There are numerous occasions where we need to estimate the likelihood of something occurring and we can get it very wrong indeed. What is the probability of encountering a monster traffic jam on the way to Auckland Airport – just how early should I leave for that flight? What are the chances that my visitor will actually turn up on time – or at all? Bookmakers make their living on estimating probabilities so it’s always amusing when they get it wrong (I have deep issues with gambling).

First, congratulations to Leicester City on winning the English Football Premiership.

At the beginning of the season, so I am led to believe by Radio NZ, one of the major bookmakers in the UK had them as 5000-1 outsiders. That’s five THOUSAND to one. Moreover, they thought it more likely, according to the odds that they were offering, that in the coming year:

1. Conclusive evidence would be found of the existence of the Loch Ness Monster

2. Barak Obama would declare the moon landings as faked

3. Elvis Presley would be discovered alive

Really? Come on. Yes, Leicester’s success was unlikely, but THAT unlikely? They had a flurry of success right at the end of the 2014-2015 season, avoided relegation (comfortably in the end) and changed their manager. There were hints that things could go well for them the following year. Offering such extremely long odds seems to fly in the face of the evidence that was there. Rank outsiders do occasionally win sporting events, or elections. It doesn’t happen only once every five thousand times.

I remember when I worked in industry in the UK we had an online tool for assessing business opportunities. If we put in a bid or project proposal to a customer, or were even having preliminary discussions with a potential customer, we entered the details into a database including such things as the likely size of the contract and what the probability was of winning it. That would be used to help with our financial planning.

However the reality, as our accountants kept telling us, was that the average person who had discussions with potential customers (for example, myself) was very bad at estimating the probability of success. We tended to severely overestimate the probability. That was evident just from an analysis of what we said were the chances and what actually transpired.

For example, they could pick out the entries where we said there was a 50% chance of securing funding and look at what fraction were actually funded. It wasn’t anywhere near 50%. Given that the organisation was full of mathematicians and physicists, this was quite amusing. It shows how difficult it is to get a real handle on probabilities.

I’m not sure what the accountants did with our estimates, but they probably halved them or more. Which is what I’ve done with my estimated chance of having my Marsden Proposal get to the second round. I find out later this week.

]]>Stuff also covered the story but without the mystery aspect, good thing because the stats given at the end of the piece kind of belie that approach.

“The previous year was another big year for twins with ten sets born out of 620 babies. In 2005 and 2006 there were 542 babies born, including six sets of twins. In 2004 and 2005 only two sets of twins were found among the 571 babies born and in the 2003 and 2004 year, there were sevens sets of twins and one set of triplets in the 557 babies born.”

So in other words the number goes up and down every year and this year just happened to be a cluster of births higher than average. Boring.

What’s the deal with randomness though and why are we so poor at recognising it? We tend to think of random events or locations as those that are approximately evenly distributed in time or space. This view of randomness however gives a false impression of what it means to be truly random.

Randomness is more a measure of unpredictability than it is of aesthetic impression. There are different ways of defining this property but one approach is to apply the criteria of an algorithm. An algorithm is essentially a series of instructions, the more instructions, the more complicated the algorithm. One such might be “1. from an initial number add 5, 2. repeat step 1.”. This would be an algorithmic representation of a sequence of numbers at regular increments of 5 eg 1,6,11,16,21.

Nothing random about that, the key here though would be that a sequence of really random numbers wouldn’t be able to be represented by an algorithm that was less complicated than the sequence itself, ie it would be it’s own algorithm and would not be able to be compressed any further.

What has this got to do with groups of twins? Well, if events such as the birth of twins are actually random (simplifying the world somewhat) then we would expect to see variations in the number of births in any one place. Based on this assumption we can look back at previous numbers to see whether this year is within the range we would expect.

Using the figures from the story and removing this year’s number and the year that only 2 twins were born as a possible outlier I get a range of between 0.5% and 2% of births being twins, with a high probability that normal variation will fall in this range. The percentage of twin births this year is 1.8%, high but apparently normal.

Now the sample size here is very small so I wouldn’t put too much trust in it but it is indicative that there is nothing really out of the ordinary going on here. According to the NZ Multiple Birth Association there were 900 multiple births last year in NZ (incl. triplets) this is about 1.4% of the 63,000 live births in NZ last year. So rough and ready these numbers may be but they aren’t too far off the mark, some places will be higher than average and others lower.

So when several rare(ish) events happen at the same time or place, consider; is this really unusual? What would we expect if it was just random?

- Miracles: What Do We Mean? (scepticon.wordpress.com)
- Is Your Boss A Better Liar Than You? Probably, Yes (scepticon.wordpress.com)
- The Big Dose of Random Returns! (escapistmagazine.com)

Filed under: Psychological, Sciblogs, Science, skepticism, Uncategorized Tagged: Multiple birth, New Zealand, Probability, randomness, Science

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