Rupa Patel never wanted to be a financial engineer — she wanted to be a maths teacher. However, her skills in conveying difficult mathematical concepts to others, as well as a love of maths, enticed her into the exciting field of financial mathematics. Now she models risk, travels Europe and occasionally finds time to herself to examine the maths of her job in detail.

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.

A biologist has developed a blood test for detecting a certain minor abnormality in infants. Obviously if you have blood samples from 100 children, you could find out which children are affected by running 100 separate tests. But mathematicians are never satisfied by the obvious answer. Keith Ball uses information theory to explain how to cut down the number of tests significantly, by pooling samples of blood.