Tobias Welz, Germany

Why this page doesn't say “this referee tends to…”

We measured whether the identity of the referee affects the result: Measured 8 August 2026: 5,645 matches across 6 leagues, 131 referees with at least 20 matches. no measurable effect.

• Spread test: The variation between referees is BELOW what chance alone would produce if referees had no effect at all (0.84×).
• Persistence test: A referee's bias in the first period does not predict their bias in the second (r = −0.12). A real tendency would persist.
• Assignment bias removed: Bias was computed against the model's expectation for that match, not the raw win rate — which cancels the “big matches get experienced referees” effect.

In samples of 20–30 matches some referees show striking deviations — but the persistence test shows these are noise. Building a story out of such figures is easy and engaging; it is not true.

Card tendency is a separate question: the card data has been ingested and measured — where a referee has a record, it appears below. The gap between referees is above chance, but a referee's past deviation is not enough to call a future match; so we publish no forward-looking card claim and there is no card market in the product. How we measure