# Usain Bolt: It’s Just Not Normal

Usain Bolt‘s wonderful run in the Olympic 200-meter sprint reminds us that the normal distribution — the familiar bell curve beloved by economists and statisticians — can be wildly inappropriate when analyzing extremely selected samples.

This morning’s New York Times shows Usain Bolt’s new world record, relative to the 250 greatest 200-meter sprints ever. Not only does this not look like a normal distribution, it doesn’t even look like the tail of any standard distribution I’ve ever seen:

The full graphic, as a story board, is available here. (It is a beautiful example of using statistics to tell a story.) It should be clear from this chart why few thought that the previous world record would be broken anytime soon. (An interesting aside: This graphic shows that it is only a fairly recent phenomenon that the 200-meter typically yields a faster average speed than the 100-meter sprint.)

Extreme outliers aren’t that unusual in sports. The greatest outlier may well be Australian cricketer Donald Bradman, whose career batting average of 99.94 puts him so far ahead of any other cricketer that it defies comprehension. (Trivia note: Bradman played the piano at my grandmother’s wedding.) Here is a histogram of career batting averages conditional on being among the top 100 (among those with at least 20 innings):

Some argue that Joe DiMaggio‘s 56-game hitting streak is pretty extraordinary. So I put together a histogram of the great hitting streaks (among those longer than 30). DiMaggio is okay, but he’s no Don Bradman.

The key to all of these strange distributions is that we are focusing on the extreme tails of highly selected samples, where the usual statistical patterns rarely hold. These situations are highly atypical, but equally, incredibly interesting when thinking about the very greatest. (I’ve never understood the urge to call these “black swans,” given that black swans are actually fairly common birds if you know where to look.)

Those interested in how things change in extremely selected samples may enjoy Tim Groseclose‘s paper, “Extreme Sample Selection Bias: Conditions That Cause the Correlation Between Two Variables to Switch Signs.” Groseclose claims that this extreme sample selection can explain why nonmillionaire members of Congress win re-election more often than millionaires; why it shouldn’t be surprising that the greatest golfer is multiracial, even though most top golfers are white; and why high S.A.T.’s may actually predict lower subsequent incomes among those attending elite universities.

#### Hephaestus

Erica (#50) -

It's not that Jamaica is a one-hit wonder. It's amazing whenever a country with a smaller population manages to consistently produce world-class athletes. This is particularly true when their facilities are not in the same league as the big-budget countries.

Does this mean that there is something fishy? Of course not! Here in the United States, there are states that have produced far more than a proportional number of champions in a particular sport. This is usually a result of youth leagues, better coaching, and local interest.

Success begets success. When Iowans began winning national and then world championships in wrestling, it became a popular sport. As its popularity increased, parents encouraged their children to take part. With more wrestlers came more and better coaches. This has led to more college championships.

Does this mean that the relatively small population of Iowans have a genetic disposition to wrestling? Of course not. Does it mean that Iowans use performance-enhancing drugs? No. It simply shows that a focused program can produce excellent athletes.

#### Bryce

Michael Johnson and Jeremy Wariner both went to Baylor - a university with a track team that specializes in th 400m. Why did they go there? Because they specialized in the 400m. You think that because Jeremy Wariner got the silver and not the gold that makes his coach not a specialist in the 400m? Jeremy Wariner won gold in the 400m in Athens and has been the most consistent of the top 3 or so fastest 400m runners since then.

#### Chewxy

Don Bradman's average is now 100...

#### Proud Jamaican

Fitzy, I so agree with you. It is amazing how people can be so judgemental and in essence 'bad minded." How come a similar discussion is not being had about Michael Phelps. He has done something no other swimmer has done but it is accepted without question. The double standard is incredible. People look within yourselves

#### NG

Let us give up on this statistical nonsense. Interpret any way you want and the result is the same: Usain Bolt has achieved what no other sprinter has accomplished in history - he has won three olympic gold medals and set three new world records. That is simply phenomenol! He is the fastet human being alive.

#### Fitzy

What's this I am hearing about Tiger Woods and Barack Obama, not being black. For you all information, being black or white, is merely a social label used by one ethnic group to describe another. I don't care what Tiger says about him not being black or what anyone else say for that sake, the fact is, if someone with the same diverse back ground as Tiger woods, were to go in say, a restaurant, which didn't particularly like to serve black people, this individual would be discriminated against just the same. But I can understand where some people, the label "black" can be used in a convenient manner to suite the circumstances. So if you say a Tiger Woods or Barack Obama, some people find it easier to suport these individuals, if they first remove the the label.

