Thinking tools
Probabilistic thinking
Think in odds rather than certainties: estimate how likely each outcome is, and judge a decision by those odds rather than by the single result that happened.
The mathematics starts with the 1654 letters between Blaise Pascal and Pierre de Fermat on the problem of points, prompted by questions from Antoine Gombaud, the Chevalier de Méré; that correspondence is widely regarded as the birth of probability calculus.
Most people speak about the future as if it will or will not happen. Probabilistic thinking replaces that with a number: this launch has maybe a 70% chance of landing on time, this bug is probably in the cache layer and less likely in the database. You then update the numbers as evidence arrives, starting from what usually happens in cases like this one (the base rate) rather than from the vivid details of the case in front of you.
It works because the world is uncertain and a forecast that admits it can be checked and improved. If you say 70% about many things, about 70 of every 100 should come true; that is a standard you can measure yourself against. It also separates the quality of a decision from the luck of its outcome. A good bet can lose and a bad one can win.
Numbers can create false precision: a 63% estimate built on guesses is still a guess. The other common failure is reading a probability as a promise. People hear 70% as "will happen" and then call the forecaster wrong when the other 30% arrives. Estimates also err more often on the optimistic side, so the likelihood of your own estimate being off deserves a place in the reckoning too.
Example
On the eve of the US presidential election on 8 November 2016, Nate Silver's FiveThirtyEight model gave Hillary Clinton a 71% chance of winning and Donald Trump 29%, while Nate Cohn at The New York Times's Upshot put Clinton at 85%. Silver was criticised before the vote for giving Trump so much room. Trump won. Looking back in 2020, Cohn told the Associated Press: "We failed at explaining that an 85% chance is not 100%."
Where it applies
Put a probability on each risk in a design review and on each deadline in a plan, then compare against what happened. When a large language model (LLM) evaluation shows a two-point gain on a few hundred examples, ask how likely that gap is to be noise before you ship.
Think about it
Which outcome are you treating as certain right now, and what probability would you honestly put on it?
Applied it to something real? Log it.
Test yourselfIf a forecaster gives an event a 29% chance and it happens, what does that tell you about the forecast?
On its own, very little: 29% events should happen about three times in ten. You judge a forecaster by whether their probabilities match outcomes across many predictions.
Related models
- Margin of safetyLeave a wide gap between what you expect to need and what you build or pay, so that your errors and bad luck do not sink you.
- Asymmetric betsTake bets where the most you can lose is small and known and the most you can win is large, even if you expect to lose most of them.
- Second-order thinkingKeep asking "and then what?" until you have looked at the consequences of the consequences.
- The availability heuristicWe judge how likely something is by how easily examples come to mind, so vivid and recent things look more common than they are.
- The planning fallacyPeople predict their own projects will finish sooner and cost less than almost every comparable past project did.