How To Calculate And Use Expected Value

Adam Chernoff
Jun 1, 2017 · 3 min read

If I I asked you to explain expected value and how it relates to sports betting, how much could you tell me?

My guess is, not a whole lot.

Do not be concerned. You’re not alone. Most people reading this article will be the same.

Similar to calculating a bookmakers margins, being able to calculate expected value is something you must know how to do.

What Is Expected Value

The easiest way to understand expected value (or EV for short) is to break it down to its simplest form.

EV is a calculation used to determine whether a bet has a positive or negative profit expectation.

For example,

If you are playing roulette and put a $1 chip on all of 36 numbers and another on zero, you will have a total risk of $37.

After the spin, 36 of your bets will lose, and one bet will win.

You will earn $35 of profit and get your $1 chip back for a total return of $36. A net loss of $1.

If you divide your net loss of -$1 by your risk of $37, you will get -0.027.

The -0.027 represents a loss in cents per dollar risked. You will lose 2.7 cents per dollar bet on roulette.

Applying Expected Value To Sports Betting

For casino games where probability outcomes are known, calculating expected value is straight forward. Calculating EV in sports betting, however, can be tricky.

Unlike games of chance, calculating expected value for a specific sports bet before the game starts is not possible.

This is a very important point and one bettors often confuse. Because the true probabilities of outcomes are not known until the game or match is complete, any attempt to speculate on the EV of a sports wager would be a estimate at best.

An easier way of thinking about the true application of expected value in sports betting would be to refer to it as Profit Expectation instead.

Profit expectation can be used to determine the skill of a bettor using his results over an extended period of time.

For example:

You make 100 wagers at even money for $1 each. You end up winning 55 and losing 45 for a profit of $10.

If you divide $10 by 100, you determine that you have a profit expectation of 0.1 or 10%.

By comparing the probability of the outcome with the implied probability of the bookmaker’s odds, you can determine if you have a positive profit expectation.

Not all bettors with a positive profit history are skilled bettors. Luck plays a large role in the success of gambling. Calculating profit expectation will tell you how much luck is influencing the true result.

Knowing that you have a positive expectancy is a way to validate your methods. This is the principal of value betting at its finest.

Knowing that you have a negative expectancy allows you to save yourself from continuing to chase bad wagers down and promote making a change.

Don’t Be Biased When Calculating

I encourage you to go back through your wager history and gather enough data so you can determine your profit expectancy.

Looking at these figures without bias can be difficult. It takes a lot to accept that luck plays a part in your results and your wins and losses are not dictated solely by your predictive ability and decisions you make.

If you approach your history without bias, you will be able to identify if your betting methods will provide you long term success, or not.

Don’t worry if the results are not what you want to see. Accept them for what they are and build on them. Self awareness is important. You are the only person holding you back from changing a negative profit expectation into a positive one.

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Adam Chernoff

Written by

Sportsbook manager at ASureWin from 2011-2015. Started my own lottery company in 2016 and lost it all. Passionate about writing original betting content.