Normal Distribution
Bell-curve averaging: many small independent effects sum to a predictable center with thin tails.
Use → Use when errors aggregate. Don't use for rich-get-richer or contagious outcomes.
Starter • Reason · Predict
The Library — 33 models, 9 families
Original summaries only33 shown • placeholder fields ready for your data dump
Power Law / Long Tail
Rich-get-richer: a few huge winners, many tiny players. Straight line on log-log.
Use → City sizes, book sales, network degrees. Never average it like a normal.
Starter • Explain · Predict
Poisson Arrivals
Counts of rare independent events per window: calls, mutations, clicks.
Use → Staffing, queues, buffers. Don't use when events cluster or cascade.
Core • Predict · Design
Linear Regression
Best-fit line plus a causation audit. A big coefficient is not a big cause.
Use → Screen relationships, then hunt omitted variables and reverse causality.
Starter • Reason · Predict
Concavity & Diminishing Returns
Curved payoffs change optimal bets: diversify when concave, concentrate when convex.
Use → Portfolios, effort allocation, pricing tiers.
Core • Design · Act
Categorical & Threshold Models
Buckets and cutoffs turn messy attributes into testable if-then rules.
Use → Segmentation, eligibility, triage. Watch boundary gaming.
Core • Reason · Predict
Schelling Segregation
Mild individual preference for similar neighbors aggregates to stark city-wide segregation.
Use → Housing, schools, platforms. Try the tolerance sandbox below.
Core • Reason · Explain · Predict
Granovetter Threshold
Each person has a riot threshold; cascades depend on the distribution, not the average.
Use → Protests, adoption, bank runs. Map thresholds before messaging.
Core • Explain · Predict
Standing Ovation (Page–Miller)
Quality plus sightlines plus personal thresholds explain why crowds stand — or don't.
Use → Social proof, launches, applause dynamics.
Fun • Explain
Network Structure & Formation
Degree, clustering, bridges and formation logic predict what flows — and what breaks.
Use → Org design, virality, resilience. Prefer bridges over hubs for novelty.
Core • Reason · Design
Preferential Attachment
New links favor already-linked nodes, manufacturing power laws from pure growth.
Use → Citations, followers, city pull. Seed early visibility deliberately.
Core • Explain · Predict
SIR Contagion
Susceptible–Infected–Recovered with an R0 tipping point. Same math for flu and pop-star fever.
Use → Epidemics, memes, outages. Push R below 1 or segment the network.
Core • Predict · Act · Explore
Bass Diffusion (S-Curve)
Innovators plus imitators make the S-curve. Spend early on seeds, later on social proof.
Use → Launches, rollouts, feature adoption.
Core • Predict · Design
Percolation / Tipping Points
Sparse links suddenly gel into a giant component — bank networks and blackouts tip fast.
Use → Fragility audits, buffers, circuit breakers.
Advanced • Explain · Predict
Cellular Automata & Game of Life
Tiny local rules aggregate into gliders, blinkers and chaos. Emergence needs no boss.
Use → Prototype emergence; don't over-interpret any single run.
Core • Explore · Explain
Random Walk & Markets
Unpredictable steps accumulate; efficient markets leave mostly randomness behind.
Use → Separate skill from luck before forecasting.
Core • Reason · Predict
Markov Chain
Next state depends only on now. Run it forward to get the long-run mix.
Use → Mobility, churn, brand switching. Check memorylessness first.
Core • Predict · Explore
Polya Urn / Path Dependence
Early draws rewrite the odds — history locks in QWERTYs, VHSs and dominant cities.
Use → Audit increasing returns; intervene early or standardize late.
Advanced • Explain
Lyapunov / Equilibrium
An energy-like function proves a system settles down — and bounds how fast.
Use → Stability checks for cities, markets, queues.
Advanced • Reason
Exponential & Solow Growth
Compounding plus capital, labor and ideas explain why some economies stall.
Use → Growth diagnostics; ideas are the non-rival engine.
Core • Explain · Predict
Capital Share (Piketty-style)
When returns on capital outrun growth, wealth concentrates without any villain.
Use → Tax and redistribution design; pair with mobility data.
Advanced • Explain · Act
Prisoner's Dilemma + Cooperation
Solo incentives wreck the group; seven routes — repeat, punish, signal, sort — rebuild it.
Use → Pricing, commons, teamwork. Change payoffs, not slogans.
Core • Reason · Design
Colonel Blotto
Split forces across fronts with no pure best move — win by being unpredictable.
Use → Campaigns, ad budgets, competitive bids.
Advanced • Act · Design
Coordination & Culture
Pure coordination games plus memory harden into culture as equilibrium.
Use → Norms, standards, onboarding rituals.
Core • Explain · Design
Mechanism Design / Auctions
Write rules so truth-telling wins despite hidden actions and hidden information.
Use → Auctions, procurement, public projects.
Advanced • Design · Act
Collective Action & Commons (Ostrom)
Shared pools survive with boundaries, monitors and graduated sanctions — no panacea.
Use → Fisheries, groundwater, shared infra.
Core • Design · Act
Replicator Dynamics (Fisher)
Winning strategies reproduce faster; adaptation speed rises with variation.
Use → Learning systems, org routines. Protect variation to adapt faster.
Advanced • Explain · Explore
Diversity Prediction Theorem
Crowd error equals average error minus diversity. Diverse models beat the lone genius.
Use → Ensembles, forecasting teams, model committees.
Core • Predict · Design
Multi-Armed Bandit
Balance pulling the best-known lever against testing new ones. Regret is the score.
Use → Trials, dosing, ad creative. Run small experiments, then exploit.
Core • Act · Explore
System Dynamics / Feedback Loops
Stocks, flows and reinforcing loops turn small pushes into addiction spirals or virtuous cycles.
Use → Map loops before adding pressure; find the balancing lever.
Core • Explain · Act
Central Limit & Six Sigma
Sample averages settle to normal; variation reduction pays until Fisher bites back.
Use → Quality programs, polling margins, A/B sizing.
Starter • Reason
Decision Trees + Value of Information
Fold back probabilities; pay for information only if it changes the action.
Use → Product, medical and policy bets.
Core • Act · Design
Spatial Choice & Aggregation
Rational individuals aggregate into irrational crowds — location and order matter.
Use → Voting, siting, assortment. Aggregate rules, not vibes.
Advanced • Reason · Predict