What is Expected Value?

Have you ever had the choice of two bets that you wanted to place and wondered what the best option was? Well we are hear to tell you a way that can help you decide and in the longer term keep a track of how much you should be winning!

Expected Value, as you can imagine by the name, is the amount you may expect to win long term from a bet in the form of return.  The formula for Expected Value (EV) is actually relatively intuitive. The amount we expect to get back from a bet is the likeliness of winning the bet multiplied by the possible win minus likeliness of losing your stake. This is expressed better in the form;

EV = (Probability of win * Potential profit) – (Probability of losing * Stake)

Let us take a fair coin toss and place a 10 unit stake on heads. Our calculation for EV would look like this;

EV = (0.5 * 10) – (0.5 * 10) = 0

So as we have bet on on a coin toss at even money we would expect to make no profit from this long term. Now this is relatively obvious to us but we can expand this slightly for other betting to provide more use. From our previous post on overround we know how to calculate added margin but that is represented as a percentage. Using this calculation we have found a different way of seeing how much a bet may cost us. We will use a real life example here;


In this example we want to place a bet of 10 units on Man City at 13/10 (2.3) and want to know our EV. Will convert the odds given into implied probabilities to do this;

EV = (Probability of win * Potential profit) – (Probability of losing * Stake) = 

EV = (0.4348 * 13) – (0.6083 * 10) = -0.4308

As the sign of the value is negative, this indicates that we expect to lose money on this bet. Now you might have noticed the percentages used here add up to more than 100% and again this is overround. This total book was priced to 104.3077%, so the expected EV in this cases is a visual representation of how much we expect to lose due to this.

Overround is added to all prices as we know but prices are not always correct and that is when the EV calculation can help us to see what we will win. Assume that the real price of Manchester City to win against Liverpool is even money (2.0). In this case we would be getting a value bet when taking the 13/10 (2.3) and the EV would look like this;

EV = (Probability of win * Potential profit) – (Probability of losing * Stake) =

EV = (1/2.0 * (13/10 * 10)) – (1/2.0 * 10) = 

EV = (0.5 * (2.3 – 1) * 10) – (0.5 * 10) = 

EV = (0.5 * 13) – (0.5 * 10) = 1.5

So for a 10 unit stake we would expect to win 1.5 back long term from this bet. This shows the value of betting value over a long period of time and how profitable it can be. Keep good records and see if your profit is matching your expectations or you may have to re-think your strategy!

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