A £5,000 allowance for a risk with a £50,000 consequence can sound implausibly small. The apparent contradiction comes from using one number to answer two different questions.
The consequence asks what the event would cost if it occurred. The expected contribution combines that consequence with its probability across possible outcomes. It is a mean, not a prediction that the project will pay a smaller version of the event.
In the practice exercise, Risk A has a 25% probability of adding £20,000. Its expected contribution is 0.25 × £20,000 = £5,000. Risk B has a 10% probability of adding £50,000, also giving £5,000. The combined expected allowance is £10,000.
| Risk | Probability | Impact | Expected contribution |
|---|---|---|---|
| A | 25% | £20,000 | £5,000 |
| B | 10% | £50,000 | £5,000 |
| Combined | £10,000 |
Expected contributions add to £10,000. This arithmetic does not establish a confidence percentile.
Keep the base estimate separate
The stated base estimate is £100,000. Adding the expected allowance gives £110,000. This assumes the impacts are additional to the base and have not already been allowed for in the rates or another contingency line.
That check matters. If an estimator increases a resource rate for an uncertain event and then adds the full expected event cost again, the same exposure may appear twice. Known, required scope should also be distinguished from uncertain outcomes. Calling an unmeasured but necessary activity a risk does not resolve the missing quantity.
An expected allowance is not a confidence level
The £110,000 figure is not automatically a P80 budget. A confidence percentile describes the cost threshold associated with a cumulative probability across outcomes. To calculate it, you need a model of those outcomes and their relevant relationships.
Expected values can be added when cost effects are defined consistently; statistical independence is not required for that arithmetic. Dependencies become important when describing the combined distribution and its percentiles. Shared causes, overlapping impacts or mutually exclusive responses need consideration.
An expected cost of £5,000 does not mean the event will cost £5,000 if it happens.
You can use expected values to understand contributions to the mean while still needing a fuller model to answer a funding-confidence question. Do not relabel the result of one calculation as the answer to the other.
Improve assumptions before adding sophistication
A precise probability can create a false sense of certainty when the event is poorly described. Define what triggers the risk, what scope the impact includes and which response has been assumed. Give the estimate a date and identify who should review it as information changes.
An access delay could affect labour, plant and programme-related overhead. If those effects are entered as separate risks, explain whether they arise from the same event and whether the cost periods overlap. A complicated model cannot rescue a confused definition.
Use the result to ask better questions
In our exercise, two very different risks have identical expected contributions. That does not make them equally manageable. One has a larger consequence and lower probability; the other is more likely with a smaller consequence. Mitigation options, timing and the ability to absorb the outcome may differ.
When checking your answer, convert percentages to decimals, multiply each probability by its impact and add the contributions once. Then add that allowance to the base. Finish by naming the result accurately: base plus expected risk cost, under the assumptions supplied.