What are the odds that a male born in 1963 who dropped out of high
school now has a net worht of 50 million dollars?

I need the exact answer as in 1 out of 1m....

Dear gapgapgap,


Please note that some of the assumptions and procedures in the following
computation are open to dispute. Due to the variety of subjective and
objective approaches that one can reasonably adopt, different people
will arrive at different results. What I offer is one of many different
lines of reasoning one might use to arrive at an answer. If you disagree
with the method detailed below, I am open to discussing it and revising
it before you rate my answer.


To compute the odds you are looking for, we must first determine how many
American males were born in 1963. We shall limit our attention to the
United States because economic opportunities are not the same in other
countries. If the male you have in mind was not, in fact, born in the US,
please advise me so that I can adjust the calculations.

According to the National Center for Health Statistics, there were
4,098,020 live births in 1963.

NCHS: Vital Statistics of the United States
http://www.cdc.gov/nchs/datawh/statab/unpubd/natality/natab98.htm

NCHS: ive births, birth rates, and fertility rates, by race of child:
United States, 1909-80 [PDF file]
http://www.cdc.gov/nchs/data/statab/t981x01.pdf


Although I have not found a breakdown by sex for births in that
year, we can arrive at a close estimate by extrapolating from current
sex-distribution statistics. In the year 2000, when people born in 1963
were about 37 years old, Americans in the 35-39 age group composed 8.07%
of the total population. Males accounted for 4.02% of this, making a
ratio of

  4.02 / 8.07  =  0.49814  =  49.814% .

Thus, we can estimate confidently that there were

  0.49814 * 4,098,020  =  2,041,388

or about 2,040,000 American males born in 1963.

University of Michigan: CensusScope: United States Distribution
http://www.censusscope.org/us/chart_age.html


Let us suppose that our male was 16 years old when he dropped out of
high school in his junior year, although you should feel free to correct
these details if they do not meet the facts of the case. At any rate,
the figures will not differ much in the vicinity of this year, grade,
and age group. According to the US Census, there were 102,000 male
16-year-old dropouts from Grade 11 in 1979.

US Census: Annual High School Dropout Rates of 15 to 24 Year Olds by Sex,
Race, Grade, and Hispanic Origin: October 1967 to 2004
http://www.census.gov/population/socdemo/school/TableA-4.xls


To compute the odds of dropping out, we divide the number of dropouts
by the number of males in this age cohort.

  102,000 / 2,040,000  =  0.05  =  5%

So the odds of this American male becoming a dropout are 5%, or 1 in 20.


Now let us turn our attention to the matter of net worth. Although I
was unable to find empirical figures for individuals worth $50 million,
we can extrapolate from other figures using the well-established Pareto
Law of wealth distribution. We should also note that it is meaningless
to consider the probability of being exactly 43 years old with a net
worth of exactly $50 million, since the number of individuals meeting
that precise description is negligible or zero. Thus, we shall consider
the probability that someone who is no more than 43 years old is worth
at least $50 million.

According to Forbes magazine's 2006 billionaire rankings, there are 18
Americans no greater than 43 years of age whose net worth is at least
a billion dollars.

Forbes: The World's Richest People, 2006: Sort by Age
http://www.forbes.com/lists/2006/10/Age_1.html


To scale this figure down to the $50 million group, we use the fact that
wealth is distributed according to Pareto's Law among the wealthiest 3%
of society.

    The wealth of the super-rich follows Pareto's Law: the number of
    people having wealth W is proportional to 1/W^e, where e is always
    between 2 and 3. [...] 3% of people's wealth follows Pareto's Law.

New Scientist: Why it is hard to share the wealth
http://www.newscientist.com/article.ns?id=mg18524904.300


    The Pareto distribution gives the probability that a person's
    income is greater than or equal to x and is expressed as:

        Pr[X >= x] = (m/x)^k,     m > 0, k > 0, x >= m,

    where m represents a minimum income.

