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Expected Value

What is Expected Value?

Here at EV Analytics, we’re all about finding Positive Expected Value. It’s in the name. But what does Expected Value (EV) mean? And how do we find Positive EV when the betting sites we play at are expected to win? Essentially, it boils down to the expected return for any wager that you might place.

EV at Its Core

A simple example can be described with a coin flip. If you were to bet $10 on the outcome of a simple, fair coin flip and you were given $11 if you got it right and lost your $10 if you got it wrong, your expected value would be $.50.

You can calculate this with the formula:

(Probability of Winning x Amount Won per Bet) – (Probability of Losing x Amount Lost per Bet)

In our example, the probability of guessing right would be 50%, the amount won would be $11, the probability of losing would be 50%, and amount lost would be $10. To do the math, we can simply express the probabilities as decimals and plug them in:

(.50 x $11.00) – (.50 x $10.00) = $5.50 – $5.00 = $.50

EV in Sports Betting

With sports betting, the probabilities of winning aren’t usually going to be as simple as a coin flip. Bets aren’t going to be 50/50 propositions. And they aren’t going to be fair: you have to account for the vigorish, commonly referred to as vig, which is the amount the house takes on the bet.

What we are going to do first is learn to read the lines and find the breakeven points for each side of the bet. Take, for example, a game between the Nationals and the Phillies. Let’s say, the Nationals are favored to win the game at -115 (odds listed are in the American format) and the Phillies are the underdog at +105.

The way to read this is that you have to bet $115 to win $100 for the Nationals but if you bet $100 on the Phillies, you’d win $105. So, what are the breakeven points?

These points can be calculated by dividing the amount you bet by the total amount returned to you if you win (your bet plus the amount you win):

Amount Wagered / Total Amount Returned

This formula will return a decimal which can be multiplied by 100 to make a percentage. For our baseball example, let’s keep our bets fixed to the whole number amounts for the sake of simplicity.

Nationals:

$115 / $215 = 0.535 or 53.5%

Phillies:

$100 / $205 = 0.488 or 48.8%

 

What you might notice first is that our percentages don’t add up to 100. This is the mathematical representation of the vig. You can use the EV formula from the first section to find the expected return for these bets at the breakeven points which gives up the amount lost to vig on each side of the bet:

Nationals:

(.535 x $100) – (.488 x $115) = $53.5 – $56.12 = -$2.62

Phillies:

(.488 x $105) – (.535 x $100) = $51.24 - $53.5 = -$2.26

Ouch. Losing EV on both sides.

Finding Positive EV

What we do at EV Analytics is provide accurate projected outcomes that can find Positive EV in lines like this. Thankfully, in the real world, our probabilities will equal 100%. Currently we have the Nationals winning 54.83% of the time and the Phillies at 45.17%. Let’s do our EV calculations one more time with these numbers:

Nationals:

(.5483 x $100) – (.4517 x $115) = $54.83 – $51.95 = +$2.88

Phillies:

(.4517 x $105) – (.5483 x $100) = $47.43 - $54.83 = -$7.40

And we’ve found it. The difference between the breakeven point of 53.5% and our predicted 54.83% gives us that elusive positive expectation and a small return on investment.