Expected Value Explained

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

When your faced with different book maker odds, you need to be able to calculate how much you could expect to win on average per bet.

Expected Value

This is the amount a player can expect to win or lose if they were to place a bet on the same odds many times over. It’s calculated through a simple equation. By multiplying your probability of winning with the amount you could win per bet. And then subtracting the probability of losing multiplied by the amount lost per bet.

An example: If you were to bet £10 on heads in a coin toss. And you’d receive £11 each time you were correct. Then the EV would be 0.5. essentially you can expect to win an average of £0.50 for each bet of £10.

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: 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 simply fill in the above formula with decimals odds with these calculations:

Find the decimal odds for each outcome (win, lose, draw)
Calculate the potential winnings for each outcome by multiplying your stake by the decimal, and then subtract the stake.
Divide 1 by the odds of an outcome to calculate the probability of that outcome

A Football Example

For example, when Real Madrid (1.263) play Celta de Vigo (13.500), with a draw at 6.500. So a bet of $10 on Celta to win would provide potential winnings of $125. The probability of that happening at 0.074 or 7.4%.

The probability of this outcome not occurring is the sum of Real Madrid 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. It suggest 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. Keep in mind that sports betting odds are subjective. Therefore if you manage to outsmart the bookmaker, then you’re going to make money.

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

Back to our example, the odds imply that Celta de Vigo only have a 7.4% chance of winning. If you think that Celta has a 10% chance of winning, then the EV for betting on a Celta win jumps to $3.262.