Expected value is the difference between the true odds of an event happening and the sportsbooks' posted odds.

Let's start with a simple example.

The true odds of a coin toss are 50/50 (+100). Half of the time, the coin will land on heads. Half of the time, the coin will land on tails.

If an oddsmaker prices tails at +120 odds (more favorable than +100 odds), then betting on tails has a positive expected value.

Here’s how it works:

• If you bet $100 on tails at +120 odds and win, you would receive $120 in profit.

• Since the true probability of the coin landing on tails is 50%, you expect to win this bet 50% of the time.

The expected value (EV) of the bet is calculated as follows:

EV = (Probability of Winning) x (Amount Won) - (Probability of Losing) x (Amount Lost)

Substituting the values:

• Probability of winning: 50% or 0.5

• Amount won: $120

• Probability of losing: 50% or 0.5

• Amount lost: $100

So,

EV = 0.5 x $120 - 0.5 x $100

EV = $60 - $50

EV = $10

The expected value of this bet is $10. Therefore, this would be a 10% positive expected value opportunity, as $10 is 10% of your $100 bet.

Positive expected value (+EV) betting helps bettors make more informed decisions about the bets to take and how to manage their bankrolls effectively.

Betting on events with positive expected value doesn't guarantee immediate success, but it increases the likelihood of turning a profit over a substantial number of bets.

Consider our coin toss example again. If the oddsmaker is willing to pay $120 every time the coin lands on tails, and we know that the true odds of the coin landing on tails is 50%, then, even if the coin lands on heads the first two, three, or fifteen tosses, we can can still expect that over the long run (twenty-five, fifty, one thousand tosses), we will win an average of $10 per toss.

As described above, expected value is the difference between the true odds of an event happening and the sportsbooks' posted odds. So, in theory, identifying positive expected value bets is as simple as finding sportsbook odds that are more favorable to the bettor than the true odds.

But, determining the true odds of an event and removing the "vig" from the sportsbooks odds to determine their expectations about an event happening is not so simple. This is even further complicated when calculating expected values of multi-leg parlays.

Fortunately, Outlier has done the work for you.

To read more about how we arrive at the true odds of an event and how we "devig" sportsbooks' odds, see How to Devig Odds - Comparing Four Methods.

Understanding how sportsbooks set odds is crucial for any bettor aiming for long-term profitability.

Read the full article here: https://help.outlier.bet/en/articles/9922960-how-sportsbooks-set-odds-soft-vs-sharp-books

By understanding what expected value is, the long-term nature of positive expected value betting, and the methods of finding positive expected value bets, you can be more confident and patient placing bets based solely on the difference between the true odds and the sportsbooks' posted odds.

Have questions? Join the Outlier Pro channel in our Discord for help!