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!