**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 calculation 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.

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.

http://www.pinnaclesports.com/online-betting-articles/09-2012/expected-value.aspx

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