Three-point estimates: ranges before guesses
Narrow ranges look confident and price risk as if it were gone. A worked example shows how the pessimistic value, not the most likely one, moves your quote.
The most likely value is the easy part
Ask someone how long a task will take and they usually answer with the most likely value, then add a pessimistic number that is only a little larger. The result is a range that feels honest and is far too narrow. The value that moves a fixed-price quote is the pessimistic end, because it controls how heavy the right tail is.
Same most likely value, three different ranges
Take a task with a most likely duration of 10 days. Three estimators agree on that number and disagree only on the range. Using Beta-PERT (λ = 4) and a large simulated sample:
| Low / likely / high | Mean | P50 | P80 | P90 |
|---|---|---|---|---|
| 9 / 10 / 11 | 10.00 | 10.00 | 10.35 | 10.51 |
| 8 / 10 / 14 | 10.33 | 10.25 | 11.33 | 11.87 |
| 7 / 10 / 20 | 11.17 | 10.90 | 13.19 | 14.42 |
The median barely moves. The P80 moves from 10.35 days to 13.19 days, a 27% difference for the same "most likely" answer. Anyone quoting from the middle of the distribution would never notice the disagreement; anyone quoting a high percentile would price a very different project.
Elicit the tails first
People anchor on the first number they say out loud. A few habits reduce that anchoring without any special software:
- Ask for the high end before the likely value. "What would have to go wrong for this to take twice as long, and how likely is that?" gives the pessimistic value some evidence behind it.
- Write the assumption beside the number. A range with a reason ("assumes the client supplies final content in week one") can be challenged; a bare range cannot.
- Use reference jobs. Compare against two or three similar completed jobs, as in calibrating estimates with completed jobs.
- Estimate independently, then compare. When two people disagree on the high end, that gap is information about scope, not a problem to average away.
What the model cannot fix
A Beta-PERT distribution is bounded by the low and high values you enter. If the true worst case is outside the range, the simulation never visits it. Treat the high value as a plausible bad case, not an absolute ceiling, and model the genuinely severe events as separate risks with a probability and an impact. The post on contingency without double counting explains how to keep the two from overlapping.
To see how one task's range feeds a probability, try the PERT calculator, then the cost overrun probability tool.
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