How to Calculate Expected Value in Sports Betting

Expected value (EV) answers one specific question: if you made the same bet an enormous number of times, what would your average result be per dollar wagered? It says nothing about what happens on any single bet. That distinction matters more than the formula itself, so it's worth sitting with before we get into the numbers.

Step one: convert odds into implied probability

American odds don't display probability directly, but they encode it. The conversion depends on whether the odds are positive or negative.

For negative odds (the favorite, e.g. -150):

implied probability = |odds| / (|odds| + 100)

For positive odds (the underdog, e.g. +130):

implied probability = 100 / (odds + 100)

A line of -150 implies a 60% chance of winning. A line of +130 implies roughly a 43.5% chance. Add both sides of almost any two-outcome market together and you'll find the total exceeds 100% — that gap is the bookmaker's built-in margin, sometimes called the vig or juice. We cover that in more detail in our piece on the vig.

Step two: compare implied probability to your own estimate

Implied probability tells you what the market thinks. Expected value only exists once you have a second, independent estimate to compare it against — from a model, historical data, or careful reasoning about matchup-specific factors. Without that second number, there's nothing to calculate; you're just reading the market back to itself.

Step three: run the EV formula

Once you have a model probability, the formula is:

EV = (model probability × net profit if win) − (loss probability × stake)

Worked example: odds of -110 (a very common line), stake of $100, and a model probability of 55%.

• Implied probability: 110 / 210 ≈ 52.4%
• Payout multiplier: 100/110 + 1 ≈ 1.909, so net profit on a win is $90.91
• EV = (0.55 × 90.91) − (0.45 × 100) = 50.00 − 45.00 = +$5.00, or +5% relative to stake

That +5% is the number our interactive terminal surfaces as the "anomaly margin" on each row — it's this exact calculation, not a subjective rating.

What a positive EV number does and doesn't tell you

A positive EV means that if your model probability is accurate, the bet is priced in your favor on average, over a large sample. It does not mean:

• This specific bet will win. Individual outcomes are still governed by variance, and a 55% probability still loses 45% of the time.
• Your model probability is correct. EV calculations are only as good as the input — a confidently wrong estimate produces a confidently wrong EV number.
• Any single result validates or invalidates the approach. Meaningful signal from a betting model typically requires hundreds of graded bets, not a handful of them.

The honest takeaway

EV is a tool for organizing your thinking under uncertainty, not a prediction engine. Treat every number here as a statistical estimate — because that's exactly what it is.