League Tables

As of the 23rd May 2022 this website is archived and will receive no further updates.

understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

Many of the animations were produced using Flash and will no longer work.

Lotto IconLeague tables are used for football teams, schools, hospitals, songs, films and everything else that can be ranked in some way. But do they mean anything? How much are the rankings just due to chance? We can explore these ideas using probability theory. We would all hope that the UK National Lottery is unbiased so that any ball is just as likely to be chosen as any other. Even so, making a ball league table based on their frequency of appearance provides many little surprises - surprises that could easily be misinterpreted in league tables presented in other contexts. Start on National Lottery - Overview , play with the animations, and go on as far as your maths will allow!

The football Premier League appears to be a straightforward league table. But we can quantify how much of the observed spread of points is due to chance, and even assess how likely it is that the team at the top of the table really is the best team! Start on Premier League - Overview and see how you get on.

We shall be dealing with league tables for institutions such as schools and hospitals at some point. For the moment we point out that:

  • there are often genuine, interesting differences between institutions
  • these differences may be reflected in the performance indicators used, but generally rather indirectly, either because of lack of relevance of the indicator, bias in its measurement, or simple random variation
  • classification and/or ranking based on performance indicators is therefore prone to considerable error
  • reporting should acknowledge this possibility of error, which should be quantified, as when reporting a clinical trial
  • errors might be reduced by by only classifying in extreme categories when there is strong evidence: this could lead to few, or even none, being placed in extreme categories