Expected Value in Sports Bets

The Expected Value is defined as the average amount of winnings on a bet. If you place the same bet at the same odds, over and over again, how much can you expect to win or lose? Clearly, knowing the answer to this question can help you to make better betting decisions, and you can find out how to do it here.

Basic Expected Value Formula

To calculate the Expected Value, or EV, you need to multiply your winning probability by your possible win’s amount first. Then multiply your losing probability by the amount you could lose, and subtract the second answer from the first. In other words, the formula is:

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

As a practical example, imagine you bet $10 on a coin toss similar to the one you’ll see at the Super Bowl. If you win you’ll get $11 returned to you and if you lose you’ll forfeit $10. Since it’s a coin toss the winning and losing probabilities are both 0.5. Let’s input those numbers:

(0.5 x 11) – (0.5 x 10)

That gives us 5.5 – 5, which means you can expect, on average, to win $0.5 for every $10 you wager.

More Complex Calculations

When you have more complicated sports betting sites in NZ as well as odds, determining the EV is still relatively easy to determine. For example, if Manchester United and Leeds United were clashing in the latest episode of their famous Roses Rivalry, The Red Devils could have a 1.263 chance of winning, while The Whites might have a 13.50 chance and the odds of a draw could be set at 6.50.

The winning probability is 1 divided by the odds, converted to decimal format if needs be. Potential winnings are determined by multiplying your stake by the odds, also easiest in decimal format, and then subtracting your punt. If you back Leeds, the probability is 1/13.5, or 7.4% and the potential winnings on $10 are (10 x 13.5) – 10 which is $125.

The probability of you losing when you bet on Leeds is the sum of the probabilities of the teams drawing plus the probability of Man U winning. Find the probabilities with the same method used above, dividing 1 by the decimal odds for both outcomes. That gives us a losing probability of 0.946, as shown below:

1/6.5 + 1/1.263 = 0.154 + 0.792 = 0.946

The amount that you could lose is your original stake, which is $10 in our example. Now, with all of these figures, you have the information you need to use the EV formula:

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

On average, you’ll lose $0.2 per every $10 that you spend.

Applying Expected Value

Once you’ve got the EV, you can find the bookmaker odds that are most favourable to you. You can also use it to find and take advantage of value bets. If the bookmaker’s EV is -$0.2 but you have inside information and you know Leeds is much likelier to win, you can place that bet and make quite a killing!