Friday, June 17, 2011

How Teams Performed Relative to Last Year

One thing we can look at with z-scores is the improvement of teams year on year relative to the average team. I wanted to see which teams improved/declined from last season to this season, so I looked at the difference in the z-scores of points between last season and this season (this obviously excludes the teams who were promoted this season, as they were not in the league last year). The results are in the table below. Positive scores designate improvement over the past year, negative scores designate decline.

Man City     +.72
Man United   +.47
Bolton       +.25
Fulham       +.11
Wigan        +.09
Arsenal      +.07
Sunderland   +.06
Liverpool    -.09
Tottenham    -.14
Wolves       -.17
Stoke        -.18
Chelsea      -.28
Everton      -.29
West Ham     -.55
Blackburn    -.57
Birmingham   -.88
Aston Villa  -.92

The top of the list is pretty straightforward. Since I spent a lot of time effusively praising United in my earlier post, it is no surprise to see them high on this list. It is also not surprising to see my beloved Manchester City up at the top, as the club spent a lot of money during the offseason to improve the team. Bolton also makes sense as they were poor last season and over-performed this season. Fulham is a bit unexpected, seeing as how they were quite good last year (particularly in Europe) under Hodgson.

The bottom of the list seems to make sense as well. Villa were top 8 last year, but tumbled down the table this year. Birmingham and West Ham were relegated and Blackburn struggled after firing Sam Allardyce.

Another interesting point is that if you add all of the above changes up, you get a sum of -2.30, meaning these 17 teams declined on average. Obviously, if we include all 20 teams the mean should be zero. This indicates that the three promoted teams from this year (Newcastle, West Brom, and Blackpool) had higher z-scores than the relegated teams from the year before (Burnley, Hull City, Portsmouth). Having some very good promoted teams clearly made it more difficult for teams to improve relative to the average team.

Wednesday, June 15, 2011

How good were United this year? Part 3

Last post on this I swear. One thing that I should have mentioned: while the z-scores do adjust for the balance of the league, they don't adjust for the overall quality. Perhaps there is more balance because the good teams got worse, not because the bad teams got better.

We can attempt to answer that question by looking at the EPL's performance in Europe. If English clubs performed relatively poorly in Europe, we could conclude that the quality of the EPL was low in that season and if they performed strongly, we could conclude the quality of the EPL was high (this of course assumes there is no worldwide drop in talent, which would seem to be unlikely in the extreme).

Fortunately, UEFA has a statistic used to judge every league's performance in Europe, called the UEFA coefficient. This year, the EPL's coefficient was the highest it has been in 5 years at 18.357. This, combined with a very balanced league, means that the EPL was stacked this year and that United were the best team of the lot. Again, all the evidence points to United being a very strong team this year, contrary to the popular narrative.

Sunday, June 12, 2011

How good were United this year? Part 2

So in my last post, I looked at Man United's z-score for points and noted that it was better than the average Premier League Champion and the second-best score of any United team over the past ten years. Clearly, if we look at points, they were very good this year.

But what if we looked at the z-score of their goal differential instead? After all, goals are what produce wins and looking at points makes all wins the same, when there clearly is a difference between winning all your games 1-0 and winning them 6-0. How did United fare in this measure?

Not as well, but not poorly either. United this year had a goal differential of 41, good for a z-score of 1.98. This is below the average goal differential z-score for a title-winner (2.04), below Chelsea last year (2.15), and similar with Liverpool two years ago. However, it is higher than their score in 2008-09 when they also won the title and is second only to the 2006-7 United team, which had an excellent z-score of 2.36. More evidence that United were actually pretty good this year.

Saturday, June 11, 2011

How good were United this year?

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.