An alert reader sent me link to a
href="http://africa.reuters.com/odd/news/usnPEK21146.html">stupid

article published by Reuters about the Olympics and Astrology.

It's a classic kind of crackpot silliness, which I've described

in numerous articles before. It's yet another example of pareidolia - that is, seeing patterns where there aren't any.

When we look at large quantities of data, there are bound

to be things that *look* like patterns. In fact, it would be

surprising if there weren't apparent parents for us to find. That's

just the nature of large quantities of data.

In this case, it's an astrologer claiming to have found

astrological correlations in who wins olympic competitions:

Something fishy is happening at the Olympic Games in Beijing. Put it all down to the stars.

Forget training, dedication and determination. An athlete's star sign could be the secret to Olympic gold.

After comparing the birthdates of every Olympic winner since the modern Games began in 1896, British statistician Kenneth Mitchell discovered gold medals really are written in the stars.

He found athletes born in certain months were more likely to thrive in particular events.

Mitchell dubbed the phenomenon "The Pisces Effect" (pisces is Latin for fish) after finding that athletes born under the sign received around 30 percent more medals than any other star sign in events like swimming and water polo.

Swimming and water-polo - but not diving or synchronized swimming. Why? Well, because if you add their data in, the 30% figure goes down, and doesn't look so impressive anymore.

In the history of the Games, the big winners in the overall medals haul were born under the signs of Capricorn, Aquarius and Aries. They boasted a significantly higher number of golds.

In other words, if you look at an arbitrarily chosen 1/4 of the year, athletes with birthdays in that 1/4th of the year have tended to be more likely to win in the olympics. And note the "significantly higher",

without any numbers to support it. It's a fake correlation: With 12 astrological signs, you'd *expect* to be able to find some way of breaking it onto fourths that produced one fourth that included an uneven distribution.

Checking out the birthdates among the Beijing winners produces some intriguing results.

For fencers looking to deliver a sting in the tail and make it to the podium, Scorpio is the right sign. Two of the three Beijing medallists in the men's individual sabre event were Scorpio, he said.

For pole vaulters charging down the track, it is better to be born under Taurus, the sign of the bull.

Look at the scorpio thing there. Wow, 2 out of 3 medals went to

people who's astrological sign is associated with their sport! Amazing, right? Not really. There are three different individual fencing

events at the olympics - epee, foil, and sabre; and each of them have

separate mens' and womens' events. So there are 18 medals in

fencing. Work it out: 12 signs, 6 groups of 3 medalists. Gosh, what are the odds that one of those 6 groups will include two people with the same

astrological signs?

The fact that you can find a fencing competition with two medalists with the same astrological sign really isn't a surprise. But it sounds nice because Scorpio's symbol has a stinger, and it's got a strike sort of like a fencing attack. But that's post-facto rationalization; for just about any other astrological sign, you could find a way of justifying it. If it was Taurus or Aries, you could talk about the charge in to strike. Sagittarius, the archer, should be obvious. Leo, the lion, like a great hunter. Aquarius, the fluid strike and defense. And so on: "patterns" like matching astrological signs are inevitable, and the human mind can always find a reason for associating the sign with the event.

Same thing with the vaulters. Why would pole-vault be associated with a charging bull? Well, because it just happened that there were winners

in the pole-vault with that sign - and you could describing the run-up

to the vault as "charging". Again, you could find all sorts of justifications if it were a different sign.

Of course, since this all sounds silly, the article needed to

throw in some reason to pretend that the crackpot behind this

rubbish was credible:

Even Mitchell was surprised by his own findings which he said were conclusive "and I really mean conclusive".

"I am talking of odds against chance of hundreds of thousands to one", he said, explaining the research he undertook after being made redundant from his IT job.

"And just for the record, I know a thing or two about statistics. I have a PhD from Glasgow University on statistical ecology and a further 33 years working on statistical data analysis," he explained on his website.

I think I know why this guy was "made redundant" from his job. It's because he's an idiot.

The most classic mathematical error of probability is what I call

perspective errors. These are errors where you take an event after

its occurred, and then work out a probability for it as if you were predicting it before it occurred. That's something that anyone with

any clue about probability should be well acquainted with; it's an

absolute textbook abuse. In fact, pretty much every probability textbook

includes a discussion of one particular example of perspective errors: the

infamous card-shuffling probability problem. Take a deck of cards, and shuffle it. Look at the order of the cards. What was the probability of getting *that particular order*? Roughly, 1 in 10^{68}.

