Calculating the Expected Value of Sports Bets

If you want to up your betting strategy game, you need to be thinking about the Expected Value of any wager that you place. A bet’s Expected Value (EV) is how great the expected winnings are, on average, per punt. In other words, if you placed the bet with same odds several times over, how much could you expect to win or lose? Knowing this will help you to make better decisions, and it’s quite simple to work out.

Formula to Determine EV

The equation for calculating the Expected Value involves determining the value of your probability of winning multiplied by the amount that you could win per bet, and the probability of losing multiplied by what you would lose on each bet. The latter figure is then subtracted from the former, and this is the wager’s Expected Value.

The Expected Value formula can be written as:

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

For example, if you bet $10 on a coin toss and were to get $11 if you won, the equation would be:

(0.5 x 11) – (0.5 x 10) = 0.5

This means that in this wager, you could expect to win $0.5 for every $10 that you put down.

That’s great for a coin toss, and it explains the principle of Expected Value, but what if you are sportsbetting? It’s easy to adapt the Expected Value to decimal odds, and use it when you’re deciding what sports wagers to place.

To determine the EV in a decimal odds sports bet, you need to make a few other calculations and then substitute them into the general formula. Find the potential winnings of a wager by multiplying the stake by the decimal, and then subtracting the stake. To find its probability, look at the odds given by any bookmaker you’re given and convert them to decimals if need be. Once you have these decimal odds, divide 1 by these odds to find the outcome’s probability.

If you’re betting on a game between Manchester United and Wigan, for example, you might be given odds like these at the bookie where you’re considering putting money down: a 1.263 chance of Man U winning; a 13.500 chance of Wigan winning and a 6.500 chance of a draw. The decimal odds of a Wigan victory are 13.5, so the probability is 1/13.5 = 0.075 or 7.4%. The potential winnings of a $10 are (10 x 13.5) – 10 = $125.

The probability of you losing this bet is the sum of the probability of Manchester United winning and the teams drawing. This is (1/0.1263) = 7.92 or 0.792 + (1/0.65) = 1.54 or 0.154, which comes to 0.946. The amount that you stand to lose is how much you were betting in the first place, which is $10 in this case. Now you have all the information you need, and the specific calculation looks like this:

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

This means that in the case of this wager, you’ll lose an average of $0.2 for every $10 that you put down. If these are the odds that your bookie has given you, it means these are the odds they expect you to lose by.

How to Use the Calculated EV

You can compare the EV at different sportsbooks to find the one that has the most favourable payouts for you, but you can also use the EV to outsmart a betting shop. Odds on sports results matches, unlike coin tosses, are subjective; if you know something that makes you calculate your own probability of a Wigan win as much higher than the implied odds, you could make a tidy profit.

It’s no wonder the Expected Value is considered the most valuable calculation in comparing bookmaker odds, and now you know how to use it. You’re sure to find out how indispensable this tool is as soon as you start applying it yourself.