s implied probability is lower than the true probability, the bet is +EV. This usually requires a fair reference (typically a sharp book’s devigged line) to estimate true probability. See no-vig odds for the standard approach.

Line shopping. The same bet at different books has different EV. A spread bet at -105 has better EV than the same bet at -110, even if everything else is identical. Line shopping, taking the best available price across multiple books, is the easiest way to move EV in your favor without changing what you’re betting on.

How EV relates to ROI

EV is the prediction you make before placing a bet. ROI is the verdict you get after hundreds of bets. They serve different functions in the same process.

If your long-run ROI is consistently negative, your EV calculations are wrong. Your true-probability estimates are off, or you’re misjudging which reference books are actually sharp, or friction is eating more than you accounted for. ROI is the feedback loop that tells you whether your EV model is calibrated to reality. No amount of theoretical EV justifies a strategy that loses money over a large sample.

The complication is that ROI takes time to stabilize. Variance means short-term ROI is noisy. 50 bets of results give you only a rough read on whether your underlying strategy is sound. A few weeks of betting can run hot or cold in ways that mislead you about the real edge.

This is where closing line value fills the gap. CLV converges faster than ROI because it doesn’t depend on whether bets won or lost, only on whether you got prices that beat the eventual closing line. If your CLV is consistently positive, your EV calculations are probably right and the ROI will follow. If your CLV is consistently negative or flat, something is off in your EV model and ROI will eventually confirm it.

The practical sequence: EV tells you which bets to place, CLV tells you within a couple of weeks whether your EV model is working, and ROI confirms within a few months whether the whole strategy is profitable.

What this means in practice

For most bettors, the practical implication is: assume your bets are -EV unless you have a specific reason to believe otherwise. Casual bets on favorites you like, parlays for entertainment, or game lines without comparison to a sharp reference are all losing money in expectation. There’s nothing wrong with this if betting is entertainment, but it’s worth knowing the math you’re up against.

For bettors trying to be profitable, finding +EV bets is the entire game. See Positive EV (+EV) for the workflow of identifying and acting on +EV opportunities, and +EV Betting Explained for a deeper treatment of the strategy.