'Rating' English football league teams

Yardstik can be applied to the English football leagues — with interesting results.

Because it doesn't impose any artificial contraints on the fixture list, but works with whatever data is provided, Yardstik is not restricted to a single, completed season for one league. It can simultaneously process as many seasons as required — completed or not —whilst still giving greater preference to the more recent results. This makes it possible to generate a consolidated rating for all four English leagues plus the Conference league. The games that relegated and promoted clubs play in their previous seasons provide the bridging evidence between leagues.

Summary

Charts and results are provided in detail in 'Leagues: Analysis'.

Yardstik ratings are based on goal differences. A rating difference between, two clubs implies a similar goal difference between those clubs.

The chart on the left shows the league difference between the top and bottom teams of each league and the extent of the overlap between successive leagues.

Average goal differences at the top and bottom are, as might be expected, quite large: four goals in the Barclays Premiership and three and a half goals in the Conference league. In the intermediate leagues the difference is much less: two goals in the Coca-Cola Championship and only one goal in Coca-Cola leagues one and two.

The degree of apparent overlap in the intermediate leagues is suprisingly high. On the basis of this analysis, clubs could be promoted from the Coca-Cola League Two to the Cocal-Cola Championship, or from the top of the Conference League to Coca-Cola League One. Certainly there appears to be a case for much larger promotion/relegation bands — particulalrly within the intermediate leagues.

The reason that ratings are compressed in the intermediate leagues is that footballing talent clusters around a mean just like any other skill or aptitude. Indeed when averaged across a team of eleven players, the clustering phenomenon might be expected to be more pronounced.

The histogram of team 'ratings' shown in the chart to the right exhibits a bell curve very similar to the example shown in 'Yardstik in Operation'.

Comparisons of the league tables versus Yardstik ratings can be found in 'Leagues: Analysis'

Interpretation

The Yardstik algorithm rewards consistency in determining its team ratings. It concerns itself with which teams are beaten, as much as how many teams are beaten. One reason why these team ratings are less discriminating than, and sometimes even inconsistent with, conventional league tables is the that for many teams the the comparative status of the opposition seems to have little impact on the outcome of a game. The Yardstik ratings suggest that there is a comparatively modest gradient in talent from the bottom of Coca-Cola League Two to the top of Coca-Cola League One. In these divisions, differences in position apparently owe rather more to luck than they do in lower or higher divisions. If it seems heretical to suggest that team rankings are as much a matter of chance as they are of skill, consider for a moment, whether the league tables would be 'flat' even if the teams were actually clones of one another — but still subject to the unpredictabilities of wind, weather, health, environment, disposition, refereee and, of course, opposition.

Another reason that Yardstik results differ from league rankings, is that it 'ages' results progressively. A match played later in the season is considered more relevant than a game played at the beginning. This means that Yardstik has absolutely no problem bridging seasons. The off-season represents nothing more than three months' additional 'ageing'. If the objective is to assess comparative football talent, it is perverse to consider the evidence of nine months to be of equal value whilst the evidence of anything older is of zero value — although with suitable changes to data and input parameters, those conditions could easily be applied.

'Home Advantage'

If the yardstik algorithm is applied directly to the results of individual football games, the resultant ratings are more compressed than those shown here.

Home advantage is an obvious source of possible distortion. In standard mode, Yardstik assumes that, except for chance, the outcome of a match between A and B reflects a difference in football playing ability — and nothing else. But if the result is biased in A's favour by the advantage confered by playing at home, then it is no longer reasonable to expect an A v B match to have the same outcome as a B v A match.

To obtain the results given here two approaches were employed. In the first case, home and away games were matched and aggregate scores alone were used to generate ratings. This is the 'single-pass variant'. The data fed to the program looked like this:

Crystal_P Arsenal 1:1,1:5 26/12/2004

The first result is as it would normally be declared: Crystal Palace 1 : Arsenal 1, whilst the score and the team order of the second have been swapped from the original: Arsenal 5 : Crystal Palace 1. The new date is an 'average' of the original dates.

The data processed by Yardstik is the 'average' result: Crystal_P v Arsenal 1:3. (This is why ratings are delivered in units of 0.5).

The disadvantage of this approach is that it invalidates all unmatched games. This means that until comparatively late in this season, few recent comparisons are available to Yardstik. To address this problem a second approach was devised. It is a two-phase algorithm (the double-pass variant) which uses the ratings that emerge from the 'single-pass variant' to infer team-specific home advantages. These can then be used to remove the home-advantage-effect from all results (whether matched or not).

The data fed to the program now incorporates all matches. Thus:.
.
.
Birmingham_C Charlton_Ath 1:2,1:1 25/01/2004 (matched)
Birmingham_C Chelsea 0:1 21/08/2004 (unmatched)
Birmingham_C Crystal_P 0:1,0:2 29/12/2004 (matched)
Birmingham_C Everton 0:1 13/11/2004 (unmatched)
.
.
The raw output looks like this:

Player, Player-group & Rating listed in descending order of Rating
                               Discounted    Player    Home
Group                  Player    Matches     Rating    Adv.
.
.
   1                Telford_U      25.5        99.8     0.0
   1                Torquay_U      59.7        99.8     0.0
   1            Brighton_&_HA      58.4        99.7     0.4
   1             Plymouth_Arg      58.4        99.7     0.9
   1              Rotherham_U      58.3        99.7     0.7
   1                Wimbledon      28.2        99.7     0.5
.
.

League Table Comparisons

Yardstik results can be compared with the League tables. This is the Premier League table as of 30/3/2005. Yardstik ratings are based on games up to and including 28 March 2005.

The output from three Yardstik runs is summarised here. The first two columns use an ageing factor of 0.1. That places significant weight on the result of the 2003/4 and 2002/3 seasons. The first column (starting with Chelsea at 104.0) has been calculated using the 'single-pass variant' of the program, whilst the second column has been calculated with the 'double-pass variant' — i.e. it exploits estimates of home advantage calculated in the first pass). The third column is the estimated home advantage (where statistical analysis suggests it to be significant at a level of 10%). The fourth and fifth columns are based on the single-pass variant using a faster 'ageing factor' of 0.5, that should make them more directly comparable with the 2004/5 league results.

Home Advantage: Interpretation

'Home advantage' is calculated as an average of the residual errors that arise when the predicted result (based on rating differences) differs from the actual goal difference. It is attributed to 'home advantage' because the average is tabulated on the basis of the home team. Viewed entirely dispassionately, it would have been equally valid to calculate an "away advantage" or to analyse the predictive residuals in terms of closeness to end of season, incidence of rain, or even direction of wind.

To a football agnostic, these estimates of 'home advantage' do pass at least one test of plausibility. They are almost all positive, the marked exceptions being those of the top three teams. Manchester United's home advantage fails to clear a 10% significance test, but would be negative if it did. Why top teams should have a negative home advantage is a mystery, but a possible reasons include: support bases that are national, rather than regional, a predisposition to field weaker teams at home, or confidence that a smaller goal-advantage should suffice for matches played at home.

yardstik.ini

The single- and double-pass variants of the Yardstik algorithm necessitate some changes and additions to the yardstik.ini file:

Notes:

1) But not necessesarily the same goal difference. Not only is chance involved, but so is the principle maximum efficiency or minumum effort. There is little point in winning by (say) five goals if two will do. Not only is less effort involved, but the risk of injury is reduced. The concept is discussed in greater detail here.

2) except when modified by the maximum efficiency or minumum effort principle.