Sportsbetting strategy: how to calculate Expected Value (EV)

The Expected Value of a bet tells us how much we can expect to win (on average) per bet, and as such is the most valuable calulcation a bettor can make when, for example comparing bookmakers. In this article, we will explore its use in Sportsbetting. EV is a concept that every gambler should know and deeply understand since a good handicapper can also have an edge over the house.

What is Expected Value 

The concept of expected value (EV) is precisely used to evaluate which option you should choose to maximize gains and minimize losses. It excludes variables like fun or personal satisfaction. Expected Value (EV) is essentially a positive (+EV) or negative (-EV) indicator that should guide you in making the best decision. EV allows us to estimate what bets are profitable and which ones are not.

How to Calculate Expected Value 

The formula for calculating Expected Value is relatively easy. Multiply your probability of winning by the amount you could win per bet, and subtract the probability of losing multiplied by the amount you stand to lose per bet:

Expected value (EV) = wager + (expected win – expected loss)

For example, 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.

Sportsbetting Expected Value (EV)

Expected value in sports betting involves the same sort of calculations: you know the house edge but don’t know your real odds of winning and losing. This is where knowledge and experience come into play. You have to estimate them adequately. If you manage to do this, you can improve your chance to be profitful in the long period.

Say that in the World Cup, team X is playing team Y. The odds for team X is 4/1 (4.0 in decimal, +300 in american). But you estimate that team X will win 40% of the time. Your expected value (EV) in betting on team X would be positive.

Expected value (EV) = wager + (expected win – expected loss)

In this scenario, it would look like this:

Expected value (EV) = 1 + ((0.4 x 4) – (0.6 x 1)) => 1.9

This means that betting on team A in such a game would be extremely favourable as you would turn 1£ into 1.9£ on average.

Another way to calculate EV is the following:

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 Real Madrid (1.263) play Espanyol (13.500), with a draw at 6.500, a bet of £10 on Espanyol 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 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, suggesting that you will lose an average of £0.20 for every $10 staked.

But if you calculate your own probability and this probability 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 Espanyol only have a 7.4% chance of winning. If you calculate (maybe using a system like Poisson Distribution) that Espanyol has a 10% chance of winning, the EV for betting on a Espanyol win jumps to £3.262.

Conclusion

Understanding and calculating expected value should be something that every gambler uses during his pre-wager analysis.