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?
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.
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.
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%.