Expected value, exact percentiles and what a flat 5 per cent really buys, on an eight-line register.
Calculate construction contingency from a priced risk register, not a flat percentage: multiply each risk's probability by its cost impact, sum them for the expected value, then set the contingency at the confidence level the client wants to fund. On an illustrative 26,301,102 contract with eight risks, the expected value is 1,981,500 (7.5 per cent), but an 80 per cent chance of staying within budget needs 2,650,000, or 10.1 per cent. A flat 5 per cent would hold in fewer than one outcome in five.
Worked in full in Construction Cost Control by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A contingency is a client's budget for the cost of things that are known to be possible but not certain. Its size should follow from the specific project, its design status, its ground and its contract, which is why the same 5 per cent copied from scheme to scheme is wrong in both directions: too much on a fully designed shed, far too little on a complex building signed on an incomplete design.
| Risk | Probability | Impact | Expected value |
|---|---|---|---|
| Design development beyond the contractor's allowance | 70% | 900,000 | 630,000 |
| Client change requests after signature | 60% | 500,000 | 300,000 |
| Provisional sums exceed their allowance | 50% | 600,000 | 300,000 |
| Compensable delay: prolongation and the client's extra finance cost | 40% | 480,000 | 192,000 |
| Escalation above the tender allowance | 35% | 420,000 | 147,000 |
| Utility diversion and statutory works | 30% | 350,000 | 105,000 |
| Unforeseen ground conditions | 25% | 750,000 | 187,500 |
| Subcontractor insolvency and re-procurement | 10% | 1,200,000 | 120,000 |
| Total | 5,200,000 | 1,981,500 |
Each impact should be priced the way the cost will actually arrive: a delay risk at the weekly time-related cost of the site plus the client's own weekly finance cost, not at a share of total preliminaries (see how to calculate prolongation costs), and an escalation risk on the value still to be bought, not the whole contract.
Expected value = Σ (probability × impact) = 1,981,500, or 7.53 per cent of the contract sum
In Excel, with probabilities in B2:B9 and impacts in C2:C9: =SUMPRODUCT(B2:B9,C2:C9).
The expected value is the average outcome over many projects like this one. On this one project it is roughly a coin toss: there is a 49 per cent chance the risks that occur cost more than 1,981,500. Funding the expected value means accepting that the budget is as likely to be broken as kept.
With eight independent risks there are 256 combinations of what happens, and each can be priced exactly: multiply the probabilities of the risks that occur and of those that do not, and add up the impacts of the ones that do. Sorting the 256 outcomes by cost and accumulating their probabilities gives the percentiles directly. With more risks than that, a Monte Carlo simulation does the same job by sampling.
| Confidence | Contingency | % of contract sum | Above expected value |
|---|---|---|---|
| P50 | 1,980,000 | 7.5% | -1,500 |
| P80 | 2,650,000 | 10.1% | 668,500 |
| P90 | 3,080,000 | 11.7% | 1,098,500 |
| P95 | 3,400,000 | 12.9% | 1,418,500 |
| Every risk occurs | 5,200,000 | 19.8% |
P80 is a common choice for a client's project budget because it covers most outcomes without funding the worst case, which here has a probability far below one in a thousand. The step from P80 to P95 costs another 750,000: that is the price of the last fifteen points of certainty, and a funder or board should choose it knowingly.
| Rule | Contingency | Chance of being enough |
|---|---|---|
| 5 per cent of the contract sum | 1,315,055 | 18.7% |
| 10 per cent of the contract sum | 2,630,110 | 79.5% |
Ten per cent happens to land near P80 on this register; 5 per cent is enough in fewer than one outcome in five. The point is not that 10 per cent is right. It is that only the register can tell you which percentage this project needs, and the answer moves as soon as the risks do.
The largest single line is design development, and it is the one the client controls before signature. Lowering its probability by issuing more of the design with the tender moves both measures.
| Probability | Expected value | P80 contingency | % of contract sum |
|---|---|---|---|
| 70% | 1,981,500 | 2,650,000 | 10.1% |
| 50% | 1,801,500 | 2,480,000 | 9.4% |
| 30% | 1,621,500 | 2,300,000 | 8.7% |
| 10% | 1,441,500 | 2,030,000 | 7.7% |
Taking that probability from 70 to 10 per cent releases 620,000 of P80 contingency. If finishing the design before tender costs less than that, the contingency calculation has just justified it.
Probability times impact gives 1,981,500; the distribution says 2,650,000 is needed for an 80 per cent chance of holding. Set the contingency from the register and the confidence level, and treat the flat percentage as a check, not an input. Construction Cost Control traces how the movement from contract sum to final account builds up line by line, and how much of it was knowable at signature, and the free workbooks for this case include a forecast of the lines whose inputs exist before the contract is signed.
Rules of thumb run from about 5 per cent for a well designed, simple building to 10 per cent or more where design is incomplete or the ground is uncertain. They are a check, not a method. In the example, 5 per cent of the contract sum, 1,315,055, covers only 18.7 per cent of outcomes, while the risk register shows 2,650,000 is needed for 80 per cent confidence.
P50 is the amount that will be enough in half of outcomes, close to the expected value: 1,980,000 in the example. P80 is enough in 80 per cent of outcomes, 2,650,000. The 670,000 difference is the cost of moving from a coin toss to a budget that holds four times in five, which most clients and lenders prefer for a single project.
No. Provisional sums, a contractor's design development allowance and escalation allowances are already priced in the contract sum. Contingency covers only the risk that they are exceeded. Including them again double counts and inflates the budget, while leaving them out of the register entirely ignores the most likely overruns.
This article is one calculation from Construction Cost Control. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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