What Is a Prior in Bayesian Forecasting? A Plain-English Guide

Every forecast starts before the data arrives. When our model says a team has a 49% chance to win tonight, part of that number existed yesterday — a starting belief about how strong each side is. In Bayesian forecasting that starting belief has a name: the prior.

What a prior actually is

A prior is your estimate of how likely something is BEFORE you look at the newest evidence. Not a guess pulled from the air — a structured summary of everything you knew up to this moment: long-run results, ratings, base rates, the boring history that doesn't change overnight.

The word comes from "prior probability" — literally, the probability prior to the new data. Its counterpart is the posterior: the updated probability AFTER the evidence is folded in. Bayesian forecasting is nothing more mysterious than a disciplined loop: prior in, evidence weighed, posterior out. Tomorrow, today's posterior becomes the new prior.

A football example you can check

Take a World Cup knockout match. Before kickoff our engine sets expected-goal rates for each team — numbers like "1.45 goals' worth of chances for the favourite, 0.95 for the underdog". Those two numbers ARE a prior: they compress team strength, form, injuries and history into a starting belief, before a single minute is played.

Then the match starts producing evidence. A goal, a red card, twenty minutes of one-way pressure — each event updates the belief. The 49% favourite who concedes early might drop to 30% in minutes. That live number is the posterior, recalculated over and over as evidence arrives.

The same structure runs everywhere forecasts exist: a weather model starts from seasonal base rates before reading today's satellite data; a market maker starts from historical volatility before reading this morning's order flow.

Why priors matter more than people think

A good prior keeps you calm. Without one, every headline drags your forecast around. One shock result and a prior-free forecaster rewrites everything; a forecaster with a well-built prior moves a little, because one match is one data point against years of history.

A bad prior poisons everything downstream. If your starting belief says an underdog has no chance at all — a prior of zero — then no amount of evidence can ever move you. Zero times anything is zero. Seasoned forecasters never assign true zero to things that are merely unlikely; the world punishes that arrogance regularly.

Priors are where honesty lives. Two forecasters can watch the same match and disagree, and the disagreement usually traces back to their priors. Making the prior explicit — writing the number down before the event — is what separates forecasting from storytelling after the fact.

Prior vs. the market price

Prediction markets offer a fascinating mirror. The price of a contract is, in effect, the crowd's posterior — thousands of participants' priors, updated by whatever each of them knows, compressed into one number. When an independent model's prior-driven forecast disagrees with the market price, one of three things is true: the model's prior is off, the crowd knows something the model doesn't, or the crowd is leaning on a bias. Watching which one it turns out to be, match after match, is one of the most instructive exercises in applied probability.

How to build a sensible prior (plain-English rules)

• Start from base rates. How often do favourites at this level actually win? How often do underdogs hold a draw? History first, story second.
• Weight slow evidence over fast. Years of results beat last week's highlight reel. Recent form matters — as an adjustment, not a foundation.
• Never use zero or one. "Almost impossible" is 2%, not 0%. Certainty is not a probability, it's a resignation letter.
• Write it down before the event. A prior recorded after the result isn't a prior; it's a story. Timestamps keep you honest.
• Let evidence move you — proportionally. Strong evidence, big update; weak evidence, small update. The math of that proportionality is Bayes' rule, but the discipline matters more than the formula.

The takeaway

A prior is simply your starting point, stated as a number and owned in public. It is the difference between "I always knew it" and "here is what I believed before, here is the evidence, and here is what I believe now". Good forecasting isn't about having no assumptions — it's about knowing exactly what your assumptions are, writing them down before reality arrives, and letting reality grade them.