Coincidence?

Football fans pay attention! How would you like to make hundreds, maybe even thousands, of pounds each week by betting on your favourite team, guaranteed to get the result right every time? Well, now you can. I have devised a computer program, based on complex statistical algorithms, which is 100% accurate every time ... and I am willing to sell one of a limited number of copies to you for the modest sum of £1,000.

It may seem like a lot of money, but just think, you could make it all back in a single bet. I know you'll need convincing after all, who wants to part with a thousand pounds without some sort of guarantee so I'll give you the first prediction for free. In fact, I'll send you one free prediction every week for the next five weeks, and when you see I'm 100% accurate I can guarantee you'll be praying there is still a copy of the program left.

Imagine you received this email from me just before the start of the football season. Would you have taken up my offer and sent me £1,000? Of course not. But what if my first prediction had been correct? Luck, you'd have thought. But what when the second and third predictions were also correct? What about when all five turned out to be correct?

At some point, surely even you would have been convinced. After all, no one's luck is that good. Is it?

So, do you take me up on my offer: yes or no?

Well, if you said yes, I'm afraid you've just thrown away £1,000. Because there is no software, no statistical method. In fact, there isn't even luck. Just quantity. What you don't know is that I sent the same email to a million people at the start of the season. I divided them into three groups and told one group that one team would win, one group that the other team would win, and the third group that the match would be a draw. Once the result was in, I abandoned the two-thirds whose predictions ended up being wrong, and sent new predictions for week 2 only to the third of a million who had the right result in week 1. After the second match, one third of those people had been given two correct predictions, so I focused my attentions on these. After week 3, we're down by a third again, and the same after week 4, but at the end of week 5, there are around 4,000 people who have still only received correct predictions.

But these 4,000 people are seriously impressed, and even if only a few percent decide to take up my offer, I'll still make around £100,000!

But why would you fall for such a scam? Well, for a start, because you don't know about all the other emails and so you have no idea that you are simply one tiny part of a huge operation. Even if your natural caution would have stopped you from sending £1,000 to a complete stranger - even such an impressive and believable stranger - your own perceptions will have pulled plenty of similar scams on you. What about the times you've been impressed by astounding coincidences, without stopping to think just how many opportunities for coincidence there are in each of our lives? We notice the one extraordinary event, the occasional collision, but not the hundreds of thousands of near misses.

Another reason is that we seem to be constituted to try to find patterns in things. And, after all, there was a fairly impressive pattern here ... perhaps also reinforced by greed and the desire to get something for nothing.

There is no question but that we have evolved to be noticing animals. Every observation contains an opportunity: maybe a new source of food, early warning of a predator, or just some regularity or change we could exploit. Information, in fact. We notice first, and reason later ... if ever.

So we are biased in favour of seeing something rather than nothing, pattern rather than randomness, certainty rather than uncertainty, existence rather than nonexistence, predator in the bushes rather than random pattern of leaves and shadows, cluster of edible berries rather than random colouring of earth.

In the natural world, individuals who miss opportunities tend to be out-evolved, which is just a nice way of saying that they don't survive. And every single person now alive comes from an unbroken line of survivors. This has led to us being quick to jump to conclusions, quick to spot - or even to invent - patterns. And when we see a pattern, we intuit a cause; we don't just say, "how extraordinary" and move on, we want to go and look, and find out if there's something there for us.

Now let's return to the modern world. What if you shuffled a pack of cards thoroughly and turned over the top 10 cards and they were all red? What if you rolled a die 10 times and 6 came up 4 times? What if you flipped a coin ten times and turned up 8 heads? What would you expect to get if you flipped again? What if the numbers 1,2,3,4,5,6 came up on the Lottery this Saturday? Or what about six numbers which appear to be random until you happen to remember that these are the same numbers that came up in the previous draw? Does this make them more likely or less?

Or is your head just spinning?

These ideas of randomness, coincidence, uncertainty, what is remarkable and what commonplace, are very slippery and, not surprisingly, we make the most elementary mistakes when we have to deal with them. This is where we're most easily confused and fooled, because we didn't evolve to be good at probability. We didn't evolve to work out the odds on 8 heads out of 10.
If we want to face the challenges of the world we live in now, we can't rely on our intuition, becuase our intuition is matched to a very different world. We have to be cleverer than that: we have to reason.

Correlation?

Now let's move along to something along a slightly different path and we'll start by spending some time with my neighbours.

First up is Brian, the boy next door, who has just been given a guitar and amp for his birthday. Now each evening I'm treated to a mixture of Brian and Kurt Cobain pounding against my walls at top volume, over and over again as Brian dreams away his musical shortcomings. But I have some bad news for Brian. I've recently discovered a cast-iron statistical correlation between loud music and acne. I've meticulously gone over the figures several times, and there's no question - the more loud rock music you play, the worse your acne is. And with Brian currently desperate to catch the eye of young Jenny from number 37, I'm sure once I've shown him my research we'll have the volume down in no time.

And talking of Jenny, there she is now, buying an ice cream from the local shop. With her family about to go out to Australia for a holiday, I ought to go and warn her that the more ice creams there are sold, the more shark attacks there are. Again, I've done my research quite thoroughly, and the numbers do not lie. Perhaps I should recommend an apple instead!

Finally, let's pop into my local primary school to chat to the head teacher. I want to tell her about research I've uncovered which shows a clear and proven link between literacy levels and hand size in children. Bigger hands make better readers, it seems. With my son starting there in the autumn, maybe now is the time to set up some sort of hand-stretching programme - perhaps on Wednesday afternoons, now that PE's been scrapped?

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