On the matter of Jamaican sprinting. It is not just any one factor, it is all the above. First you must have the natural propensity, which is the genes which is responsible for the quick twitch muscle fibers, secondly, you must have the right environmental factors, conducive to the development of top sprinters, etc. a long history of achievements, dating back to the 1940s and an elaborate Boys and Girls Championship. These are just a few.
You must also take into account that most kids that discovers that he or she has a talent to run, sees this as a ticket to getting them out of poverty, and they have seen where it worked for numerous Jamaicans in the past, it gives them an enormous drive. So while it has been established that West Africans have a disproportionate amount of people with this gene, their environmental circumstances are different. Don't get me wrong, there are allot of poor people in West Africa but that is not the only factor we are looking at.

Jamaica has a long history of achievement in the field of Track and it's now becoming a well oild machine.

As far as Usain Bolt goes, what you are seeing, is a genetical anomaly. Some how genics have combind an above averege height sprinter with the fast turn over legs of someone allot shorter, this is not the norm. So now giving this combination and the perfect environmental conditions, you now have the recipe for the extraordinary.

People with lazy mentality like to simplify that which they do not comprehend, or just too lazy to do the research which would enable them to come to an informed decision. It is way too easy to just say, oh! he must be on drugs. When in reality he is not running any faster than anyone else but because of his height, he is covering more ground than everyone else. The same way you have people with extraordinary intellectual abilities which are given to the human race once every few hundred years. Extraordinary abilities in track and field are no different. and the beauty about that is, nature does not discriminate, it will drop one of these individuals anywhere it sees fit, even in Jamaica. So to all you arrogant and condescending "First World" people, I know it's hard to accept because you all for whatever reason, are supposed to be supreme. And as far as the Americans are concerned, remember you all voted in Bush twice, that clearly does not say much for your ability to judge a person.

(Pay attention to the message not my grammar I am a a Primary School Drop-out, not by choice but by circumstances)

Hear Ye! Hear Ye!

Citizens of Gotham, isn't it ingenious?
It is so easy to become an athlete that goes to the Olympics. Conversely, it is not easy to remain one.

Standards are all illusory. Just look at the honey bee; so does this insect need cement to build it's hive? That would be improving standards! How modern and nice would it all be to have cement honey combs, and what would happen to the honey?

Athletic standards are defined by each country, and if by some shot of the gun - they supercede an irrelevant expectation ....it's only excellence and true ambition.

#### and I'm not a Yankees fan

How about Babe Ruth as an example of a sports statistical outlier? Wasn't he hitting more homeruns than entire teams were in his best seasons?

#### Tina

I agree with Erica. Jamaica's training centers are definitely below the standards in the US yet they have continued to excel.
A one hit one wonder brings to mind someone who has achieved a task and has never been able to replicate it (Correct me if I am wrong). This is not the case for Jamaica. The first olympics we entered in 1948 - yielded us two gold medals and a silver...not bad for an upstart. While this was credited to Great Britain (we were not yet independent). We have done well ever since. Why it may seem a "one-hit wonder" is that WE have figured out how to hold on to OUR athletes.
Asafa Powell, Usain Bolt and Shelly Ann Fraser are loved and Respected because they turned down US scholarships and decided to study at home.
Had they not turned down these scholarships...Things definitely would have gone the other way.

#### Brian

There is no ONE REASON why athletes from a particular region, race, or country excel in any area. Or in any other area of life, for that matter. Why are we so quick to ask for one reason why all the Jamaicans are winning races but we accept a multitude of reasons (hard work, natural ability, student of the game, etc) why different white athletes excel at what they do?

http://www.racialicious.com/2008/08/20/white-men-can%e2%80%99t-jump-or-run-some-say/

#### erik de koster, brussels

before claiming that this graph is not a normal distribution, you should test for normality (using for instance a kolmogorov test). My hunch is that this is a perfectly normally distributed graph. Your batters seem to be on a Poisson distribution.

