The reaction to this year's incarnation of Manchester United, the champions of England, was very interesting to watch. The consensus of the punditry seemed to be that they were not a very good United team, maybe even not as good as last year's team (which finished with five more points despite losing the title to Chelsea), but certainly the worst of United's title-winning squads. This is despite the fact that they had a long unbeaten run during the beginning of the season, with some comparing them to the Invincibles; they made it to the Champions League Final rather easily, only losing to one of the best teams of all time in Barca; they were so deep that they didn't include the Premier League's top goalscorer in the team for their most important game of the season; and they won the title by nine points. These facts appear hard to reconcile with the common view of United's season. If we look closer at the data though, we see that, surprise, it is the pundits who are wrong. Not only was this year's United one of their better teams in recent memory, they were one of the best teams of the entire decade.
One thing people seem to be forgetting is that we have to judge United's season in the context of the league this season. Due to relegation/promotion and the purchase/sale of players, the quality of the league can vary greatly from year to year. The league this year was very strong as all the newly promoted clubs made a good showing and one of the relegated teams even won the Carling Cup. We can look at how balanced the league was this year by looking at the standard deviation of the points earned by teams in the league. The lower the standard deviation, the more balanced the league. This year, the standard deviation was 12.8 points, signifying a highly balanced league, with less of a difference between the top and bottom teams (for reference, the last two seasons have seen a standard deviation of 18.3 and 18.9 points respectively).
So the league is more balanced this year. What does that tell us about Man United's season? Well, it tells us that we can't rely on points. Yes, United had fewer points this year, but they were playing a tougher schedule; we should expect them to have fewer points. What we can do instead is look at the z-score, a statistical measure that shows how many standard deviations above (or below) the mean a data point lies. In this case, United's points total was 80, the mean points total of the league was 51.5, and the standard deviation was 12.8, good for a z-score of 2.23. This score is basically telling us how well United are playing compared to the average team, the higher the z-score the better they are relative to the average team.
The great thing about z-scores is that since they look at performance in relation to the league mean in a given season, we can directly compare z-scores between seasons since they already adjust for league quality. So how did this season's United fare? In the past ten seasons, their 2.23 z-score was second only to their 2.33 mark in 2006-07, when they also won the title. Not only that, but their mark was the 4th best mark of any team in England over the past ten years, losing out only to 2004-05 Chelsea (z-score of 2.55) and 2003-04 Arsenal (z-score of 2.53).
(Note: I don't yet know how to post tables on here, but when I figure that out I'll post the data up here)
Now, if United were so good, why did some many pundits say exactly the opposite? The main answer is their points total is historically low for a title winner. Over the past ten years, the average points of the team that won the title is 87.8 points; United this year were 8 points below that (in fact, they were also below the average for the second-place team: 81.3). But when you look at their points relative to the league as a whole, it's clear that United had a great team this year.
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