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.

Best 10 New Bookmakers

£50 SIGN UP HERE

New players only. 100% up to £50 sports bonus. Rollover: 17x deposit & bonus at minimum odds 2.00 within 365 days. If bonus is cancelled, bonus funds will be lost. Full terms apply. 18+, begambleaware.org

£100 SIGN UP HERE

New UK customers only; 6x wagering of deposit and bonus with 90 day expiry; Only sports bets contribute to wagering; Min 2 selections at 1.4 min odds per selection; Max £100 per bet; See full terms; 18+.

£10 SIGN UP HERE

New players only. Mini Deposit £10, odds 1.5, stake not returned. 10X wagering the winnings from the free bet. Valid for 30 Days. Max conversion: £20. Excluded Skrill deposits.

£10 SIGN UP HERE

18+, New Players only, 1st deposit, Min Deposit: £10, max £10 free bet valid for 14 days, bets must be placed at odds of 1/1 or greater. Full Terms Apply

£15 SIGN UP HERE

18+, New Players only, 1st deposit, Min Deposit: £10, max £10 free bet valid for 14 days, bets must be placed at odds of 1/1 or greater. Full Terms Apply

£10 SIGN UP HERE

Opt-in required. Minimum £/$/€25 qualifying bets, on select events only. No cash-outs allowed. Free Bet & General full terms apply. Excludes Skrill deposits.

£31 SIGN UP HERE

Deposit and bet on any Sportsbook Markets of your choice at odds of Evens (2.00) or greater. Get 50% Back of your first days losses as a Free Bet up to £25 + a Guaranteed £5 Free Bet Either Way plus 10 Free Spins! 18+

£10 SIGN UP HERE

T&C’s Apply. New Customers only. Visa/Mastercard deposits. Min Deposit £10. Max one £10 free bet. Odds of 1.8 or greater. Free Bet given once qualifying bet has been settles. Valid 7 Days from Issue. 18+

£100 SIGN UP HERE

Opt in. Min. Odds Evs, Max. £10 stake, Max. additional profit £100. Skrill and Neteller deposits are not eligible

£200 SIGN UP HERE

New customers only. Min deposit £20. Wager 10 times at odds of 1.65 (3/5)or bigger. Expires after 5 days (no Skrill, Neteller & Paysafe). T&Cs apply