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Go figure

2 Feb 2009(Mon)

One of the most important things I ever learned about in school was correlation coefficients. It was ten years ago, I was sixteen, and a free-scoring Manchester United were fighting tooth and nail for the 1998/99 Premier League title with an Arsenal side boasting the best defence in the division. On the premise that this would fit my maths teacher’s instructions to ‘apply correlation coefficients to real life’ and produce a piece of A-Level coursework, I decided to use what I had learned in class to settle a debate amongst friends over the destination of the championship trophy. Which of football’s two most basic elements – scoring goals and ensuring that your opponents do not – was likelier to translate into more points in the context of a league season?


I won’t bore you with the details of the calculations – basically, you get a figure between -1 and 1, and the closer it is to either extreme, the stronger the relationship – but the results, as a United fan, were pleasing. The Premier League table for the previous campaign (1997/98) showed that the positive correlation between points and goals scored (0.905) was stronger than the negative correlation between points and goals conceded (-0.822), and similar results were repeated for each of England’s top four divisions. This meant that our Cole and Yorke should, therefore, trump their Adams and Keown when it came to the probability of trophies.


United, of course, went on not only to win the league but the FA Cup and Champions League as well, but despite having now assembled arguably the most valuable strikeforce on the entire planet, the team of 2009 is fast becoming better known for its strength at the back. Edwin van der Sar has just set a new English league record with 12 consecutive clean sheets, while five of United’s seven straight league wins since returning from the Club World Cup have been by a score of one to nil. Is defence, then, now becoming the best form of attack?


Again, the maths is looking good for United. Last season, conceding fewer goals (-0.945) was a stronger factor in winning points throughout the Premier League than was scoring more at the other end (0.879), and this has now been true in three of the last five seasons (with one, 2005/06, producing virtually identical correlations for each). In all but one – ironically, as it turns out, 1998/99 – of the five seasons before that, goals for had proved to be the more significant factor, and often by a comfortable margin.


Correlation coefficients (English Premier League)

1997/98: 0.905, -0.822 Attack most influential

1998/99: 0.827, -0.845 Defence

1999/00: 0.852, -0.806 Attack

2000/01: 0.905, -0.901 Attack

2001/02: 0.911, -0.798 Attack

2002/03: 0.931, -0.833 Attack

2003/04: 0.889, -0.899 Defence

2004/05: 0.837, -0.891 Defence

2005/06: 0.914, -0.914 No difference

2006/07: 0.954, -0.859 Attack

2007/08: 0.879, -0.945 Defence


The J League, too, may now be seeing the beginnings of a similar transition. The goals for column had always previously enjoyed the closer relationship with the points column since the single-stage season was introduced in 2005, but this trend was dramatically reversed last year, as goals conceded had a far stronger bearing on league position. This is not too hard to imagine if we compare the gung-ho nature of the title-winning Gamba Osaka side of 2005 (82 goals scored, 58 conceded) with the rather more cautious championship season for Kashima Antlers last year (56 goals scored, 30 conceded); nor if we remember that restricting their opponents to a meagre total of 24 goals helped Oita Trinita to a fourth place finish despite only scoring 33 times – fewer than everyone bar Albirex Niigata – themselves.


Correlation coefficients (J League)

2005: 0.807, -0.710 Attack

2006: 0.877, -0.740 Attack

2007: 0.820, -0.795 Attack

2008: 0.667, -0.810 Defence


This is not, however, necessarily indicative of a wider global trend. Figures for the top leagues in Spain, Italy, and Germany all suggest that scoring goals remains the most effective way of gaining points, while here in Asia, the same is also true of the South Korean K-League. Perhaps, then, a greater emphasis on defensive solidity is indicative of the strength of the leagues themselves – Manchester United’s European title in 1999 was the first for an English team in the post-Heysel era, and while only two more subsequently reached the last four of the Champions League before the trend shifted in 2003, the Premier League has produced two winners, three runners-up, and five beaten semi-finalists since. Japanese domination on the Asian stage, meanwhile, has also come at a time where domestic competition throughout the J League is more even and intense than ever before.


Correlation coefficients (other, 2007/08)

Germany (Bundesliga 1): 0.888, -0.737 Attack

Italy (Serie A): 0.934, -0.846 Attack

Spain (Primera Liga): 0.848, -0.788 Attack

South Korea (K-League): 0.769, -0.749 Attack


This could, therefore, mean that the stronger defences are again likely to prevail in the forthcoming 2009 J League season, and may also explain the fact that most of the few high-profile transfers this close season have involved defenders, but one should too perhaps exercise caution when considering these figures. It would take far more exhaustive analysis of more leagues over more years to come up with anything resembling definitive conclusions. Benjamin Disraeli did, after all, famously warn us of ‘lies, damned lies, and statistics’, and as worded no less profoundly by Homer Simpson, ‘facts are meaningless. You could use facts to prove anything that’s even remotely true’.

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