# 'Expected value' and how to calclulate it in sports betting

Nov 13, 2013 |
Have you ever incorporated 'expected value' into your daily handicapping? Maybe you should. Jack Ratcliffe from Pinnacle Sports explains what it is in this article and how to calculate it.

The Expected Value of a bet tells us how much we can expect to win (on average) per bet, and as such is the most valuable calulcation a bettor can make when, for example comparing bookmakers. So how do you calculate EV – and how does it affect sports betting?
“Expected value” – or EV – is the amount a player can expect to win or lose if they were to place a bet on the same odds many times over. For example, if you were to bet \$10 on heads in a coin toss, and you were to receive \$11 every time you got it right, the EV would be 0.5.

This means that if you were to make the same bet on heads over and over again, you can expect to win an average of \$0.50 for each bet of \$10.

How to Calculate Expected Value

The formula for calculating Expected Value is relatively easy – 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:

(Probability of Wining) x (Amount Won per Bet) – (Probability of Losing) x (Amount Lost per Bet)

To calculate the expected value for sports betting, you can fill in the above formula with decimals odds with a few calculations:

1. Find the decimal odds for each outcome (win, lose, draw)
2. Calculate the potential winnings for each outcome by multiplying your stake by the decimal, and then subtract the stake.
3. Divide 1 by the odds of an outcome to calculate the probability of that outcome
4. Substitute this information into the above formula.

For example, when Manchester United (1.263) play Wigan (13.500), with a draw at 6.500, a bet of \$10 on Wigan to win would provide potential winnings of \$125, with the probability of that happening at 0.074 or 7.4%.

The probability of this outcome not occurring is the sum of Man Utd and a draw, or 0.792 + 0.154 = 0.946. The amount lost per bet is the initial wager – \$10. Therefore the complete formula looks like:

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

The EV is negative for this bet, suggesting that you will lose an average of \$0.20 for every \$10 staked.

How Does Expected Value for Sports Betting Help?

Remember, a negative EV doesn’t mean you’re going to lose money. Unlike a coin toss, sports betting odds are subjective, and therefore if you outsmart the bookmaker, you’re likely to make money.

If you calculate your own probability for a match that differs from the implied probability of the odds, you could see where to find a positive EV, and therefore the best chance to win.

For example, the odds imply that Wigan only have a 7.4% chance of winning. If you calculate (maybe using a system like Poisson Distribution) that Wigan has a 10% chance of winning, the EV for betting on a Wigan win jumps to \$3.262.

It’s also a perfect measure for comparing odds in arbitrage betting, which is discussed in more detail here.

Calculating the EV of bets gives bettors more information about the value of their bookmaker. While low-margin bookmakers like Pinnacle Sports have EVs of around -\$0.20, it’s not uncommon for typical bookmakers to have an EV of -\$1.00 – for every \$10 stake you would be likely to lose a \$1 .

*Odds subject to change
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