You meet an old friend on holiday, you find your colleague shares your birthday, you win the lottery. Exactly how rare are these rare events? David Spiegelhalter investigates in his regular column on uncertainty and risk.

This is the second part of our new column on risk and uncertainty. David Spiegelhalter, Winton Professor for the Public Understanding of Risk at the University of Cambridge, continues examining league tables using the Premier League as an example. Find out just how much — or how little — these simple rankings can tell you.

League tables are controversial and for good reason. Few things are simple enough to be measured by a single outcome like, for example, the number of exam passes or successful heart operations. But even if we do accept a single yardstick, we haven't yet reckoned with chance, which by itself can produce apparent patterns to delight any tabloid editor.