But some card ordering had to be the result. The probability of getting

*a* result from shuffling the cards is exactly 100%; and the odds of any particular outcome are the same. You can't

take the result of the shuffle after the fact, and then say that it's

miraculous, because the odds of this happening were so small!

But that's what the crackpot astrologer is saying. He's taking a bunch

of facts that he's gathered after they've occurred, finding an apparent pattern to them, and then calculating the a priori odds of the pattern

he discovered. But patterns are inevitable.

There is a way to check things like this: there are some very nice

tools from the world of Bayesian probability that allow you to work

out the probability that the pattern you're seeing is really unlikely. But bozo's like this guy never bother to do that. For one thing, it's *hard*. Working out all the factors in the correct way is

a laborious process, where it's easy to make mistakes, miss elements, etc. But more importantly, the proper analysis has a tendency to make

an apparently impressive thing look unimpressive. You do a lot of work, and

and the end, that work tells you that you're wrong. No crackpot is going

to risk that!

And now, for the real prize of this piece. They saved the stupidest bit for last.

Explaining his eureka moment with all the zeal of a statistical crusader, he concluded: "Did you know that the distribution of Olympic swimming medallists against the tropical astrological zodiac signs can be almost exactly mapped by a polynomial function of the third degree?

"That's one to shut people up at a pub." (Editing by Nick Macfie.).

One of my least favorite topics back when I was studying CS in college was numerical analysis. I hated it. In NA, we spent a *lot* of

time on curve fitting. If you never went through the torture of an NA class,

curve fitting is a technique of taking a set of data points, and trying

to find a polynomial that fits those points.

Given any set of two points, you can find a line that goes through them. Given a collection of points that aren't a precise line, you can use linear regression to find the line that's the closest match (for various definitions of closest.)

Curve fitting is basically a generalization of that. Given any three points, you can calculate a quadratic equation that will fit them perfectly. Given a collection of data points, you can find the quadratic that's closest.

And so on. One interesting property of polynomials is that as the degree increases, it gets easier to create a polynomial that's very close to matching those points. Given almost any twelve points, I can find a cubic

equation that comes pretty close to matching them.

But the distribution of astrological signs isn't just any set of twelve points. In fact, it's a set of twelve points that we would expect to follow something close to a normal distribution. And for any set of twelve points with a normal distribution, I can guarantee that there's a cubic curve that's a really good match. There's just no way that that's *not*

an expected result.

Pretty much the *only* thing that that kind of reasoning is good for is impressing the folks down at the pub - with a few pints under

your belt, it might sound pretty good.

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I love how astrology is so vague that you can use it to explain almost anything. I'd like to see the data on what the ratio of of winners within a certain sign and total Olympians with that sign, and a ratio of the number of athletes per sign to total number of athletes for each sign. Also, is there a sign that is more common than others, I'd heard that September b-days are most common, so that could also change results....

Sometimes, very rarely, I start to feel bad for these people. They usually invest so much time, effort, and energy into their pet "theories", that they are completely unable to consider for a moment that they're wrong. In fact, I think they would self-destruct.

There

aresporting events where birth month has an uncanny effect on success. In particular youth athletics, and any events stratified by birth year or with age cutoffs are prone to an effect where at a particular birth month, performance seems to jump extraordinarily. You don't need astrology or even a complicated causative justification to explain this phenomenon, though -- the average competitor who is ten years and 364 days old tends to have an edge in most athletics on the average competitor who is ten years and 1 day old.Jack: The description I read of that effect (long enough ago that I don't remember details like where it actually was) also mentioned that once it's established it tends to last well beyond youth - the people who did better at eight or twelve years old (because of the extra eight or twelve months then) were more likely to stick with it into adulthood, even though fractional years make less difference once they get there.

Coincidentally, the signs mentioned as correlating with medal-winning success in the quotes at the beginning of the post appear, if Wikipedia is correct, at the beginning of the calendar year, which seems like a likely cutoff point for age divisions.

This might be a fun game: try to pick specific sports and random signs and try to see how hard it is to justify why they should be connected. I suppose you didn't mention Virgo as an example with fencing because the obvious connections are a bit puerile...

I wonder if we took the Chinese women's Gymnasts signs (using the Chinese astrological calendar - year of the horse, pig, dog, etc. since they are Chinese) and found an inverse correlation for those girls whom may not be 16. (sarcasm on) Yeah that would be proof that they were too young. (sarcasm off)

Er, for that last part, don't you mean a uniform distribution? I realize there is a slightly stronger likelihood of being born in certain months than others, but I don't see any way that a normal distribution would make sense in this context.

