Expected Value and Expected Return

+EV Sports Bettor

I’m sure you’ve seen that one in a Twitter profile before. People love to tout the fact that they generate positive expected value (+EV) from sports betting. But what does this mean and how is it calculated?

Expected Value

To calculate the expected value, or EV, of a single bet, all you need is three inputs:

1)     Payoff of a win (Pw)

2)     Payoff of a loss (PL)

3)     Probability of winning (p)

I’m the type of learner than needs numeric examples to make sense of any formulas. So let’s start with a simple example.

Example:

You’ve had your eye on this game since the NFL schedule came out:

Your model really likes Raiders offense and you feel that the market is underrating the Colts offense as well. As a result, you think there is a 55.0% chance that the point total goes over 45.5. You can estimate the required inputs as follows:

1)     Payoff of a win (Pw): \$100

2)     Payoff of a loss (PL): -\$110

3)     Probability of winning (p): 55.0%

And you compute:

\$5.50 is your Expected Value represented in nominal dollars.

Expected Return

The expected return is a calculation of the profitability of a wager measured as a percentage. To determine your Expected Return, or E(R), you simply divide your Expected Value of \$5.50 by the size of your wager, which is \$110.

E(R) = EV / Wager Size is:  5.0% = \$5.50 / \$110

Therefore, your expected return for this single bet is 5.0%.

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