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# Dwarfs, the normal distribution and the exceptional

A Page 1 article in today’s Wall Street Journal describes an extravagant bachelor party for a Fidelity Investments trader that was held in March 2003. I am not particularly given to reading about the excesses of the upper classes. This is perhaps a defense against bouts of jelousy.

What caught my attention in this account, however, is that the expenses for this party included hiring a dwarf. The dwarf in question, Danny Black, is the part-owner of Shortdwarf.com which rents dwarfs for rates that start at \$149 per hour. Mr. Black is quoted as saying, “Some people are just into lavish dwarf entertainment.”

I am pleased to report that I am not among that group of people. I did not have a bachelor party when I was married but, if I had, I am absolutely certain that it would not have occurred to me to hire a dwarf for it.

In the interest of full disclosure, I wish to report that I have more than a passing interest in the subject of dwarfs. At 5 feet 5 inches, I am below the average height for American men which is at present about 5 feet 9 inches. The standard deviation for height is just under 3 inches. For those of you who have forgotten everything you might ever have known about statistics, the standard deviation is a measure of dispersion from the mean. To keep things simple (since my concern is not mathematical in its origins), roughly 68% of men will be between 5 feet 6 inches and 6 feet in height. My height places me within 2 standard deviations from the mean. In practical terms this means that when I stand among a group of men, I cannot see anything.

My height has presented few problems. Once when shopping for a new pair of blue jeans I discovered a store that had sorted them by inseam with the shortest ones on the top shelf. Now, this shelf was not at eye-level. In fact, I was unable to reach the jeans that were in my size. I concluded that the jeans had been organized by a person of average height since both the very short and the very tall were similarly inconvenienced. Beyond clothes-shopping and getting a good seat at the movie theater, however, falling outside one standard deviation from the mean has not presented any serious problems in my life.

Neither has it presented any significant opportunities. I do not begrudge Mr Black his \$149 per hour. (Well, OK, maybe a little.) This might well be a very good way to make up for the lack of opportunities in other areas that his short stature might cause. As it happens, Mr. Black’s business is headquartered very near where I live. Unfortunately I am not short enough to cash in. And yet, despite my capabilities in other areas, I cannot expect to be paid at the rate of \$149 per hour.

Which finally brings me to my point. Neither is Mr. Black compensated for his capabilities. Here is an individual with the motivation and insight to start up a niche business that caters to the desires of some individuals to have a very short person about. (I do not know how successful he is but a mention in the Wall Street Journal cannot hurt.) He is rewarded only incidentally for his motivation and insight. In fact, he is paid for having a height that is on the extreme tail end of the normal distribution.

There is a lesson here for all of us and a commentary about the state of our society. We reward most highly the exceptional. This is as it should be. But it is significant to note that that aspect of the individualf that is exceptional might make very little difference. It is only important that it fall far from the center of the normal distribution.

It is little wonder that movie and sports celebrities are idolized, particularly by youth, since money and attention will tend to go toward individuals outside the mainstream. It is only in our maturity that we might come to realize that those particularly worthy of note are of average height, intelligence and ability who do the important work of everyday living without expectation of riches or recognition.