Less than a month into the new season and some people are already asking if the season is settled. In France PSG have won their first four games, scored 7 and conceded none. In England Manchester City has won its first four, scored 10 and conceded none. This is all the more striking given that these are the two European clubs that have elevated themselves from also-rans to major powers with the brute force of player investment. But in Germany the traditional power, Bayern Munich has won three out of three, scored ten and conceded one and is behind the resurgent Dortmund only on goal difference. While neither Barcelona nor Real Madrid top the Spanish league at the moment they have between played four, won three and drawn one, scored seven and conceded none- it seems likely that one or the other will be on top soon.
So just how much can we infer after only a few games? I look at this in my new book Money and Football/Soccer. Based on English data, the more expensive team (measured by wages, but a suitably adjusted transfer value figure would be almost as good) wins about 50% of the time, loses 25% and draws 25%. The bigger the gap in spending the higher the probability. This does not sound so overwhelming. On a good day, the less expensive team can do well and two good examples on the weekend were Swansea beating Manchester United and West Ham beating Liverpool.
But over time, the Law of Large Numbers will apply. This law is the bedrock of much statistical analysis and says simply this- if a trial is repeated many times over then the frequency of any particular outcome will equal the probability of the outcome on any given trial. So if the probability of a coin coming down heads is 50%, then if you toss a coin 50 times or 100 times then percentage of results that are heads will be close to 50%. If the more expensive team has a 67% probability of any game that does not end in a draw, then over the season the more expensive team will win about 67% of all games, which will be a higher percentage than any other team, and hence will almost certainly win the league.
This is borne out by the data. In the 20 year period 1993/94 to 2012/13 the most expensive team (measured by wages) won 9 Premier League championships, the second most expensive won 7 times, the third most expensive won 3. Not exactly a guarantee of success, but almost.
So yes, PSG and Manchester City are likely to win their national leagues, but less because of their flying starts and more because they are vastly outspending most of their rivals. By the same token, while Bayern, Barca and Real are not on top of their leagues yet, they are likely to do so thanks to the law of large numbers.