I spent an evening adjusting football statistics for how much of the ball each team had. The correction was obvious, took ten minutes, and made the result measurably worse. The mistake is not specific to football. It happens any time you normalise a count by an exposure variable — requests per user, errors per deploy, sales per visit — and it is invisible unless you measure the thing you were trying to fix. The setup I have a vector space of 1,419 footballers built from 5.3...