Wednesday, 16 October 2013

Can Seven Games Change The World?

Seen in the context of recent Premiership history, Manchester City's 4-1 win over cross city rivals, United on match day five was a most impressive result. The champions of 2011/12 put the champions of 2010/11 and 2012/13 to the sword in a convincing win. However, when viewed through the lens of the early 2013/14 table, the outcome was much less noteworthy. Following the derby, United shared 8th spot with four other sides, including newly promoted Hull  and Newcastle, while City stood third, two points off joint leaders, Arsenal and Spurs. Had City beaten say Newcastle by a similarly large margin, the result wouldn't have been as noteworthy.

If United's defeat at City was embarrassing, their late September home 1-2 demise at the hands of WBA a week later, was probably even more disappointing. United now shared 12th to 16th, again with Newcastle and they found themselves gazing up towards two of the three promoted teams, Cardiff and Hull.

Untangling the mess that is early season results, as opposed to longer term class is fraught with problems. Ignoring home field advantage for a moment, City's 4-1 win taken in isolation indicted a single performance that may imply that they were superior to United by three goals. But one performance, heavily influenced by random chance isn't really sufficient to even show that City are the better side. Repeated matches between the sides are extremely unlikely to see City's average margin of victory maintain the heady heights of three clear goals. Indeed, they may not even win the majority of such games. In 2011/12, City recorded an even more impressive 6-1 win at Old Trafford, yet both sides ultimately finished on identical points totals, once 37 respective, additional games were added to that single result from late October, 2011.

The unwanted intervention of WBA also adds to the confusion. A single goal win away at United is the equivalent of a near two goal margin of victory on home soil. An achievement of similar, but slightly inferior magnitude to City's 4-1 win. So in a pecking order derived solely from three early season matches, the only possible conclusion is that City are better than WBA, whom are superior to United.

Interlocking formlines soon appear in league based tournaments. Stoke haven't played United yet, but both sides have entertained Premiership new boys, Crystal Palace, so an interconnected relationship does exist between the two sides. By the end of week seven, sufficient matches have taken place for common opponents to exist directly or indirectly for every side. Therefore, twenty connected simultaneous equations exist with the fixture list as the input and a result based parameter such as goal difference as the output and goal based ratings, that best describe these actual sequence of results can be relatively easily produced.

Least squares regression, usually via a matrix based approach is the standard way to solve simultaneous linear equations and provide team ratings based around a number of inter-related match outcomes. However, if City's 6-1 win in 2011 proved an unreliable indicator as to the true, long term worth of each side, how useful are such strength of schedule adjusted conclusions even after nearly 1/5th of a season.

An Inverted 20 x 20 matrix narrowly avoids meltdown.

Just as raw supremacy figures, derived from a single match, invariably greatly over or understate the likely long term talent gap between teams, the problem persists when the best ratings fit is produced by solving the linear equations for a two month season. The supremacy gap between the best and worst sides in the EPL over one completed season is usually in the order of 2.4 goals. The "gap" between United and City two likely top four finishers, on a single day was 3 goals and solving the 20 inter connected form lines after seven matches also produces wider than usual goal ratings gaps between the sides. The best side under this strength adjusted ranking is Manchester City, around 3 goals ahead the two worst sides in the 2013/14 EPL.

Strength of Schedule Adjusted Ratings After Seven EPL Games.

Team. League Position. SOS Adjusted Rating.
 (in Goals).
Change in Position.
Arsenal 1 2.19 -3
Liverpool. 2 2.13 -4
Chelsea. 3 2.64 +1
Southampton. 4 1.98 -5
Man. City. 5 3.12 +4
Spurs. 6 1.81 -4
Everton. 7 2.18 +2
Hull. 8 1.99 0
Man. Utd. 9 1.73 -2
Aston Villa. 10 2.31 +7
Newcastle. 11 1.63 -2
WBA. 12 1.62 -2
WHU. 13 2.09 +6
Cardiff. 14 1.69 +2
Swansea. 15 1.26 -2
Stoke. 16 1.33 0
Fulham. 17 1.02 -1
Norwich. 18 1.46 +3
Crystal Palace. 19 0.32 0
Sunderland. 20 0 0

The method combines a side's recorded goal difference and the "to date" records of their opponents, to seemingly quantify the difficulty of the task against the size of the achievement. West Ham jump six places under a revised, goal based, SOS appraisal. Manchester City jump to the top of the  new league by partly by virtue of an ability to score many and concede relatively few, coupled with a universal inability of teams to fully control how they distribute their scoring patterns. But disappointingly for WBA, they actually fall two places despite playing leaders, Arsenal because their outstanding win at Old Trafford came against a side currently in 9th.

The biggest climbers once SOS is factored in is predictably Aston Villa, who has faced the current 1st, 2nd, 3rd and 5th sides. The Villains are rated the 3rd best side over seven matches, despite their more lowly 10th actual placing. On Sunday, Villa entertain Spurs, an over achieving side based on their narrow wins against mediocre sides and failure to beat Chelsea or Arsenal from the top three. Therefore, if this short term methodology, when based around goals, is to have any validity, it would be expected that Villa should have an excellent chance of beating Spurs at Villa Park.

The goal gap between Villa and Spurs, corrected after seven matches is half a goal, stretching to 8 tenths once home advantage is allowed for, indicating a win% of around 55% for the hosts if these figures are to be taken wholly at face value. However, in the real world of bookmakers odds, Villa aren't even favourites, being afforded less than half the winning probability based around strength of schedule adjusted form from 2013/14 alone.

Villa are a mid to lower league side in the eyes of the bookmakers and Spurs are top four potential, despite the results of any manner of tinkering with their relative seven game achievements in an apparently unbalanced early season.

What should be evident from this exercise is that just as random variation can see equals thrash near equals on a single day, the record of a side over single figure matches can also be greatly influenced by chance. Villa benefited from an Arsenal red card on opening day (and red cards can be a disproportionately large influence on the goal difference acquired over a run of a few games) and they then recorded an unlikely, but permitted victory, both pre-game and in running against Manchester City.

What happened, happened, but even attempting to allow for differences in schedule strength, seven games are extremely unlikely to even partly remove chance from skill

In short "luck" influences short term results both in recorded, individual records and in the results of their opponents, which then are sometimes used to "better understand" a side's win loss record. Luck is recycled on both sides of the ledger to add certainty, but it merely replaces a much better arbiter of team ability, namely their record over a much longer stretch of matches.

As a way of celebrating recent, short term achievement, such as manager of the month awards, these methods are fine (as long as achievement is recognised as a combination of both the best and most likely the luckiest), but they fall well short, at least in the case of football's universal currency, goals, if they are used as an improved indicator of actual repeatable skill....or Villa would be 4/5 on Sunday against Spurs, rather than 3/1 and Manchester United would be 6/4 and not 8/15 to see off high-flying Southampton at Old Trafford.

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