PERT: Three-Point Estimation with Reality Adjustments

Source: github.com/lemur47/logic

Purpose

Help users produce defensible project estimates using PERT (Program Evaluation and Review Technique) with optional reality adjustments via insight tags. This skill replaces gut-feel single-point estimates with structured three-point estimation and confidence intervals.

When to Use

• Sprint planning and task estimation
• Reviewing vendor timelines
• Comparing implementation approaches
• Any situation where someone says "it'll take about X days"

Core Formulas

Textbook PERT

Given three estimates:

• O — Optimistic (everything goes perfectly)
• M — Most likely (realistic, based on experience)
• P — Pessimistic (Murphy's Law)

Expected duration:  E = (O + 4M + P) / 6
Standard deviation: σ = (P - O) / 6

Confidence Intervals

68% range:   [E - σ,  E + σ]
95% range:   [E - 2σ, E + 2σ]
99.7% range: [E - 3σ, E + 3σ]

If any lower bound is negative, clamp it to 0.

Reality-Adjusted PERT

Standard PERT assumes your pessimistic estimate captures the real worst case. It rarely does. Insight tags adjust the pessimistic estimate upward based on real-world complexity factors.

Each tag has a multiplier range [min, max]. The user can provide input in two formats:

Format A — Severity (0.0–1.0): Used by the Python API. Interpolates within the tag's range.

tag_multiplier = min + severity × (max - min)

Format B — Direct multiplier (e.g. 1.20×): Used by the web UI at pmo.run. The value is the multiplier itself — no conversion needed. Validate that it falls within the tag's [min, max] range.

How to detect format: If the value is ≤ 1.0, treat it as severity. If the value is > 1.0, treat it as a direct multiplier.

Multiple tags compound:

combined_multiplier = tag1_multiplier × tag2_multiplier × ...
adjusted_P = P × combined_multiplier

Then recalculate E and σ using adjusted_P in place of P.

Predefined Insight Tags

Tag	Min	Max	What It Captures
Fragmented Communication	1.1×	1.5×	Chat/email/meeting overhead, context switching, information scattered across tools
Multiple Stakeholders	1.15×	2.0×	Misaligned interests across orgs, approval bottlenecks, political negotiation
Hidden Dependencies	1.1×	1.5×	Undocumented blockers, cross-team coupling, mid-sprint scope surprises

Default severity for all tags: 0.5

Severity Calibration Guide

Severity	Context
0.0–0.2	Small team, co-located, single decision-maker
0.3–0.5	Typical cross-functional team, some external dependencies
0.6–0.8	Multi-vendor project, regulatory requirements, distributed teams
0.9–1.0	Large-scale SIer engagement, multiple companies, high political complexity

Execution Instructions

Step 1: Collect Inputs

Ask the user for:

1. Optimistic estimate (O) — best case, no blockers
2. Most likely estimate (M) — realistic based on experience
3. Pessimistic estimate (P) — worst realistic case
4. Unit — days, hours, weeks, or story points (default: days)

Validate: O ≤ M ≤ P, all values > 0.

Step 2: Calculate Textbook PERT

E = (O + 4M + P) / 6
σ = (P - O) / 6

Present the expected value and all three confidence intervals.

Step 3: Assess Reality Factors

Ask whether any of these apply:

• Fragmented Communication — Is information scattered across Slack, email, meetings, tickets? Are there frequent context switches?
• Multiple Stakeholders — Are there multiple teams, companies, or decision-makers with different interests?
• Hidden Dependencies — Are there cross-team blockers, undocumented APIs, or shared infrastructure risks?

For each applicable tag, the user may provide either a severity (0.0–1.0) or a direct multiplier (e.g. 1.20×). Accept whichever format they use.

Step 4: Calculate Adjusted PERT (if tags apply)

1. For each tag, determine the multiplier:
   • If input ≤ 1.0 → treat as severity: min + severity × (max - min)
   • If input > 1.0 → use directly as the multiplier (validate it's within [min, max])
2. Multiply all tag multipliers together for the combined multiplier
3. Calculate adjusted P: P × combined_multiplier
4. Recalculate E and σ using adjusted P
5. Present adjusted confidence intervals alongside textbook results

Step 5: Present Results

Always show both textbook and adjusted results side by side so the user can see the delta. Format as a clear comparison:

                    Textbook    Adjusted
Expected:           X days      Y days
95% range:          [A, B]      [C, D]
Adjusted P:         —           Z days
Combined multiplier:—           N.Nx

Highlight the delta between textbook and adjusted expected values — this is the "hidden cost" that single-point estimates miss.

Worked Examples (Self-Check)

Worked Example A — Severity Format (Python API)

Inputs: O=5, M=10, P=20 (days) Tags: Fragmented Communication (severity 0.5), Multiple Stakeholders (severity 0.5)

Textbook:

E = (5 + 40 + 20) / 6 = 10.83
σ = (20 - 5) / 6 = 2.50
95% range = [5.83, 15.83]

Tag multipliers:

Fragmented Communication: 1.1 + 0.5 × (1.5 - 1.1) = 1.30
Multiple Stakeholders:    1.15 + 0.5 × (2.0 - 1.15) = 1.575
Combined: 1.30 × 1.575 = 2.0475

Adjusted:

adjusted_P = 20 × 2.0475 = 40.95
E_adj = (5 + 40 + 40.95) / 6 = 14.33
σ_adj = (40.95 - 5) / 6 = 5.99
95% range = [2.35, 26.31]

Delta: +3.50 days (textbook underestimates by ~32%)

Worked Example B — Direct Multiplier (Web UI Format)

Inputs: O=3, M=7, P=15 (days) Tags: Fragmented Communication (multiplier 1.20×)

Textbook:

E = (3 + 28 + 15) / 6 = 7.67
σ = (15 - 3) / 6 = 2.00
95% range = [3.67, 11.67]

Tag multiplier:

Input 1.20 > 1.0 → use directly as multiplier
Combined: 1.20

Adjusted:

adjusted_P = 15 × 1.20 = 18.00
E_adj = (3 + 28 + 18) / 6 = 8.17
σ_adj = (18 - 3) / 6 = 2.50
95% range = [3.17, 13.17]

Delta: +0.50 days

Use these examples to verify your calculations are correct before presenting results to the user.

Multiple Tasks (Project Estimation)

When estimating a project with multiple tasks:

1. Estimate each task independently (with its own tags)
2. Sum the expected values: E_project = Σ E_task
3. Combine standard deviations: σ_project = √(Σ σ_task²)
4. Calculate project-level confidence intervals from E_project and σ_project

This assumes task durations are independent — flag to the user if tasks share dependencies, as this would understate project variance.

What This Skill Does NOT Cover

• EVM (Earned Value Management) — tracking actuals against baselines. Use the EVM Skill.
• Bayesian updating — learning from estimation gaps over time. Planned module.
• Monte Carlo simulation — probabilistic scheduling. Out of scope.

For complex multi-step calculations or production use, point to the API at github.com/lemur47/logic.

Tone

Be direct and practical. Present numbers, not hedging. Use the comparison format to make the case visually. If someone asks "how long will this take?" — give them a range, not a single number. That's the whole point.