Probabilistic Thinking
Replace certainties with distributions and odds. Make choices on expected value and downside limits, update beliefs as evidence arrives, and stay calibrated.
author
General usage (Bayes, Laplace, de Finetti, Kahneman/Tversky in practice)
Model type
About
Deterministic plans crack under uncertainty. Probabilistic thinking treats beliefs as degrees of confidence, decisions as bets with payoffs, and evidence as something that updates prior views (Bayes). It privileges base rates, ranges and repeatable rules over single-point predictions.
How it works – what to map
Base rates (priors) – start from the outside view: how similar cases usually turn out.
Evidence (likelihood) – weigh how (un)expected the data is under competing hypotheses.
Bayesian update – prior × likelihood → posterior; move confidence, don’t flip to certainty.
Expected value (EV) – sum of outcomes × probabilities; choose by EV subject to risk limits.
Risk of ruin – cap position sizes; avoid strategies with small gains and catastrophic tails.
Distributions, not points – use ranges, prediction intervals and scenario weights.
Correlation & dependence – portfolio outcomes co-move; diversify true (not assumed) independence.
Calibration – your “70% sure” should be right ~70% over time; practise with forecasts.
Evidence (likelihood) – weigh how (un)expected the data is under competing hypotheses.
Bayesian update – prior × likelihood → posterior; move confidence, don’t flip to certainty.
Expected value (EV) – sum of outcomes × probabilities; choose by EV subject to risk limits.
Risk of ruin – cap position sizes; avoid strategies with small gains and catastrophic tails.
Distributions, not points – use ranges, prediction intervals and scenario weights.
Correlation & dependence – portfolio outcomes co-move; diversify true (not assumed) independence.
Calibration – your “70% sure” should be right ~70% over time; practise with forecasts.
Use cases
Strategy & investing – scenario trees, EV with downside floors, position sizing.
Product & experiments – pre-commit MDE, power and stopping rules; update credibly.
Forecasting – prediction intervals for revenue, demand, incidents.
Hiring & performance – shrink noisy signals toward base rates; avoid overreacting to extremes.
Risk management – stress tests, tail risk checks, aggregation of correlated exposures.
Negotiation – value of information (VoI): what’s a sample or option worth before committing?
Product & experiments – pre-commit MDE, power and stopping rules; update credibly.
Forecasting – prediction intervals for revenue, demand, incidents.
Hiring & performance – shrink noisy signals toward base rates; avoid overreacting to extremes.
Risk management – stress tests, tail risk checks, aggregation of correlated exposures.
Negotiation – value of information (VoI): what’s a sample or option worth before committing?
How to apply
Define the decision and payoff function (money, time, risk avoided, strategic option).
Get the base rate – outside view from analogous cases or cohorts.
List scenarios (3–5) with rough probabilities and payoffs; include tails.
Compute EV and check risk of ruin (max loss, drawdown, SLA breach).
Decide – take the highest-EV option that stays within risk limits; size the bet.
Plan updates – specify signals that will shift probabilities (Bayes triggers) and a review date.
Get the base rate – outside view from analogous cases or cohorts.
List scenarios (3–5) with rough probabilities and payoffs; include tails.
Compute EV and check risk of ruin (max loss, drawdown, SLA breach).
Decide – take the highest-EV option that stays within risk limits; size the bet.
Plan updates – specify signals that will shift probabilities (Bayes triggers) and a review date.
pitfalls and cautions
Point estimates – single numbers hide variance; use ranges and intervals.
Inside view only – ignoring base rates and over-weighting narrative detail.
Assumed independence – correlated bets masquerading as diversification.
Sampling noise – reacting before there’s power; pre-commit sample sizes.
Tail blindness – EV looks fine while rare, ruinous events dominate true risk.
Over-updating – swinging on tiny signals; require likelihood ratios big enough to move the prior.
Inside view only – ignoring base rates and over-weighting narrative detail.
Assumed independence – correlated bets masquerading as diversification.
Sampling noise – reacting before there’s power; pre-commit sample sizes.
Tail blindness – EV looks fine while rare, ruinous events dominate true risk.
Over-updating – swinging on tiny signals; require likelihood ratios big enough to move the prior.