#### Matt Clancy

Extreme outliers are not called black swans because black swans are rare, but because the existence of the black swan was supposedly viewed as impossible. If Nicholas Nassim Taleb is to be believed, people used to say 'sure as a swan is white' to express the sentiment that something was certain.

#### Mike

Barricade - would love a link to one of those studies, particularly one of the 200m ones. As you said, Bolt's graph in the link you provided is sort of useless because he intentionally slowed down at the end.

As for the 400m... lung capacity is, in my opinion, the culprit there. I don't understand what you mean when you say the person who slows the least, wins. Seems sort of obvious, doesn't it?

#### Caribbean Queen

A high proportion of the world records are made by Jamaican born athletes (i.e. Sprinters who went to college and then became naturalized citizens). USA, Canada and Great Britain have the highest number of Jamaican immigrants. And most of the world record holders just happen to be "Jamaican -born" citizens of these countries - Linford Christie among others. Maybe there is something to the "gene theory".

Interesting piece - the comments about guys maintaining their speed is a good one.

It's actually been very well established that ALL the sprinters slow down at the end of the race - nobody is able to sustain the speed all the way to the finish, even in a 100m race.

Typically, what happens is that peak speeds are hit somewhere between 40 and 60m, and then held for about 10m before a gradual slowing down happens. You'll find this if you look at the 10m times from any world record ever set.

What sets Bolt apart is that he held his top speed between 50m and 80m, which means that for 30m, he was running faster than anyone in history has ever run. You can find these speeds here:

http://www.sportsscientists.com/2008/08/beijing-2008-men-100m-race-analysis.html

Unfortunately, Bolt celebrated in the last 20m and kind of cost us a 'full analysis", but every study ever done has found that the final 20m, athletes are slowing down.

This is even more true in the 200m event - peak speeds happen at about 130 to 150m, and then athletes slow down progressively. The winner is often the one who slows least. Same for the 400m - it's been researched to death and well known to be true.

B

#### Caribbean Queen

"Another question: How does a country as small as Jamaica always produce so many world-class sprinters every Olympics?"
I did a paper on this once in high school. And one other question is "Why don't we do as well in the middle distance and long distance sports?"
Some scientists argue that it is genetic because of our west african ancestry (I don't necessarily agree since that means that we would see a larger proportion of west african sprinters also.
I think it is a social factor. Sprinters in my country are revered. Most long and middle distance runners give up the sport after high school because there is no prestige. Or they leave the island for other places where they can excel (eg Sanya Richards). It is for this reason I think Brazilians tend to dominate World Cup Football.

Jamaica has always had sprinters but not many people realize that this set eg. Bolt, Fraser, Simpson and Powell are the first set of sprinters who are attending college at home (The University of Technology).Previously they were not awarded scholarships at home. About five years ago the University set up a plan to retain some of our own track stars by giving them the oppurtunity to stay at home and attending school with free tuition if they represent the school at the various meets. I expect jamaicans to do even better since now more than ever more of our sprinters are opting to stay home.

#### Erica

First and foremost, I want to say to Mike B. that you come across as a condescending and pretentious American. While it is true that Jamaicans dominate at sprints, I think it is unfair of you to deem us a "one hit wonder". It is also quite unfair for you to compare the US and their athletes vs. Jamaica's athletes.

Let's see where to begin; America is a country of 300,000,000+ while Jamaica is a country of less than 3,000,000; I would hope that US produces a multitude of talented athletes in lots of sports. Furthermore the US is the richest country in the world, that's a far cry from the third world status of Jamaica. I'm sure given a similar population size and financial resources, Jamaica could also produce a vast amount of talented athletes across the board.
Instead of downplaying Jamaica's accomplishments as that of a one trick pony, perhaps you can appreciate it even more given the aforementioned obstacles I have outlined.

#### TJ

"It's great to see, and yes, despite everything that's gone before, I do believe he's clean. "

Some people are just naturally gullible.

#### Larry Lard

"Runs scored, per out" ? That's just not cricket!

#### Dan Dartington

Wonderful to see Bradman get a mention in a US newspaper. His career is so dominant that any list of 'greatest ever athletes' without him at least in the top 5 is ridiculous.
I remember watching Michael Johnson setting his time and being sure I would never see anyone run that fast. It's great to see, and yes, despite everything that's gone before, I do believe he's clean.