      # How to calculate expected value in sports betting

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Calculating Expected Value In Sports Betting
Our last blog post covered what margins are, and how to get the best out of your bets by comparing margins between sports betting sites. This post will discuss what ‘expected value’ is, and how to calculate it.

Firstly, what is expected value?

Expected value shows bettors how much they can expect to win/or lose (on average) per bet. The expected value is simply calculated through an equation which multiplies the probability of winning, with the amount you could win per bet, and subtracts the probability of losing, multiplied by the amount lost per bet. It may sound a little confusing at the moment, but it is a lot simpler than you think. Calculating the expected value of your bets may be the most valuable or useful calculation in your arsenal.

Expected Value & Sports Betting

Secondly, how do we go about calculating expected value in sports betting? As stated in the previous paragraph, 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. The formula looks something like this:

(Probability of winning x Amount won per bet) – (Probability of losing x Amount lost per bet)

You may look at this and wonder..

‘Where do I get the information to input into the formula?’.

Before you can use the formula, you need to follow a few simple steps:

Calculate the decimal odds for each possible outcome (i.e. win or lose)
Calculate potential winnings for each outcome by multiplying your stake by the decimal (the values you calculated in the previous step), and then subtract the stake.
Divide 1 by the odds of an outcome to calculate the probability of that outcome.
After these steps, you can now input those values into the formula to calculate the expected value of your bets.

Let’s break it down
To make this easier to follow, let’s use an example and go through the steps.

Virtus.Pro are playing against Cloud9, and are paying \$1.30 to win, while Cloud9 are paying \$2.12. Here, a bet of \$10 on Virtus.Pro would have a potential winning of \$3 (\$13 in total winnings, but \$10 of your stake), while Cloud9 would be \$11.20 (\$21.20 in total winnings, but \$10 of your stake).

expected-value-example
The probabilities of these outcomes would be 61.99% (or 0.6199) for Virtus.Pro to win, and 38.01% (or 0.3801) for Cloud9 to win. To calculate these outcome probabilities, we take the sum of both odds (\$3.42) and minus the odd we are interested in (\$1.30 for Virtus.Pro, OR \$2.12 for Cloud9). We then divide that number by the total sum of odds (\$3.42) which will return the probability of that outcome.

From here, we can now calculate the expected value of this bet. Let’s say we are betting on Cloud9 to win.

(0.3801 x 11.2) – (0.6199 x 3) = \$2.40

The expected value is \$2.40. This is great news, and indicates that for every \$10 you bet, you will win an average of \$2.40.

Our last post covered bookmaker margins. Although calculating margins is helpful, calculating the expected value of your bets gives you more information about the value of the bookmaker. For more information please visit our Blog

https://sportsflare.io/calculating-expected-value/