# 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

£10 | SIGN UP HERE | |

New Players Only. Minimum stake $/£/€10, at minimum odds 1.5. 10X wagering the winnings from the free bet. funds. Free bet is valid for 30 Days from issue. Excluded Skrill deposits. Full Terms Apply |
||

£30 | SIGN UP HERE | |

New UK players only Valid for 14 days after registration / any sport with 3 selections / deposit and min. 4/5 (1.8) odds per selection / minimum stake £5 maximum £30 / T&C apply/ +18 / begambleaware.org |
||

£10 | SIGN UP HERE | |

New Players Only. Minimum stake $/£/€ 10, minimum odds 1.5, stake not returned. 10X wagering the winnings from the free bet. Free bet is valid for 7 days from issue. Excluded Skrill deposits. Full Terms apply. |
||

£10 | SIGN UP HERE | |

18+, New Players only, 1st Deposit, Min Deposit £10, max, valid for 14 days, bets must be placed at odds of 1/1 or greater and be settled within 14 days of placement. System bets no eligible |
||

£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 |
||

£100 | SIGN UP HERE | |

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

£15 | SIGN UP HERE | |

New customers only.£10 Minimum Deposit at 2.0 (1/1) (no Skrill, Neteller & Paysafe). Expires after 14 days. T&Cs apply |
||

£10 | SIGN UP HERE | |

New Customer Offer Only | Max FreeBet Amount £10 | Min Deposit £10 | Odds Over 2.0 | Expiry Date 14 Days | Sports Betting Bonus Only | 18+ | T&Cs Apply |
||

£50 | SIGN UP HERE | |

New players 18+ only. valid 31/12/2019 - 10x wagering req. on accumulator bets of a min. 3 selections, min odds of 1/5(1.20), and min. selections total odds 1/1 (2.00) (within 30 days). T&Cs apply. BeGambleAware.org |
||

£100 | SIGN UP HERE | |

New customers only. Min Deposit £10 (UK Credit/Debit cards only). Deposit & bonus amount must be wagered 6 times (min odds 1.80 (4/5)). Bonus on sports betting only | T&Cs apply |