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IQRM Glossary · Quantitative risk management

Three-Point Estimate

A three-point estimate describes an uncertain cost or duration with three values: optimistic (minimum), most likely, and pessimistic (maximum). The three points define a distribution, usually triangular or PERT, that a Monte Carlo simulation samples from. Three-point estimates are the main input to QSRA and QCRA models.

The formulas

PERT mean = (Min + 4 × Most likely + Max) / 6
Triangular mean = (Min + Most likely + Max) / 3

Worked example

A pipeline tie-in is estimated at 20 days minimum, 25 days most likely and 40 days maximum.

  • PERT mean = (20 + 100 + 40) / 6 = 26.7 days
  • Triangular mean = (20 + 25 + 40) / 3 = 28.3 days
  • Triangular P80 = 32.3 days, seven days more than the "most likely" figure a deterministic plan would use

The long right tail is why a plan built on most likely durations finishes late: each activity has more room to overrun than to underrun.

Why most three-point estimates are wrong

  • Too narrow. Experts anchor on the most likely value and set a maximum only slightly above it. Real outcomes regularly fall outside workshop ranges.
  • Absolute extremes are hard to judge. People estimate a P10 and P90 more reliably than a true minimum and maximum.
  • Double counting with risk events. If the maximum already includes a discrete risk, and the same risk is in the register, it is counted twice.

Calibrating with data

The strongest three-point estimates come from evidence: productivity records, procurement lead times and performance on past projects. IQRM's Risk Data Engine (RDE) builds ranges this way, then tests workshop opinion against the data rather than taking it at face value.

Common mistakes

  • Using a single percentage range such as -10% / +20% for every activity.
  • Letting the planner who built the schedule set all the ranges.
  • Ignoring correlation between activities that share a cause, such as the same crew or the same weather.

Related terms

Triangular distributionQSRAP10Quantitative risk assessmentMerge biasFull glossary
Go deeper
Three-point estimates: why most are wrong and how RDE fixes them

Frequently asked questions

What is a three-point estimate?
It is an estimate made of a minimum, most likely and maximum value, which together define a probability distribution for a cost or duration.
What is the three-point estimate formula?
The PERT mean is (minimum + 4 x most likely + maximum) / 6. The triangular mean is (minimum + most likely + maximum) / 3.
Should I use PERT or triangular?
Triangular gives more weight to the tails and is more cautious when data is sparse. PERT concentrates results near the most likely value. Many practitioners use triangular unless data supports a tighter shape.

Replace guessed ranges with evidence

The Risk Data Engine builds three-point estimates from productivity, procurement and performance data, then tests workshop opinion against it.

See the Risk Data EngineLearn the method
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