Get to grips with a basic Expected Value formula

Learn how to work out whether you should make a bet or not

Expected Value

The amount a player can expect to win or lose if they were to place a bet on the same odds many times over, calculated through a simple equation multiplying your probability of winning with the amount you could win per bet, and subtracting the probability of losing multiplied by the amount lost per bet.

A simple example of Expected Value (EV) put into practice - if you were to bet 10€ on heads in a coin toss, and you were to receive 11€ every time you got it right, the EV would be 0.5.

This means that if you were to make the same bet on heads over and over again, you can expect to win an average of 0.50€ for each bet of 10€.

How to Calculate Expected Value ?

The formula for calculating Expected Value is relatively easy – simply multiply your probability of winning with the amount you could win per bet, and subtract the probability of losing multiplied by the amount lost per bet:

(Probability of Winning) x (Amount Won per Bet) – (Probability of Losing) x (Amount Lost per Bet)

To calculate the expected value for sports betting, you can fill in the above formula with decimals odds with a few calculations:

1. Find the decimal odds for each outcome (win, lose, draw)
2. Calculate the potential winnings for each outcome by multiplying your stake by the decimal, and then subtract the stake.
3. Divide 1 by the odds of an outcome to calculate the probability of that outcome
4. Substitute this information into the above formula.

For example, when Manchester City (1.263) play Everton (13.500), with a draw at 6.500, a bet of 10€ on Everton to win would provide potential winnings of 125€, with the probability of that happening at 0.074 or 7.4%.

The probability of this outcome not occurring is the sum of Manchester City and a draw, or 0.792 + 0.154 = 0.946. The amount lost per bet is the initial wager – 10€. Therefore the complete formula looks like:

(0.074 x $125) – (0.946 x $10) = - 0.20 €

The EV is negative for this bet, suggesting that you will lose an average of 0.20€ for every 10€ staked.

How Does Expected Value for Sports Betting Help ?

Remember, a negative EV doesn’t mean you’re going to lose money. Unlike a coin toss, sports betting odds are subjective, and therefore if you outsmart the bookmaker, you’re likely to make money.

If you calculate your own probability for a match that differs from the implied probability of the odds, you could see where to find a positive EV, and therefore the best chance to win.

For example, the odds imply that Wigan only have a 7.4% chance of winning. If you calculate (maybe using a system like Poisson distribution) that Wigan has a 10% chance of winning, the EV for betting on a Wigan win jumps to 3.262€.

It’s also a perfect measure for comparing odds in arbitrage betting, which is discussed in our article 

What is arbitrage betting

Calculating the EV of bets gives bettors more information about the value of their bookmaker. While low-margin bookmakers like Pinnacle have EVs of around -0.20€, it’s not uncommon for typical bookmakers to have an EV of -1€ – for every $10 stake you would be likely to lose a 1€ .