How to calculate Expected Value

How to calculate Expected Value

In our previous article we learnt about the concept of value, and how finding value is more important than finding just winners. In this article we will use this knowledge to help us know which bets provide value, and the profits we would expect to make long term.

Luckily for us there is a formula that not only tells us when a bet is providing value, but can also tell us how much money we would expect to win over the long term. The “expected value” (also known as EV), is the amount a punter would expect to win or lose if they placed the same bet many different times.

How to calculate expected value

To calculate the expected value of a bet we need to know the probability of an event occurring, the amount of money that will be bet (stake), and the amount of money that will be won if the bet is successful. The formula used for calculating expected value is:

Expected value = (probability of winning x amount won) – (probability of losing x amount lost)

Probability of winning– is the percentage chance of the bet winning according to your handicapping expressed as a decimal (eg 70% should be inputted as 0.7)

Amount won- is the amount of money you would expect to win if the bet wins. To calculate this, times the decimal odds by your stake, and then subtract the stake (eg $10 x $1.70 – $10 = 7)

Probability of losing- is the percentage chance of the bet losing expressed as a decimal. Can also be calculated by subtracting the probability of winning from 100.

Amount lost– Is the stake of the bet (eg $10)

Example of how to calculate expected value

To see how expected value works, lets use the example of a match where the home team is priced at $1.70. Our punter has assessed the home teams chance of winning as 70% and is looking to bet $10. The expected value calculation this bet would be:

 (0.7 x 7) – (0.3 x 10) = 1.9

This means that for every $10 bet, over time our punter would expect to win $1.90. This is a positive expected value bet, and assuming that our punter’s handicapping is accurate he would expect to generate profits over the long term.

Lets look at another example where our punter is looking to make the same $10 bet on the $1.70 home team, only this time he rates their probability of winning as 30%.

 (0.3 x 7) – (0.7 x 10) = -4.9

In this example for every $10 bet, our punter would expect to lose $4.90. The expected value for this bet is negative, meaning over time our punter would expect to lose.

Using expected value in your betting

Calculating expected value for each bet is an important process for every punter. It is the best judge of whether you will be successful in the long term with your betting, as well as telling you if each individual bet is providing value. As we saw in our previous article, it is possible to have as much as a 70% winning rate, yet still lose money long term if you are placing negative expected value bets.

However due to the subjective nature of sport betting compared to games like poker or a simple coin toss, there may be occasions where you may place negative expected value bets. But for long term profitability it is vitally important to have a strong handicapping model and place bets which represent positive expected value.

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