Here’s where the use of Expected Value can help. I’m going to be using an example from health economics - so bare with me - but it will be useful for this analysis.

Expected Value is defined (by Google) as:

A predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.

So in layman’s terms, it’s the probability of an event happening multiplied by that event. Taking an example from health economics - you may have a person who has just had surgery. That person has two possible outcomes - they’ll die or they’ll live:

Decision Tree displaying the probabilities and values post surgery

Each of these outcomes have a probability attached to them, and an end value. The value used in this case is years left to live. These are displayed at the end of the branches (0,15 and 0.5). The probabilities are the values in red that are on the branches (0.05, 0.95, 0.8 and 0.2).

These mean that if the person has surgery, there’s a 95% chance of them living, if they live there’s an 80% chance they survive and so on.

The Expected Value is then multiplying the probabilities by the values along the branches to see what the likely outcome is. The outcomes are as follows:

Die: (0.05*0) = 0 years left

Live: 0.95 * (0.8*15+0.2*0.5) = 11.495 years.

So overall the Expected Value of having surgery is 11.495 + 0 = 11.495 years.

If we were to compare this to - say - a course of drug treatments and not surgery, we could compare the Expected Value’s of both options and see which one is likely to maximise our output. For example if the drug treatment had an Expected Value of 15 - you’d choose that over the surgery.