Big Team Bias and Penalty Favoritism

Since I had the two hours Spurs usually waste to fill up, I decided to look at club popularity, penalties given and conceded, and average league rank from 2014-15 through 2020-21. The idea was to see if penalty favoritism correlated better with league rank (and, arguably, merit) or popularity, in order to get some data regarding the presence or absence of big team bias in awarding penalties. Here are the three lists:

A. Penalty favoritism; net difference between pens awarded and pens conceded from 2014-15 through 2020-21 (from Transfermarkt)
1. Man U 29
2. (tie) Man City 23
3. Chelsea 23
4. Liverpool 14
5. Spurs 3
6. Arsenal 1

B. Average league position from 2014-15 through 2020-21
1. Man City (2)
2. (four way tie) Chelsea (4)
3. Liverpool (4)
4. Man U (4)
5. Spurs (4)
6. Arsenal (6)

C. Current-ish popularity (from
1. Manchester United 73,209,297
2. Chelsea 49,017,967
3. Manchester City 40,103,333
4. Arsenal 37,758,903
5. Liverpool 37,485,389
6. Tottenham Hotspur 22,109,552

As you can see, the stronger correlation is between penalty favoritism and club popularity. The large gap by which Man U leads in penalty favoritism is congruent with the large gap by which it leads in popularity. The correspondence between lists A and C would be perfect if Arsenal were two places lower in C. If we admit the probability that penalty favoritism correlates positively both with league position and with popularity, one explanation for that is that Arsenal have been crap. A reasonable conclusion based on this data is that while we would expect league position to have some positive relationship with penalty favoritism, popularity correlates more strongly with it.

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