Many experienced bettors use the concept of expected value to identify profitable betting opportunities. The expected value of a bet refers to the amount that you would expect to win or lose on this bet, on average, if you were able to place the same bet a large number of times. Expected value can be positive, negative, or zero.
Let's consider an example - say a $100 even money wager on the flip of a coin. We all know there is a 50% chance of a coin landing heads, and a 50% chance of tails. If we were to repeat this same bet over and over, we'd expect to win around half the bets, and lose the other half.
Expected Value = (Probability of Win) x (Bet Payout) - Amount Wagered
In the case of our coin flip, EV = 50% * $200 - $100 = $0. We would say that the expected value of this bet is zero.
Bettors are looking for betting opportunities with positive expected value. Consistently placing positive expected value bets should result in a growing bankroll, in the long run.
Let's now consider the same coin flip example, except that we now bet $100 to be paid $300 when the coin lands heads. Our expected value for a single coin flip is EV = 50% * $300 - $100 = $50. On average, for every bet placed, we expect to win $50.
When bets are independent (they do not depend on each other), you can add the expected values together to get the total expected value. So, for a series of nine coin flip bets at the same odds, we expect to win 9 * $50 = $450.
Does this mean that we are sure to be making money after 9 bets? Since we understand how coin flips work, we can calculate the probability of each outcome.
We see that even though we have positive expected value, we still lose money 9% of the time.
Also note that despite our expected value being $450, there is no way we can profit exactly $450 - the two most likely outcomes are profiting $300 or $600.
This is not a problem - expected value is an average - there is no reason why we need to be able to achieve exactly the expected value.
Coin flips are easy because we understand how a coin works - there is a 50% chance of the coin landing on each side. How do we apply this to sports betting?
Bettors can build mathematical models, or apply their intuition, to determine what chance a team has of winning a bet. If a bettor figures that a team has a 70% chance to win a bet, and he is being offered decimal odds of 1.50, he can calculate his expected value on a $100 bet:
EV = 70% * (1.50 * $100) - $100 = +$5
The bet has positive expected value, so it is worthwhile to place this bet if the bettor is confident in his evaluation of this team's strength.
Expected value can also be used to determine which bet out of a series of bets is the best pick. Going with the highest expected value bet will grow you the largest bankroll, in the long run.
Consistently finding positive expected value betting opportunities is the best that you can do as a bettor - from that point you just have to hope that luck is on your side. To quickly calculate the expected value of a bet you are considering, you can use an expected value calculator.