How To Calculate Expected Value (Worked Examples)

This video covers expected value, which in the context of sports betting could be called expected profit (or loss). To work it out you need to multiply each possible outcome by its probability of happening, then add up all your answers.

A quick example would be the roll of a die where we want to know the expected value of rolling. Assuming it's not weighted then you have an equal (1 in 6) chance of each outcome, in decimal that's 1/6 = 0.16666...

For every outcome 1,2,3,4,5,6 you need to multiply each one separately by 0.166666.. and you'll get these six numbers.

0.16666..
0.33333..
0.50
0.66666..
0.83333..
1

Add those six numbers up and you get 3.5, which is your expected value. It's often the case that your expected value isn't one of the outcomes (i.e. there is no 3.5 to roll, only a 3 or a 4). It's easier to think of multiple rolls, so if you roll the die 100 times, added all the results up and divided by 100, you should get roughly 3.5.

So it's the SUM of all (outcome x probability of outcome).