David Spiegelhalter OBE is Winton Professor for the Public Understanding of Risk in the Statistical Laboratory, University of Cambridge and author of The Norm Chronicles. He is a fellow of Churchill College, Cambridge, a Fellow of the Royal Society and has a string of honorary fellowships and doctorates.  He is an ISI highly-cited researcher.

Professor Spiegelhalter’s background is in medical statistics, particularly the use of Bayesian methods in clinical trials, health technology assessment and drug safety. In his post, he leads a small team that attempts to improve the way in which the quantitative aspects of risk and uncertainty are discussed in society. He also works closely with the Millennium Mathematics Project in trying to bring risk and uncertainty into education.

You can catch Professor Spiegelhalter talking about coincidences, What a coincidence! on Thursday 13 March.

The Science Festival asked Professor Spiegelhalter a few questions about coincidences, taking risks and how to measure whether it’s worth taking a risk.

CSF: What is a coincidence?

DS: I use the definition suggested by some famous statisticians: “a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection.”

CSF: Why do we take such stock of coincidences?

DS: The phrase ‘perceived as meaningfully related’ says it all – humans seem to be hard-wired to construct meanings to events, even if the rational part of our thinking (if such a thing exists) tells us that it’s just good or bad luck, with no reason at all.

CSF: What’s the most surprising coincidence you’ve come across?

DS: Personally, I don't experience coincidences much, but that’s probably because I’m not only spectacularly unobservant, and also uncommunicative with strangers, and so I miss all the wonderful connections that we may have had.  I believe that mindful, social people will experience more coincidences, but I don’t have empirical evidence for this.  But some great ones have been sent to our website – I particularly like the occasions in which someone is walking past a phone box, which rings, they pick it up and it is for them (which also happened in an episode of Sherlock, but that wasn’t chance).

CSF: Is chance the same as probability?  

DS: When putting numbers on events, I try to use chance for situations which, practically speaking, have agreed odds due to the physical set-up, such as flipping fair coins, lottery balls, radioactive decay and so on.  I say ‘practically speaking’, since the movement of coins and lottery balls might be considered completely physically determined, but just too complex to analyse and predict.  In contrast, I use probability for the more common situations where our uncertainty is due both to what we can’t know and also to what we don't know, such as the voting intentions in Scotland, future climate change, who will win the World Cup, or what happened to Lord Lucan.  In fact, any situation where we have to use judgement, rather than just maths, to make reasonable bets.

CSF: Based on probability, can you predict the outcome for most things?

DS: No, using probability is not about making predictions, but producing good odds.  People say that Nate Silver got all the US States right in the last election, but in fact he did not make any concrete predictions – he just gave more than 50% probability to the winning candidate in each State (and he was extremely lucky with Florida, where he was only just in favour of Obama, with a probability of 50.3%).

CSF: What’s the difference between a bad risk and a good risk?

DS: Every action in the face of uncertainty carries risk – things may turn out as you would most like them to, or not.  I would say a bad risk is where a reasonable observer would feel the odds are stacked against you; a good risk is when they appear in your favour.  Of course, these are all just judgements about ‘good’ and ‘bad’ – neither the odds nor the value you give to the consequences are objective states of the world.  In fact, I believe that the entire edifice of risk assessment is a human, subjective construction, and that it is pointless, although tempting, to talk about the ‘true’ risks (except in the situations of ‘pure chance’ I discussed above, where we would generally agree on the odds).

CSF: What are the chances of someone winning the lottery? And could they increase their chances?

DS: There’s around 1 in 14,000,000 chance of winning a share in the jackpot. And, in spite of what some websites claim, there is nothing you can do to increase these chances except buy more tickets, possibly 14,000,000 of them. Of course, if you want to increase your share of any jackpot you are lucky enough to win, maybe you could choose less popular numbers, such as above 31 to avoid birthdays.