Cards, fouls, and what the referee is actually worth
The booking markets are priced off season averages by most of the people quoting them, and off referee folklore by most of the people betting into them. We measured both. One of those two things is real, and it is not the one with the following.
The test that decides it
Split every official's matches in half by date, take the league-season average out so a strict competition is not mistaken for a strict official, and ask whether the first half of their career predicts the second. If it does, the effect is a fact about the person. If it does not, it was noise that looked like a pattern.
What moves a card line
The largest pre-match term is not the official at all: it is how close the match is priced. A contest produces cards and fouls; a mismatch produces neither, because one side has the ball and the other has stopped contesting it. Corners run the other way, and are not modelled here for the reason given below.
The officials, shrunk
Every multiplier below has already been pulled towards one by how little we know about that official. A referee with nine matches barely moves off average however strict those nine looked, which is the whole difference between a model and a list.