Refereeing stats

When @fitzpas posted the stats below, I got a bit excited about them, partly as they matched my worldview



However, when I thought more about it, I'm not sure it was really reliable. Both the graphs are related to the number of red cards, and the number of red cards in each case is a very small number. Two more sendings off would entirely change the nature of the graph. The sample size for sendings off is too small to be conclusive - it might be a sign that refs are going easy on Rangers, or it might be a statistical anomaly.

So I decided to process the data from the year before to see if stood up to scrutiny. Also added some new metrics, for example for each team i also processed data for the team playing against that team. So Celtic's opponents are the all the other teams in the league, but just in their games against Celtic. I also added stats for all home teams and all away teams, and, because the rest of Scotland go on about it, the combined stats for the "old firm" and their opponents.

Here's a league table sorted by fouls per red card



the first thing to point out is that Falkirk had no sendings off, so though I artificially made it 1000 to keep my spreadsheet happy, technically their rating is "infinity". In general, the stats are all over the place. It takes Aberdeen 47 fouls to get a sending off, and Hamilton
507. If referees were 10 times stricter with Aberdeen than Hamilton, we would know about it.

So I think this stat has little practical value. The only possible exceptions are that home teams have to do a lot more fouling to get a man sent off than away teams. This can be backed up because cumulatively there is a lot more data to back that up. To a lesser extent you could argue that there is no evidence that the old firm combined are treated more leniently than their opponents, as there is quite a lot of data for that too.

here's the league table sorted by Yellows Per Red. Again, Falkirk have infinity, and the other results are similar to the previous table, so I'm not going to go in to that in detail.



Now on to Fouls per Yellow



the advantages of this sorting is that there are a lot more yellows than reds, so there is enough data to suggest that it might be reliable. One thing I would point out is that Celtic's opponents can commit over 10 fouls before it leads to a bookings. With Rangers' opponents that is cut by a third. The stats for Celtic and Rangers are similar to each other, but the way their opponents are treated are significantly different. People were also slow to get booked in Motherwell; both Motherwell and their opponents. The home team are slightly favoured over the away team, and Aberdeen are not treated particularly well (though there opponents are treated in a neutral way).

The strength of this measure is the amount of data available in one year, but the downside is it has less impact on the outcome of the game. The number of sendings off would be more significant, but you would have to process about 10 years of data to make it reliable, which I haven't done.