Methodology & Formulas
Every number PyratechAI shows is a formula you can see and reproduce. This page documents each one in plain language — the same math the free calculator, the Analyzer and the paid toolkit files use.
ROI (Return on Investment)
ROI % = (3-year total benefit − 3-year total cost) ÷ 3-year total cost × 100. Costs include the initial investment and three years of annual operating cost. Benefit is the total realized annual benefit multiplied by three. Example: benefit $1,243,200, cost $436,900, ROI = (1,243,200 − 436,900) ÷ 436,900 × 100 = 184.5%.
Payback period
Payback (months) = Initial investment ÷ (Total annual realized benefit ÷ 12). Answers 'how many months of benefit does it take to earn back the up-front spend?'. Example: $379,000 initial ÷ ($414,400 / 12) = 11.0 months.
Benefit-cost ratio (BCR)
BCR = 3-year total benefit ÷ 3-year total cost. Any BCR above 1 means the initiative more than pays for itself over three years; BCR of 2.85 means every dollar spent returns $2.85 in realized benefit.
Net value (3-year)
3-year net value = 3-year total benefit − 3-year total cost. The absolute dollar figure your organization ends up with after three years, in constant terms. We do not add a hidden discount rate — you can layer NPV on top externally if your finance team requires it.
Adoption × Realization discount
Realized productivity value = Theoretical productivity value × Adoption rate × Realization rate. Theoretical productivity value = Affected employees × Fully-loaded annual cost per employee × (Hours saved per week ÷ 40). Direct cost savings and revenue contribution are also discounted by Adoption × Realization; risk avoidance is discounted by Realization only, because avoided losses don't depend on how many users adopted the tool. This is what makes a business case survive scrutiny — most models fail because they book gross theoretical savings without discounting for the fact that not every user adopts and not every reclaimed hour converts to money.
How to estimate adoption and realization
We deliberately don't publish generic benchmark percentages for adoption or realization rates — your own historical data, if you have it, is a better input than any industry-wide number we could give you. What actually drives Adoption UP: a specific pain the target user already feels, a workflow that integrates into their existing tools, executive sponsorship visible to line managers, active champions inside the target team, and time invested in enablement. What drives Adoption DOWN: a solution the user was not asking for, workflow friction (an extra click, tab or login), lack of ongoing measurement, and adoption reported as 'has access' rather than 'used this week'. What drives Realization gaps: reclaimed time that goes to slack rather than higher-value work, quality-review overhead on AI output, partial adoption inside a workflow (assist without acting), and business processes that block converting time savings into headcount or revenue outcomes. Practical rule: if you don't have historical adoption/realization data from a comparable rollout, estimate conservatively and use the sensitivity view to see how much the decision moves. If the decision only holds at high adoption × high realization, it is a Pilot, not a Fund — regardless of the projected ROI.
Revenue contribution (margin-adjusted)
Revenue contribution = Incremental annual revenue × Gross margin %. Only the margin portion is treated as new value — a $1M revenue lift at 60% gross margin contributes $600K to the business case, not $1M.
Weighted scorecard classification
Weighted total = Σ(score × weight) across dimensions, with complexity and risk dimensions inverted as (6 − score) so that a low complexity/risk score contributes positively. Classifications: ≥ 4.0 = PRIORITIZE, ≥ 3.0 = PILOT, ≥ 2.0 = INVESTIGATE, < 2.0 = DEFER. The AI Readiness scorecard uses AI-READY / EMERGING / DEVELOPING / NASCENT at the same thresholds; the Agent scorecard uses PRODUCTION-READY / PILOT-READY / PROTOTYPE / NOT READY.
Two scores in the Analyzer, kept separate
Investment Attractiveness × Evidence Confidence → Investment Decision. Attractiveness aggregates six dimensions (Business Value, Financial Viability, Technical Feasibility, Execution Readiness, Risk Manageability, Time-to-Value). Evidence Confidence weights each material assumption by how much it moves the outcome — so a well-supported small assumption doesn't rescue a shaky big one. PyratechAI never averages them into a single score.
Sensitivity analysis
Each numeric assumption is stressed ±20% to see how much ROI, payback and net value move. Assumptions that swing the result the most while resting on weak evidence become the biggest business-case risks.
Hard blockers override the score
Data that cannot legally be accessed, no accountable owner, or a specific regulatory barrier will override the numerical scores. When a hard blocker is present, PyratechAI will not recommend FUND regardless of how attractive the initiative looks.
Decision gates
Recommendations map to a stage: Discover → Validate → Pilot → Fund → Scale. The system tells you both the current gate and the next one, plus what would move you between them.
Deterministic, not generative
The calculations and recommendations are 100 % deterministic — the same inputs always produce the same result. We use LLMs only to help you generate first-draft inputs when a field is blank; the LLM never invents financial projections or the decision itself.
What we keep private
The exact weight vectors, precise thresholds and the full internal rule list are intentionally not published — this is our methodology. What you always see: your inputs, the major formulas above, your evidence grades, and the reasons behind your recommendation.
Not professional advice
PyratechAI provides structured decision-support analysis based on information, assumptions and evidence you supply. Scores, scenarios and recommendations are estimates designed to support, not replace, independent business judgment. PyratechAI does not provide financial, investment, legal, regulatory, accounting or other professional advice and does not guarantee outcomes.