Applied inference on real-world risk — open, rigorous research and the datasets behind it.https://inference.institute/enhttps://inference.institute/papers/three-in-a-hundred/https://inference.institute/papers/three-in-a-hundred/Of every hundred rapes recorded by the police in England and Wales, about three end in a charge and roughly two in a conviction. This paper takes that number apart and asks what would move it, reading the public record of how the system counts, resolves and fails these cases as structure, at three scales, with formulas borrowed from economics, statistics, machine learning, data mining, signal processing, stochastic processes, information theory and graph theory. The numbers that frame the field measure regime, not harm: recorded rape is spread across European states with a Gini coefficient of 0.52, as unequally as household income in Brazil. The outcomes those numbers meet, modelled on ~2 million rows of Home Office open data, are steep and uneven: only 3.5% of recorded rapes are charged, half are closed because the complainant withdraws, the charge rate varies almost fourfold across forces (18 of 44 outside statistical control limits), and a calibrated model shows offence type and the force — the location — drive whether a case is charged. The failures behind those outcomes are not formless: predictable bundles, three latent archetypes dominated by institutional self-protection, a decision grammar that recognises harm only when forced, an agency network with no single point of failure — so the breakdown is unread signal, not missing connection. Finally, simulations make the repair quantitative: supporting complainants so fewer withdraw roughly trebles convictions per recorded rape (the single biggest lever); closing the postcode lottery adds one to four thousand charges a year; and moving recognition upstream lifts the simulated share of cases reaching prosecution from 39% to 50%. The contribution is a reusable method, calibrated outcome models, three reform simulations, a structural leverage index, and a map from each pattern to a named reform owner; the work performs record-integrity analysis only, and excludes by design any judgement of a complainant's credibility.Thu, 04 Jun 2026 00:00:00 GMTSafeguarding