Probabilistic Thinking
Probabilistic thinking means considering possible outcomes, estimating their likelihoods and weighing their consequences. The theory behind it developed partly from Pascal and Fermat’s 1654 correspondence about gambling. Useful estimates make uncertainty explicit and can be revised as evidence changes.
THE IDEA
Probabilistic thinking means considering several possible outcomes and estimating how likely each is. It helps you make a decision without pretending to know exactly what will happen. A probability estimate should have a basis: observed frequencies, a model, informed judgment or some combination of these.
The correspondence between Blaise Pascal and Pierre de Fermat over a 1654 gambling dispute helped establish modern probability theory. Over the following 150 years, work on games of chance developed alongside applications to scientific and practical problems, including those pursued by Pierre-Simon Laplace. In 1933, Andrey Kolmogorov set out an axiomatic framework for probability. Benoit Mandelbrot described its usefulness this way: “The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.”
To use the approach, start with a decision and the outcomes that could affect it. Estimate their likelihoods, then consider the consequences of each. A likely outcome may have little effect on your choice, while a less likely outcome may deserve close attention because its consequences would be severe. The estimate and the consequence are separate parts of the decision.
A formal model defines a sample space of possible outcomes and assigns probabilities to events within it. The model’s usefulness depends on whether it represents the situation well. Missing outcomes, unreliable data and mistaken assumptions can make a precise-looking estimate misleading. Even a deterministic process may be difficult to predict when we lack information about its initial conditions or cannot calculate all the relevant interactions.
Tail risks need particular care. In a fat-tailed distribution, extreme outcomes occur more often than a bell-curve model with a comparable scale would suggest. Financial losses or other outcomes shaped by feedback and cascading effects may be poorly represented by a model built around ordinary fluctuations. Recognizing that possibility can change how much protection you want against a severe loss; it does not make the probability of that loss easy to estimate.
Probability is useful without being a complete account of judgment. As Vannevar Bush put it, “If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.” Choosing what to model, interpreting evidence and deciding which consequences matter still require judgment.
Personal preferences also belong in a decision. Two people can agree about the chance of an outcome and reasonably choose differently because they value the consequences differently. The task is to examine factual beliefs for evidence and bias, while being clear about the preferences guiding the choice.
When evidence conflicts, ask what each source actually measures, how reliable it is and whether the sources are independent. Revise an estimate when the evidence warrants it, and explain what remains uncertain. Combining evidence should make the basis for a judgment clearer; it need not produce a conclusive answer.
When to use it
Evaluating investment portfolios by assessing probabilities of different returns and tail risks.
Forecasting demand for a new product using probability distributions rather than single-point estimates.
Making medical decisions by weighing the likelihood of a diagnosis against false positives and false negatives.
Planning large projects with probabilistic scheduling (e.g., PERT) to account for uncertainty in task durations.
Evaluating risks in financial investments by calculating expected values.
Making predictions in science by incorporating uncertainty and updating beliefs with new evidence.
Deciding whether to undergo medical treatment by weighing probabilities of success and side effects.
Evaluating a hiring method by comparing its predictions with later job performance and examining uncertainty and possible bias.
Medical diagnosis: Using Bayesian networks to update the probability of a disease given symptoms and test results.
Project management: Estimating the likelihood of meeting deadlines by modeling task durations probabilistically.
Public policy: Assessing the probable impact of a new regulation using stochastic simulations.
FROM THEORY TO EVERYDAY LIFE
In practice
Weather Forecast Decision
A 70% chance of rain is forecast. Instead of ignoring this or thinking it will definitely rain, probabilistic thinking leads you to bring an umbrella, balancing the cost of carrying it against the risk of getting wet.
Project Success Estimation
A project manager estimates the likelihood of on-time completion based on historical data (e.g., 60% chance). This probability helps decide whether to allocate extra resources or set a buffer, rather than assuming guaranteed success.
Gambling Dispute (1654)
Pascal and Fermat solved a gambling problem involving unfinished games, leading to the foundation of probability theory.
Medical Diagnosis
A doctor uses probabilistic thinking to interpret test results, considering base rates and false positives rather than relying on intuition alone.
Weather Forecasting
Meteorologists use probabilistic models to estimate the chance of rain by considering numerous atmospheric variables, rather than giving a deterministic yes/no prediction.
Investment Decision
An investor evaluates the probability of various economic scenarios to allocate assets, balancing potential returns against risks.
A MOMENT TO REFLECT
Put it to work.
Think of a recent important decision. How could assigning probabilities to different outcomes have changed your choice?
Identify a situation where you assumed a binary outcome (success/failure). How might a probabilistic perspective reveal more nuanced possibilities?
Consider a fat-tailed risk in your life or work. What low-probability, high-impact events might you be ignoring?
What is a decision you recently made that was heavily influenced by subjective feelings rather than objective probabilities?
How might you reframe a personal belief as a probability estimate with a range of uncertainty?
In what areas of your life could adopting probabilistic thinking reduce the influence of bias?
Think of a recent decision where you were uncertain. How would you have approached it probabilistically?
How can you identify the key variables that influence outcomes in your field, and assign probabilities to them?
What are the limitations of probabilistic thinking in predicting complex human behavior?
References
- Gambling dispute correspondence — Blaise Pascal and Pierre de Fermat (1654)
- Applications of probability to scientific problems — Pierre-Simon Laplace (1774)
- Axiomatic probability — Andrey Kolmogorov (1933)
CONTINUE THE CONVERSATION
Source texts
- Wisdom Theory 100 Mental Models (2020) (Wisdom Theory)
- Evidence-Based Decision-Making How to Leverage Available Data and Avoid Cognitive Biases (Andrew D. Banasiewicz)
- Thinking in Systems and Mental Models Think Like a Super Thinker (Dawson, Marcus P)