# Weighted Cost Theory

Risk exposure, or project weighted cost, is a statistical concept. Like many statistical concepts it is best described by assuming that a large number of independent trials of the same activity are being held. The average of all the possible results that could occur over all these trials represents the ‘most likely’ value, in this case the additional risk costs for the project as a whole.

In the case of a project it is difficult to imagine that the same project could be performed independently a large number of times. However, for the sake of argument, let’s imagine there are a number of parallel universes in which similar groups of people all perform the same project with the same set of risks, but with different results each time with regard to which risks do or do not occur.

Suppose that the ith risk has a probability Pi. This means that, if there are a total of N parallel universes in which the project is being performed, where N is a large number, this risk will occur in NPi of those universes. If the cost effect of this risk is Ci the total cost incurred for this risk, summed over all those universes, will be NPiCi.

If there are M risks in the project, all with different cost effects and probabilities, the total risk cost for every risk, realized over all N parallel universes, will be:

The average cost realized for all M risks for any one universe would therefore be:

The quantity on the right hand side is the sum of the weighted costs for all the (identified) project risks, and is known as the project weighted cost. It represents the most likely additional costs that the project will incur, based on these risks.