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How well are Premier League teams really doing?

[Skip straight down to the alternative league table]

Update, morning of 2016-09-10

I got asked last night: How come United are above City in your table? (It's the Manchester derby this afternoon, United v City.)

The answer is in two parts:

  1. United have beaten Hull (2nd in the alternative table below, with 100% record in their other matches), whereas City's three wins were all against lower-ranked opponents (West Ham the highest of them, ranked 7th);
  2. United have played 2 of their 3 matches away from home, but City have played away from home just once.

So the evidence so far, limited though it is after just 3 weeks of the season, is that United are very strong. City, because they have played lower-ranked opponents and more of their matches at home, have not yet had the same opportunity to show how good they might be this season.

More subtle is the answer to an obvious follow-up question: How come Hull are above City and Chelsea? The explanation is that Hull's two victories were both against high-ranked opposition (Swansea in 6th place, Leicester in 8th); and Hull's only defeat was against Manchester United who are very strong. Had Hull won or drawn against Man Utd they would be top of the alternative league table, by quite a distance; the fact that they lost that match moves Hull down, but not very far down because they lost against such strong opponents. By a narrow margin, Hull still get ranked ahead of Chelsea and Man City.

We are only 3 weeks into the season, though. It could all change after today! (If City win today they will go top --- I hope that's obvious.)

By David, on 2016-09-09

Here is the alternative league table that I showed at the end of my talk at RSS 2016 yesterday. After the teams have all played just 3 matches:

  Pts alt  
MnU 9 2.33 They won against Hull; and have played 2 matches away.
Hul 6 2.04 Beat Swansea (away) and Leicester; lost only to Man U
Che 9 1.95 Their wins include lower opponents; and only 1 away match
MnC 9 1.94 Their wins include lower opponents; and only 1 away match
Liv 4 1.63  
Swa 3 1.60  
WHU 3 1.54  
Lei 4 1.54  
Eve 7 1.53 Beat Stoke and WBA; drew with Tottenham
Bur 3 1.45  
Ars 4 1.36  
Tot 5 1.35  
Mid 5 1.19  
Sto 1 1.15 Lost to Everton and Man City; drew with Liverpool
WBA 4 1.01 Only win was against Crystal Palace
Bou 1 1.00  
Sun 1 0.77  
Wat 1 0.77  
Sot 2 0.68 Drew with Sunderland and Watford at home
Cry 1 0.64  

The teams are ordered not by the usual "points already in the bag", but by their "alt" (alternative league table, or adjusted league table) values which reflect, in a mathematically consistent way that takes account of opponent strengths and home advantage, the teams' relative standings as of today. The alternative league table answers the question "How well would we expect each team to fare in the league if they continue performing as well/badly as they have done in the matches they have already played this season?" The numbers in the "alt" column are interpretable as expected points per match over the whole season.

The right-hand side of the table explains why some teams move up or down the table, relative to their "points in the bag" standing. The most striking change is that Hull are ranked narrowly above Man City and Chelsea who each have 3 more points in the bag --- the reason being that Hull have only played relatively strong opponents so far (as judged by the "alt" position of those opponents).

The statistical model that underlies the "alt" calculation is a generalization of the well known Bradley Terry model --- a generalization tuned specifically to the purpose of answering the above question. It comes out of joint work with Heather Turner, and we are currently finishing a paper on it for formal academic publication.

It's important to know that the "alt" score is not a prediction. It is what is often called "retrodictive" --- see, for example, a brief explanation of the difference here by Ken Ashby. In our forthcoming research paper we'll show mathematically why our method, i.e. the one that leads to the "alt" above, is the right retrodictive method for double-round-robin leagues with a 3-1-0 points system.

Given the high level of interest in it at the RSS conference, I'll keep the table updated online as the season progresses. And will do the same for some other leagues!