Expected value in sports betting: the formula and its limits

Expected value, or EV, is the probability-weighted average profit or loss of a wager under a set of assumptions. It helps explain why the price matters as well as the outcome you expect.

The difficult input is the probability. Sports outcomes do not come with a known true win probability, and a convincing explanation is not a substitute for a tested estimate.

The expected-value formula

For a wager with only a win or a loss:

EV = (probability of winning × profit if it wins) − (probability of losing × stake).

Use net profit for the winning amount, not the payout that includes the returned stake. If a market can push or has other settlement outcomes, include those possibilities explicitly. A push normally contributes zero net profit under the assumed refund rule.

A simple hypothetical example

Imagine a $10 wager at +120. A win produces $12 profit; a loss costs $10. Assume, solely for this example, a 50% chance of each outcome.

EV = (0.50 × $12) − (0.50 × $10) = +$1 per wager.

If the actual win probability were 40%, the same price would give:

EV = (0.40 × $12) − (0.60 × $10) = −$1.20 per wager.

The odds did not change. The probability assumption did. A calculation can be arithmetically correct and still be unhelpful if its probability input is wrong.

Converting American odds into a break-even rate

For a simple market with no push:

• Positive odds +A: 100 ÷ (A + 100).
• Negative odds −A, using the positive magnitude A: A ÷ (A + 100).

These are price-derived thresholds. They are not forecasts. When both sides of a two-outcome market are -110, the implied percentages add to about 104.76%, illustrating the margin embedded in those quotes. Simply treating either percentage as a fair probability ignores that margin.

Hit rate, probability, and confidence are different

Historical hit rate describes what happened in a selected sample. Eight hits in ten games is 80% for those games, but the next matchup can involve different conditions.

Estimated probability is a forecast. It needs a method and validation. A model described as calibrated should have evidence that outcomes occur at frequencies consistent with its forecasts over suitable test samples.

AI confidence is not automatically either of those things. Do not interpret a confident answer, a qualitative label, or an unsupported generated percentage as a measured probability.

Statr helps explain available evidence and uncertainty. Its confidence labels should not be plugged into an EV or Kelly formula as though they were validated win probabilities. Read how Statr works.

Positive estimated EV does not guarantee profit

One outcome cannot validate a probability estimate. A losing wager may have followed a reasonable assessment, and a winning wager may have followed weak reasoning. Even a sound probability model would still face variance and changing conditions.

To evaluate a claimed edge, ask how predictions were recorded before events, which available prices were used, whether every result was included, and whether the method was tested on data outside its development sample.

Use the calculation to ask better questions

Before accepting an EV claim, identify the source of the probability, the exact price, and the settlement assumptions. If the probability is unsupported, label the EV result hypothetical.

Research a matchup in Statr, learn how to read line movement, or review budget and unit concepts.

Statr provides analysis and information, not guaranteed outcomes or bet placement. For adults 21+. Gambling support.