Three-Point Estimating (Optimistic, Most Likely, Pessimistic)
Three points, two formulas, one trap
Three-point estimating replaces a single duration with a range: O (optimistic - everything goes right), M (most likely - the mode, the duration you would bet on), and P (pessimistic - a realistic worst case, not a disaster scenario).
Two weighted formulas appear on exams:
- Triangular: TE = (O + M + P) / 3 - equal weights, a simple average.
- Beta / classic PERT: TE = (O + 4M + P) / 6 - the mode is weighted four times.
The beta model also gives spread:
- Standard deviation: σ = (P − O) / 6 (the range approximates ±3σ)
- Variance: σ² = ((P − O) / 6)²
Variance is what you add. When combining independent activities on a path, sum the variances, then take the square root to obtain the path standard deviation. Summing standard deviations is the most common arithmetic error in this domain.
Traps. Mixing triangular and beta formulas in one calculation; reversing O and P; weighting M by 4 but forgetting to divide by 6; treating M as the mean when the beta is skewed (TE exceeds M whenever P is farther from M than O is); using a "range/2" or "range/4" spread rule that does not belong to PERT; and combining variances for activities that are not on the path being analysed.
Worked example. O = 4, M = 9, P = 20 days. TE = (4 + 36 + 20)/6 = 10 days. σ = (20 − 4)/6 ≈ 2.67; variance ≈ 7.11. The triangular estimate would be 11 days - if an option shows 11, check which formula the question asked for.
Rule of thumb. A range of 12 days gives σ = 2 days; a range of 6 days gives σ = 1 day.