UFO Occurrence Base-Rate Simulator

Base-Rate Fallacy

True anomaly base rate 1 in 10,000

Report reliability P(report|anomaly) 95%

False-positive rate P(report|mundane) 3%

Naive intuited P(anomaly)

–

Bayesian posterior P(anomaly)

–

Reports observed

— from genuine anomalies

— from mundane causes (false positives)

How it works

A "sighting report" almost always feels like strong evidence for the rare explanation, because report reliability sounds high (often 90%+). But reliability alone doesn't tell you the odds — you also have to weigh it against how rare the genuine anomaly is versus how common the mundane look-alike is. Bayes' theorem combines both:

P(anomaly|report) =
   P(report|anomaly)·P(anomaly)
 ───────────────────────────────────────────
   P(report|anomaly)·P(anomaly) + P(report|mundane)·P(mundane)

True anomaly base rate — how rare genuine anomalies really are in the population of events. The rarer, the harder even a reliable report has to work to overcome it.
Report reliability — the chance a genuine anomaly actually produces a report (true-positive rate). This is the number people mistake for "the answer".
False-positive rate — the chance a mundane event (aircraft lights, drones, satellites, balloons, ball lightning) also produces a report that looks the same. Because mundane events vastly outnumber genuine anomalies, even a small false-positive rate floods the report pool with mundane cases.

The classic medical-testing version of this same fallacy: even a "99%-accurate" test gives mostly false positives if the disease itself is rare enough. The diagram on the right partitions every simulated event into genuine vs. mundane, then into reported vs. not — the reported slice is what you actually observe, and its two colors show the true mix. Watch how the gold (genuine) reported slice stays razor-thin next to the orange (mundane false-positive) slice even at high reliability.

Genuine anomaly (rare) Mundane cause (common) True-positive report False-positive report