Nice post, thorough as ever. You have to wonder about his alleged qualifications...I've not studied much probability myself (I have a degree in maths, but didn't pay very much attention) and even I can see the parallels with the birthday problem.

In all the competitive sport I've done the cut off was 1st September for each age bracket, because it went on academic years. Not sure what happened if you were good enough to get beyond that system though.

Although it is worth noting that the time of year that people are born does make a real difference since they begin school at different ages and thus test differently in their first year etc etc and this has been shown to make a lasting difference in academia so I wouldn't say it's too far a leap to guess that it also makes a difference in sporting performance.

I happen to be an Aquarius, one of the "water" signs, so I should be good at some water sport. At 48 years young, I think the only event I might have a chance of winning the gold medal in is farting in the bathtub.

"He may know statistics, but he sure doesn't know his astrology. Everybody knows athletic success is determined by the position of Mars at birth. Sheesh." /Poe

"I think I know why this guy was 'made redundant' from his job. It's because he's an idiot."

Absolutely brilliant!

"In fact, it would be surprising if there weren't apparent PARENTS for us to find. That's just the nature of large quantities of data."

I think you meant patterns. I can see how that's a Freudian slip :D My parents are quite superstitious too

After comparing the birthdates of every Olympic winner since the modern Games began in 1896, British statistician Kenneth Mitchell discovered gold medals really are written in the stars...He found athletes born in certain months were more likely to thrive in particular events.Actually, there's a phenomenon called the relative age effect that suggests there's some truth to this. As an example, it has been shown that a greater portion of NHL hockey players are born in the months Jan-Mar than Nov-Dec. The proposed explanation for this is that when athletes first become involved in competitive sports, they all roughly enter around the same age. However, at the youngest ages, there are significant changes in motor development that occur within a short space of time. So, for example, a kid that turns 5 in January, has some motor advantages over a kid that turns 5 in December. These developmental differences may (perhaps unconsciously) be detected by coaches, and a self-fulfilling interaction ensues between coach and athlete (e.g., the developmentally advanced kid gets more attention).

The effect has been noted for both sports and academics.

My, my, my, it seems that astrology influences clear thinking of their critics,too.

Cherrypicking signs on one sport event is in fact pointless, right. Assigning "obvious" signs like Scorpio

to fencers, too. But it is not ok to defend distribution anomalies with "data patterns".

Let's gather all data about all Olympic games(~24, some are problematic because only few nations attended in the first games) and calculate the probability of medals during the year assuming equal chances. That will be very hard because

the days are unequal per sign, we need birth distributions (of different nations !) and and and....

If we did that successfully and find then that a high enough number of athletes in a field are differing strongly over their birth data without apparent reason (see below), then we have a problem where "data patterns" are irrelevant.

Apparent reasons could be found: Jack Bishop and others already mentioned that due to terms some children have eventually one more year to train which can give them a definite edge. Another natural reason, again without planet positions, is the perfect correlation between seasons and signs which cause possibly a difference (even when other variables haven't shown an effect).

If you never went through the torture of an NA class, curve fitting is a technique of taking a set of data points, and trying to find a polynomial that fits those points.You are not obliged to use a polynomial, you can use any function by calculating the sum of deviations and fed this to a minimizer.

One interesting property of polynomials is that as the degree increases, it gets easier to create a polynomial that's very close to matching those points.True, but it will be more a pseudo polynomial with many coefficients near zero. One to three coefficients will normally dominate.

Given almost any twelve points, I can find a cubic equation that comes pretty close to matching them.I see. How about a demonstration:

{11,12,14,18,23,15,8,13,25,18,15,13} ?

In fact, it's a set of twelve points that we would expect to follow something close to a normal distribution.I don't know what you expect, but I would expect an equal distribution with random noise.

And for any set of twelve points with a normal distribution, I can guarantee that there's a cubic curve that's a really good match.Would you like to sleep over that statement again ?

And, by the way, it is always easy to label others as "idiot" and forget that there is no way that someday somehow you will embarass yourself completely. You would like to be called an "idiot" for your lifetime, wouldn't you ?

I've not done much with statistics since a torturous class forming part of my Computer Science degree so don't feel hugely qualified to comment here.

One thing did strike me though - the three signs he mentions as being better than the others (Capricorn, Aquarius and Aries) are not sequential in the zodiac - they are separated by Pisces.

