Signal Labs / Tools / Expected Value Calculator

Expected Value Calculator

Enter your estimated win probability, the offered odds, and stake. The calculator returns expected value in dollars, expected value percent, and break-even probability.

Enter inputs to see expected value.

How the math works

Expected value is the single most important concept in sports betting and the one most commonly hand-waved. It is the average outcome of a bet repeated under identical conditions an infinite number of times. A positive expected value means the bet, on average, gains money. A negative expected value means it loses. Any individual bet can still win or lose — variance is enormous in a small sample — but over hundreds and thousands of wagers, expected value is the gravity that pulls a bankroll up or down.

The calculation is simple. The probability of winning is multiplied by the profit from winning, and the probability of losing is multiplied by the amount lost. The two are summed. At a price of plus-100 with a 55 percent win rate, a hundred-dollar bet has an expected value of plus ten dollars — fifty-five percent of the time it wins a hundred, forty-five percent of the time it loses a hundred, and the difference is ten dollars per bet on average. At minus-110 with the same 55 percent win rate, expected value drops to plus four dollars and ninety-one cents because the price is worse. At minus-150 with that same 55 percent win rate, expected value flips negative.

The honest test of any betting strategy is whether the expected value calculation is positive after vig, and whether the win probability used in that calculation is well-calibrated. Plenty of bettors compute glowing expected values using probability estimates that are too optimistic, then attribute the inevitable losses to bad luck. The calculator above does not check the probability estimate — it cannot — but it does show two numbers that make calibration easier to see. The first is the break-even probability, which is the win rate the price alone implies. The second is the edge in percentage points over that break-even. A bettor claiming a five-point edge bet after bet over a long sample is making a strong claim. If the actual results do not match, the probability inputs are the part to revisit.

Expected value is also the variable Kelly sizing is built on. The Kelly fraction is essentially expected value per dollar staked divided by the net decimal odds. Knowing the expected value of a bet is the prerequisite to sizing it correctly, and the prerequisite to deciding whether to take it at all.

FAQ

What does +EV mean?
Positive expected value. The average outcome of the bet, repeated many times under identical conditions, is a profit. A single +EV bet can still lose, but a portfolio of +EV bets grows the bankroll over time.
How is expected value calculated?
Win probability times profit on a win, minus loss probability times the stake. The result is the average dollar gain per bet at that stake size.
What is break-even probability?
The win rate a price requires to be neutral. It is one divided by the decimal odds. A win probability above the break-even is +EV; below it is -EV.

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