Working out contingency you can defend
The usual method adds each risk's expected value to the estimate. No outcome ever equals that number.
The expected value trap
The standard shortcut multiplies each risk's probability by its cost and adds the results. A 20% chance of a 100k problem contributes 20k of contingency.
No outcome ever equals that. The problem either happens and costs 100k, or does not and costs nothing. A 20k contingency is wrong in both worlds — far too much in one, nowhere near enough in the other. Expected value is the right tool for deciding whether to accept a bet you will make many times. You are running this project once.
What a simulation gives you instead
Sampling every cost item and testing every risk event thousands of times produces a distribution. From that you can say: this figure covers us in 80% of the futures we modelled.
That is a different kind of statement and a far more defensible one in a funding conversation. It also lets you price the difference between 80% and 90% confidence, which is a real decision that a flat percentage contingency hides entirely.
Two sources of variance, kept apart
Estimating uncertainty is roughly symmetric and always present: the line items will cost about what you think, give or take.
Risk events are discrete and one-sided: they either happen or they do not, and they can only make things worse.
Blending them into a single padded estimate hides which is which, and they call for entirely different responses. Estimating uncertainty is reduced by better information; risk events are reduced by doing something about the risk.
The point estimate is not the middle
Because risk events only push one way, the sum of your likely costs is beaten less than half the time. The gap between the point estimate and the median is the optimism built in before any risk was considered, and measuring it for the first time is usually a surprise.
Correlation understates the tail
Simulations of this kind fire events independently. Real ones cluster — the supplier who fails is the same supplier whose delay hits the schedule, and a market shift moves several line items at once.
Independent sampling therefore understates the tail. Treat a P80 as a floor on your exposure rather than a ceiling.