Thursday 27 November 2014

Why Uttoxeter Probably Isn’t A Hotbed of Swimming Talent.

Occasionally the newspapers publish stats based articles that do not relate to sport, but do serve to highlight some of the dubious assumptions that can be made from such studies.

In the run up to Christmas, a raft of newspapers, including the Daily Telegraph reported that the drink driving capital of Britain was Llandrindod Wells, a small rural town in mid Wales.

LW had over the last 12 months 1.98 convictions per 1,000 drivers, second to Blackpool with 1.85 such convictions. After establishing the drink driving hotspot, a couple of reasons were then devised to explain the results, lack of public transport and a belief that an offender will not be caught in a rural setting, for example.

However, studies comprising very different sample sizes inevitably lead to conclusions that may fail to represent the true picture. Most famously a study decided that small schools are inherently better than large ones because they appeared in disproportionate numbers at the top of a performance table and is quoted in Daniel Kahneman’s book “Thinking, fast and slow”.

In short, sometimes samples are too small to come to a reliable conclusion.

LW has a population of just over 5,000. If the town follows national trends around 80% of the population will be able to legally hold a driving licence. So, 1.98 convictions per 1,000 drivers implies that 8 cases of drink driving were successfully caught and prosecuted in LW over the previous 12 months.

If we imagine that one such case went undetected. Now LW has a conviction rate of 1.75 per 1,000 and they fall to 4th in the table. Blackpool is now top and it may seem that seaside towns lead to drink driving.

If convictions drop to 6, LW fall to the middle of the roll of shame with entirely unexceptional conviction rates per 1,000 drivers. However, two extra cases added to the actual total catapults the town to 2.5 cases per 1,000, well above the next worst, Blackpool.

So it is possibly the size of LW population that has contributed to making them a headline in the national press. Blackpool, in contrast has around 118,000 drivers and the conviction rate is much less susceptible to large changes occurring in that headline rate because of small numerical changes in convicted or non-convicted cases. Blackpool has probably prosecuted around 280 drink drivers.

Percentages derived from small sample sizes can bounce around if the raw number of cases alters by just one or two. Just as small schools can be shown to be the best, as in the study quoted in Kahneman’s book, they can also quickly become the worst if just a handful of students produce poor results rather than excellent ones.

To keep the blog sports orientated, let’s use this dubious method to “prove” that Uttoxeter, population 12,000, a small town on the correct side of the Staffordshire/Derbyshire border is a hot bed of swimming world records.

Around 12% of the population are in the age group that would typically hold a world swimming record. So Uttoxeter has around 1,400 potential champions. They currently have one actual world record holder, Adam Peaty.

Therefore, Uttoxeter has 0.7 world record swimmers per 1,000 likely candidates. This of course would double if we made the conditions gender specific, but it is still good enough to give it the best headline rate in the country.

So Uttoxeter can be shown to be the place for swimming excellence, but only by using percentages applied to small sample sizes which obscure, rather than illuminate the less startling reality of the situation.

Sadly, it is a flawed conclusion, based on the exploits of a single outstanding swimmer, especially as the town doesn’t currently have a swimming pool!

(Update, we do now).

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