# How to Calculate Expected Value

A term used in probability theory and statistics, Expected Value is considered a useful tool in betting as well which can help you measure whether a certain selection is potentially profitable.

The Expected Value is also known as a mathematical expectation as it represents the average number of results of an experiment in the long-run.

When it comes to betting, the Expected Value will determine the relative value of a two-fold choice, weighing up the two options to determine the amount a bettor can expect to win or lose in a given bet.

Naturally, a positive Expected Value indicates a profitable bet as it will yield winnings for every pound invested. An Expected Value of +£1 will theoretically have you winning £1 for every £1 wagered.

Calculating Expected Value

Expected Value is determined through a relatively simple and straightforward formula. All you need to do is to multiply the probability of winning by the amount you can win per bet, and subtract the probability to lose multiplied by the amount you would lose per one bet.

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

Calculating the Expected Value in sport betting is done using a different calculation that will allow you to have all the necessary input. First you need to find the decimal odds for each of the three outcomes – win, draw, lose.

Before we calculate the Expected Value the potential winnings for each of the three outcomes need to be determined which is done by multiplying the stake by the decimal, and then subtracting the stake.

The probability of an outcome is determined when you divide 1 by the odds and here is an example to illustrate it even better.

If we take a game between Arsenal against Leicester City with the Gunners priced at 2.76 and the Foxes standing at 2.78 and a draw at 3.40 the implied probability on Arsenal would reach 36.23%, on draw 29.41% and on Leicester 35.97%.

The winning amount on the bet is: 2.78 x 50 – 50 = £89, whereas the winning probability is 1 / 2.78 = 0.36. The other side of the calculus is £50 as the losing amount at 0.66 in losing probability.

Ultimately, the Expected Value on Leicester winning a £50 bet is calculated like this using the aforementioned formula:

`(89 x 0.36) – (50 x 0.66) = -0.6`

In this particular case, the Expected Value is negative which suggest that there is an average of 60p lost on every £50 stake you make.

Negative Expected Value does not necessarily mean you are going to lose money, however, sports betting is subjective matter and your aim is to beat the betting operator in order to have any chance of winning.

Finding the Expected Value that goes closer to the positive amount is hard, but given the fact that most of the bookmakers will usually tend to lean towards -£1, anything better than that is considered an Expected Value you can work with.