Expected Value: What It Means in Betting
Expected value (EV) is the mathematical foundation of all profitable betting. It represents the average amount a bettor stands to win or lose per bet if the same wager were placed an infinite number of times. Understanding EV is essential for anyone who wants to approach betting analytically rather than relying on gut feeling.
The EV Formula
The expected value of a bet is calculated using a simple formula:
EV = (Probability of winning x Net profit) - (Probability of losing x Stake)
Alternatively, for decimal odds:
EV = (True probability x Decimal odds x Stake) - Stake
The result tells you how much you can expect to gain or lose, on average, for each bet placed at those odds.
A Worked Example
Suppose Manchester City are playing Fulham, and a bookmaker offers 1.80 on a City win. You estimate that City have a 62% chance of winning.
Using a 10 pound stake:
- Profit if you win: 10 x 1.80 - 10 = 8 pounds
- EV = (0.62 x 8) - (0.38 x 10)
- EV = 4.96 - 3.80
- EV = +1.16
This means that, on average, each 10 pound bet on City at these odds is expected to return 1.16 pounds in profit. Over 100 similar bets, you would expect roughly 116 pounds in profit, assuming your probability estimate is accurate.
Positive EV vs Negative EV
A positive EV (+EV) bet is one where the odds offered are generous relative to the true probability. These are value bets. Over time, placing +EV bets consistently leads to profit.
A negative EV (-EV) bet is one where the odds are not generous enough. The bookmaker's price implies a higher probability than the true one, or alternatively, the bookmaker's margin eats into your expected return. The vast majority of bets available at any bookmaker carry a slight negative EV, because the overround ensures the bookmaker profits regardless of the outcome.
For example, in a coin toss, fair odds would be 2.00 on each side. But a bookmaker might offer 1.91 on both heads and tails. At true odds of 50%, the EV of a 10 pound bet at 1.91 is:
- EV = (0.50 x 9.10) - (0.50 x 10) = 4.55 - 5.00 = -0.45
Every 10 pound bet loses 45 pence on average. That is the bookmaker's edge.
Why EV-Positive Betting Is the Goal
The single most important principle in analytical betting is to place bets only when the expected value is positive. This does not mean every bet will win. It means that, across a large enough sample, the total winnings will exceed the total losses.
This requires two things:
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Accurate probability estimation. If your probability estimates are wrong, your EV calculations will be wrong. A bet you believe is +EV might actually be -EV if you have overestimated the chance of success.
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Discipline to bet only when value exists. Many bettors place wagers because they have an opinion on a match, regardless of whether the odds represent value. EV-focused bettors only act when the numbers justify it.
EV and Sample Size
Expected value is a long-term concept. In the short term, anything can happen. A +EV bet can lose, and a -EV bet can win. Over 10 bets, results might look random. Over 1,000 bets, the results tend to converge towards the expected value.
This is why professional bettors think in terms of processes rather than individual outcomes. A losing week does not invalidate a +EV approach, just as a winning week does not validate a -EV one.
The Relationship Between EV and Other Metrics
EV connects directly to other key concepts. Value betting is simply the practice of finding +EV opportunities. Yield measures the actual percentage return on stakes, which over time should approximate the average EV of your bets. Closing line value provides an independent check on whether your bets are likely to be +EV.
Past performance does not guarantee future results. Expected value is a theoretical measure that depends on the accuracy of your probability estimates.
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