R&D Portfolio Funnel: Stage-Gate Attrition Under a Budget

Cohort Setup

Cohort size 24

Budget per round ($M) 40

Gate rigor 1.00×

Funnel State

Next gate: Feasibility Review

Active projects

Round

0 / 5

$ spent so far

$0M

$ / active project

$0.0M

Pass prob. (next gate)

—

Launched (success)

Survivors by stage

How it works

Each round, every surviving project shares the round's budget equally, then rolls independently against a logistic pass probability set by funding-per-project versus that gate's cost threshold — the classic "rising cost of the next stage" pattern behind the real-world R&D funnel and its "valley of death":

fundingPerProject = totalBudget / activeCount
p(pass) = 1 / (1 + exp(-k · (fundingPerProject − threshold(stage) · rigor)))
threshold = [3, 7, 14, 26, 45]  ($M, Research → Launch)

Cohort size — how many independent projects enter Stage 0 together.
Budget per round — total $M split evenly across every still-active project before that gate is rolled; spreading it over more survivors raises each one's odds.
Gate rigor — multiplies every stage's threshold; a stricter review board (rigor > 1×) demands more funding-per-project for the same pass chance.
Run Gate Round — evaluates the next gate for every active project (independent Bernoulli draw at its p(pass)); failures are cut and shown falling away, survivors advance one ring down the funnel.

Five gates model the standard stage-gate pipeline: Research → Feasibility → Development → Validation → Launch. Because later thresholds grow roughly geometrically while a fixed cohort shrinks, per-project funding usually rises each round even on a flat budget — the model that keeps a portfolio's survivors from starving even as the total headcount falls.

Stage 0 · Research

Active project Launched (success) Cut at gate

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