# Cost-Weighted Probability

Cost-weighted probability is used when calculating the overall probability for a risk when cost allocation is in force and different probabilities have been assigned to a risk for each allocation block.

The obvious way to calculate overall probability in such situations is simply to average the probabilities over all the allocation blocks. However, this can give unrealistic results.

In the example shown below, no costs will ever be incurred, because in years 1 and 3 there are no costs, and in year 2, while there is a \$1,000,000 cost, there is zero probability of it being incurred. However, if we were to average the probabilities over all three years, we would arrive at the result that there is a 67% probability of a \$1,000,000 cost.

 Allocation Block Year 1 Year 2 Year 3 Estimated Cost \$0 \$1,000,000 \$0 Probability 100% 0% 100%

To get around this problem Mandrel uses cost-weighted probability, which is the sum of (probability x cost) for each allocation block divided by the sum of the costs:

Applying this to the example above gives an overall probability of 0%, which is the correct answer in this case.

Zero-Cost Case

Cost-weighted probability breaks down if there are no costs, in which case Mandrel calculates overall probability as a simple average. This situation might arise, for example, where you have one or more non-cost risk impacts, and a particular risk has these impacts but no cost impact.