Now to the mind of a layperson finding three sequential elements from a 12 point set and demonstrating a difference between them and the rest is far more convincing than taking three non-sequential elements. As soon as one drops the sequential approach (even if they're just separated by one element), one may as well just pick any old three, in which case we are surely likely to see some kind of distinction between those elements and the set as a whole.

At least, that's what my brain intuitively tells me - I'm sure there's a good reason why that's not right :)

I bogged down with trying to determine the astrological signs of the top 5 countries ranked by total medals.

rank / medals / country / birthday / sign

1 / 110 / USA / 4 July 1776 / Cancer

2 / 100 / China / 1 Oct 1949 / Libra

3 / 72 / Russia / ?

4 / 47 / Great Britain/ 1 Jan 1801 / Capricorn

5 / 46 /Australia/ 1 Jan 1901 / Capricorn

Because China (with its own calender and astrology) is taken here by People's Republic of China. Harder is Russian Federation, given that Russia dates as a state to 862, and the Russian Federation by what date in the fall of the USSR?

For Great Britain I used the effective date (1 Jan 1801) of the Act of Union (1800), but what is the real date for the United Kingdom of Great Britain and Northern Ireland, and is that what we want? And USA celebrates 4 July 1776, but that's a somewhat arbitrary day, not when the key document was approved, nor signed, nor published, nor the date that the founding fathers expected to celebrate.

There's a good list in today's Los Angeles Times of top medal winners PER CAPITA:

rank medals country per capita medals

1 2 Bahamas 153,725

2 11 Jamaica 254,939

3 1 Iceland 304,367

4 5 Slovenia 401,542

5 46 Australia 447,844

6 9 New Zealand 463,717

7 10 Norway 464,445

8 24 Cuba 475,998

9 6 Armenia 494,764

10 19 Belarus 509,777

Anyone want to "explain" that astrologically?

COMMENTARY

Bahamas takes the crown in medals per capita

By Chuck Culpepper, Special to The [Los Angeles] Times

August 25, 2008

Just as England once lived under the Tudor, China once lived under the Ming and the American League East once lived under the Torre, we earthlings live under a dynasty these days.

It's a benevolent dynasty, the Bahamas dynasty -- its people do let us come visit their islands and serve us drinks with tiny umbrellas sticking out of them -- until it comes to the quadrennial test known as the Olympics, when they fluster the rest of us again.

The rest of the world tried everything to overthrow the Athens 2004 kings and queens in the crucial, telltale medals per capita ranking. We sent our Australia, runner-up in Athens with its population of only 20,600,856 and its vast collection of studs and studesses. We proposed Armenia, wrestling and weightlifting with the best from a population shy of 3 million.

We offered Slovenia, No. 5 in Athens, and we sent in Jamaica, No. 6 in Athens with its bolting Bolt and other track prowess, and we tried New Zealand, hearty archipelago, and as it concluded we even summoned Iceland with its 304,367 population and its gaudy handball team.

We just couldn't get to the Bahamas' MPC score of 153,725 -- one medal for every 153,725 Bahamians -- forged by medals in the triple jump and men's 1,600-meter relay. We couldn't stave off the three-peat, what with some connoisseurs of long division having figured the Bahamas the medals per capita winner in Sydney 2000 as well.

The ancient and misguided medals table claimed either China or the United States won the Olympics, depending on who does the miscounting, but we recognize arithmetical propaganda when we see it.

We know that although 110 medals or 100 medals can disappear into the U.S. or China with their tactically unwise populations, there are so many medals per person in Australia that it's practically a fashion accessory, that 47 medals for 60 million Britons constitutes a paradigm shift given Britain's recent sporting history, and that two medals in the wee Bahamas doth an empire make.

Medals per capita minutiae from Sunday's final day:

* The United States, 40th out of 70 countries in Athens with 103 medals and an MPC rating of 2,844,928, wound up 46th out of 87 with a better rating of 2,762,042. It really does supply hope for the future, just imagining how a gutty little overmatched MPC country might continue to make slight strides, like maybe if it goes rummaging around that pool in Baltimore for another giant fish-boy.

* Jamaica went from five medals and No. 6 in Athens to 11 medals and No. 2 in Beijing, while Cuba went from 27 and No. 3 to 24 and No. 8, while Trinidad and Tobago logged in at No. 11, which all goes to show that if you seek victory -- just as with the former Soviet republics -- you don't want to go messin' around down there in those islands. Sure, they look all sanguine and relaxing and everything, but that's just part of the lull.

Mitchell says, " I know a thing or two about statistics..."

It reminds me of my (departed) father's favorite adage, "Figures don't lie, but Liars can figure"