# 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.

## The Premier League

The Premier League is the main English football league, with 20 teams each playing a home and away against each other team making, 38 matches for each team in a season, and 380 matches altogether.

## The National Lottery

The UK National Lottery began on 19th November 1994 and there had been 1242 draws up to 20th October 2007. The jackpot prize is won by choosing in advance the 6 numbers drawn from a set of balls numbered from 1 to 49.

## League Tables

League 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!

## Refining Lottery Tests

National Lottery Level 3 showed how the standard $\chi^2$ goodness-of-fit statistic could be adjusted to allow for non-independence induced by the need to have exactly six unique numbers appear at each draw.