I was looking through this blog at the number of posts that I’ve written about referee performance, and it turns out that there are, as of this date, five posts under that category.  Three of the articles are reviews of research publications, so I’ve actually written very little about the subject.  That’s about to change very shortly.

As I’ve written before, referee analytics is a delicate area of football analytics.  Most of the current analysis is very simplistic and not very valuable, from tabulations of fouls, cards, and penalties to team records in matches called by a referee.  Context is important in order to make effective analysis of teams and players, and for referees even more so.

Yet contextual data on referees is not readily available; it’s not possible to detect correct rulings or incorrect non-rulings without a human, and knowledge of a referee’s position is rarely made public.  Moreover, match referees are not only responsible for enforcing the laws of the game, they are also expected to manage the flow of the game while keeping tensions from boiling over.  Currently, there are few metrics that communicate the flow of a match with the exception of effective match time.

I’m introducing a couple of metrics that could inform the conversation about the flow of a football match.  They are mean time between fouls (MTBF) and mean time between stoppages (MTBS).  Mean time between fouls/stoppages are arithmetic means of the intervals between foul events (those that are whistled by a referee and awarded with a free kick) or stoppage events (foul events and all other events that stop play).  Both ideas are borrowed from concepts in reliability engineering that measure failure rates and the average time between mechanical failures.  One shouldn’t press the analogy too far, but the flow of a football match can be likened to a machine.  In that respect, it is reasonable to ask the following:

• How often does the match stop?
• How often does the match stop due to actions by the two teams in the match?
• How often does the match stop due to actions by the referee?

I expect MTBF and MTBS to inform answers to these questions as well as follow-on questions from the answers.  In future posts I will apply the metrics to data from this summer’s World Cup.