What really bugs me about football is the siege mentality that a lot of fans have: that the FA/UEFA/refs hate their club specifically. This is particularly relevant given who is refereeing the Chelsea game today. One particular prevalent conspiracy theory is that Howard Webb is biased in favour of United. Because FIFA would definitely hand control over a World Cup final to a biased ref, right?
I'm aim to prove that this theory is false by a statistical analysis of Manchester United's results in the premier league under Webb compared to their results under other refs. If Webb really favors United, their goal differential should be higher when they get ref'd by Webb compared to when they get ref'd by others.
EDIT: skip to the bit at the bottom if you can't be bothered to read this.
United's performance in the EPL under Webb (2005-2006 season to 2011-2012 season)
Games: 31; Goals For: 66; Goals Against: 38; Average Goal Differential: 0.9. Source: http://www.transfermarkt.co.uk/en/manchester-united/schiedsrichterdetail/verein_985_318.html
And under other refs:
Games: 266; Goals For: 492; Goals Against: 169; Average Goal Differential: 1.21. Source: http://espnfc.com/team/stats/_/id/360/season/2011/league/eng.1/manchester-united?cc=5739
Wow! So United actually do significantly worse under Webb! But there is a selection bias issue here: given that Webb is considered one of the best refs in the league, he often gets the big games (i.e. games against good opponents), and we ought to expect United to score fewer and concede more against better teams. A good (but by no means the best) way of determining the quality of their opposition is whether or not they qualified for the Champions League that season (I have not got the time to look at the league position and GD of every one of their opponents).
Webb ref'd 11 games against CL qualifying opponents in this period, 35% of the total games he ref'd. Others therefore ref'd (7 (number of seasons) x 6 (number of games against qualifiers per season - Utd qualified every season) - 11 = 31, which is roughly 12% of the total games they ref'd.
Now let's normalise the quality of these opponents. In other words, lets assume they were of average quality. How do we do that? Let's see what the average goal differential of a CL qualifying team was compared to league average (0) over this period.
My source (http://www.premierleague.com/en-gb/matchday/league-table.html) gives a value of 41.9, which means that on average (divide by 38), CL qualifying teams had a 1.1 goal differential per game.
This lets us calculate what United's average goal differential would have been if the CL quality opponents they'd faced been of average quality: we should expect that United would have had an extra 1.1 goal differential against these opponents if they had been average. But let's be as generous as possible to the conspiracy theorist and assume that the CL teams perform particularly well against United and have an extra 1.5 goal goal differential against United compared to average teams.
So the normalised goal differential under Webb is: 0.9 + (0.35 x 1.5) = 1.425, and under others is: 1.21 + (0.15 x 1.1) = 1.435. United still performs (slightly) better under Webb!
This means that there is no statistical evidence that Webb treats United any differently from any other team. There are methodological flaws in this analysis (e.g. I didn't take into account number of home vs away games (which looks pretty similar anyway), I didn't account for the difference in quality of non-CL qualifying opponents faced under Webb compared to others), but I hope my generosity to the conspiracy theorist (giving CL teams an extra 1.5 GD) convincingly makes up for these.
P.S. Of course, all the refs could be United fans - to disprove this would require a statistical analysis of ref mistakes made in United games versus other games, rather than United results, but those statistics will not be easy to compile.
TL;DR: Howard Webb is not a United fan - people who think that he is are suffering from confirmation bias, where people only take into account the evidence in favour of their position. The powers that be are not in some big conspiracy against anyone, just enjoy the football :)
I did a proper regression with this to see what the average effect of Webb reffing was on the number of points (not GD) United earned. I found that accounting for the fact he ref'd more 'big games' (defined as any against the 'big six'), we see that Webb does slightly improve United's results, but not enough to yield a significant result. In other words, this is probably caused by random sampling variation (the p value is .699 which is very high; that means that 70% (!) of the time if we took a random other ref would give United a higher average result). Stats is fun you guys! (the STATA output is in the comments) So yeah, Webb doesn't really hate us.