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Among all the headline grabbing Olympic statistics from the past two weeks, you can’t have missed this one. GB’s four most successful male Olympians were all born 23 March. Amazing isn’t it?

Sir Steve Redgrave, Sir Chris Hoy, Mo Farah and Jason Kenny all get Happy Birthday sung to them on the same day.

It’s generated many articles suggesting that there must be some significance to what seems too incredible a coincidence. And last week Peter Allen, host of BBC’s 5live afternoon radio show, invited listeners to call in with their own stories of personal success relating to that auspicious birthday.

One gentleman suggested that, like the Olympians and others born under the star sign of Aries, he was a determined and successful individual. A mother expressed regret that her daughter, born on that date, was a gifted athlete who wasn’t spotted and slipped through the net. If only someone had realised the significance of her birthday?

Well perhaps that is the case. I can’t prove otherwise.

But, Sir Chris Hoy won his first gold in 2004 and next up was Jason Kenny in 2008. So, until 2008, March 23 wouldn’t have been seen as a trend setting birthday.

Then there is the question of how likely shared birthdays are anyway.

In fairness to Peter Allen, he did have a statistician on the show briefly, who explained what’s known as the ‘birthday effect’. I’ve written about that before here. It demonstates how many people you need in a group so that the chance of two sharing a birthday is 50%.

And it’s a surprisingly small number. You only need a group of 23 people.

You can show this using a mathematical equation, but there is another way which is easier to understand. Using a spreadsheet and a small algorithm it’s possible to create multiple groups of 23 people, all with random birthdays and check the results.

So, I created 1000 groups and, as expected, in almost exactly 50% of them two or more people shared a birthday.

And we can use the same ‘monte-carlo’ technique of trial and error to look at birthdays in thousands of much larger groups and compare them with real life examples – such as a team of Olympic athletes.

Team GB sent a group of 366 athletes to Rio, which is a rather convenient number since that’s just one more athlete than there are days in the year.

And I’ve compared their birthdays with those generated by 1000 separate trials . Each trial is the same size as Team GB and contains 366 randomly generated birthdays.

Now, you might expect that the birthdays would be evenly spread over the 365 days of the year without much repetition for both Team GB and the 1000 random trials. But, that’s not the case.

Here are the answers to some obvious questions comparing the two groups.

**On how many days of the year does no-one have a birthday?**

On over a third of the days in the year, 134, no-one in Team GB has a birthday. That is exactly the same as the average of the 1000 random groups of the same size.

**How many share a birthday with, at least, one other member of the group?**

For Team GB the answer is 63%, which is again exactly the same as the average of the 1000 trials.

**On how many dates do three people share a birthday?**

There are 18 dates where three members of Team GB share a birthday. In the trial group there is an average of just over 22.

**On how many dates do four people share a birthday?**

Now this is a bit unusual, there are 11 dates on which four people in Team GB share a birthday. That’s much higher than the trial average of just under 6. In only 7% of trials were there 11 dates generated.

The actual 11 Team GB dates are – 30^{th} Jan, 13^{th} Feb, 12^{th} March, 23^{rd} March, 24^{th} April, 9^{th} May, 20^{th} May, 21^{st} May, 19^{th} Sep, 6^{th} Oct and 30^{th} Dec.

*(NB There are no dates on which five athletes in Team GB share a birthday, theoretically there would be one.)*

**How successful were those eleven groups of current Team GB athletes?**

You’ll know that the four born on 23^{rd} March were the most successful as it includes Mo Farah and Jason Kenny. The others born on that day are Tom Farrell who was competing with Mo in the 5k metres and Katie Clark, Synchronised Swimming.

On eight of the other dates the athletes earned at least one gold medal between them.

Hopefully, from the above you can see that shared birthdays in large groups are far more likely than you might have imagined beforehand.

The only part of the analysis of Team GB that seems particularly unusual is the weighting of birthdays towards the earlier part of the year. This is consistent with some academic studies relating to sports. However, in itself it isn’t that meaningful.

It’s also very easy to get caught up looking for patterns that in reality aren’t there. In other words, there isn’t a reason for the pattern or trend as they’ve been generated randomly. Nassin Taleb wrote a book, ‘Fooled by Randomness’ that explains how serious this is in relation to financial markets. From managing risk to spotting fraudulent activity it’s a major issue.

There’s also the problem of ‘data-mining’, which is looking for data which fits your argument.

If I look at a separate group of the top 366 Olympians of all time, the most successful shared birthday *IS *the 23^{rd} March. There are five birthdays on this day, our four greats and a Soviet speed skater born in 1931 called Yevgeny Grishin.

It isn’t amazing that there are five sharing the same birthday. We should expect that in a group of that size. All that is unusual is that four of them are British.

But, I could sort the data differently.

March 23^{rd} is the 82^{nd} day of the year, but in leap years the 82^{nd} day falls on the 22nd March. And if I sort the information using the 82^{nd} day we get a different group. Chris Hoy and Jason Kenny were born in leap years on the 83^{rd} day of the year. While Steve Redgrave, Mo Farah and our Russian speed skater are joined by Alfred Schwarzman. Schwarzman was born in a leap year 22^{nd} March 1912, he was a gymnast representing Nazi Germany who later won the Iron Cross in WW2.

That isn’t quite such an auspicious group, but I deliberately searched for a more negative outcome to make a point.

As another example, there are 910 inmates at HM Prison Belmarsh according to Wikipedia. It’s very likely that six or more share the same birthday – would you see that as significant?

Would you phone Peter Allen if you shared that birthday?

- past performance is no guide or guarantee of future returns;
- the value of stock market investments can rise and fall over time, so it is quite possible to get back less than what you put in, depending upon timing;
- this blog does not constitute financial advice and is provided for general information purposes only.