Hewlett-Packard: Zipf, Power-laws, and Pareto: Appendix 1
http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html#ap1


We are considering the population of males no older than 43, which,
according to the CensusScope data cited earlier, makes up close to 34%
of the total American population, or

  .34 * 296,500,000  =  100,800,000

which is about 100 million. The figure of 296,500,000 comes from a
non-profit organization called the Population Reference Bureau.

Population Reference Bureau
http://www.prb.org/


So the proportion of billionaires in this population is 18 per 100
million. Using a minimum income of m = $1 and setting x = $1 billion,
Pareto's Law says that the probability of being a billionaire in this
group is

  (1 / 1,000,000,000)^k  =  18 / 100,000,000

          (1 * 10^-9)^k  =  1.8 * 10^-7

       (1 * 10^-9)^0.75  =  1.8 * 10^-7 .

Using the implied value of k = 0.75, we compute the probability of having
a net worth of at least $50 million within this group as

  (1 / 50,000,000)^0.75  =  1.68 * 10^-6

                         =  0.00000168 .

So the chance of a 43-year-old American male achieving this kind of wealth
is 0.000168%, which is much slimmer than the 5% high-school dropout rate
in his age cohort.


As for the combined probability of these two events -- dropping out and
acquiring a net worth of $50 million -- we must consider the influence
that one has on the other. If we assume that dropping out of high school
has no influence on one's earning power, the joint probability is the
product of the individual probabilities:

  0.05 * 0.00000168  =  0.000000084

                     =  1 / 12,000,000 .

However, it is not true that someone who drops out of high school has
the same economic opportunities as someone who stays in school. While
the effect of dropping out cannot be precisely quantified, especially
for this age group and income level, we shall use as a rough estimate
the fact that young men who did not earn a high-school diploma earn 27
percent less than those who did. 

    Men and women aged 25?34 who dropped out of high school earned
    27 and 30 percent less, respectively, than their peers who had
    a high school diploma or GED.

Public Broadcasting System: Society & Community: Starting From Behind
http://www.pbs.org/now/society/dropouts2.html


If dropouts earn 27 percent less, or only 73 percent of what high-school
graduates earn, then we might say that their probabilistic share of
every dollar is

    0.73 / 1.73  =  0.422

so we multiply the odds by this factor to obtain

  0.422 * 0.000000084  =  0.000000035

                       =  1 / 28,000,000 .
  

In conclusion, I estimate that the odds are 1 in 28 million that an
American male dropout born in 1963 is worth $50,000,000 today.


It has been an interesting challenge to answer your question. If you
have any concerns about the completeness or accuracy of my research,
please advise me through the Clarification Request feature and give me
the opportunity to fully meet your needs before you rate this answer.

Regards, 

leapinglizard
  

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billionaire list
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Request for Answer Clarification by gapgapgap-ga on 07 Apr 2006 06:29 PDT

Good answer but could we get more specific about the 50M net worth.
There at least has to be some exact statistics on that.

---

Clarification of Answer by leapinglizard-ga on 07 Apr 2006 19:55 PDT

There are some empirical figures for the number of American males
having a certain net worth, but none that I have been able to find at
the $50 million level. The closest thing I've found is a table of
Personal Wealth Statistics from the IRS. It shows that in 2001, the
most recent year for which these figures are available, there were
31,000 American males with a net worth of at least $20 million. Higher
dollar figures are not mentioned, nor is the population broken down by
age and high-school graduation status. This is where extrapolation
becomes necessary.

Internal Revenue Service: Personal Wealth Statistics
http://www.irs.gov/taxstats/indtaxstats/article/0,,id=96426,00.html

Internal Revenue Service: Male Top Wealthholders by Age: 2001
http://www.irs.gov/pub/irs-soi/web_table_4.xls

leapinglizard

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Clarification of Answer by leapinglizard-ga on 07 Apr 2006 20:00 PDT

Oops! I accidentally linked to the wrong table in my previous
Clarification. The one that shows how many American males are worth at
least $20 million is at the following address.

Internal Revenue Service: Male Top Wealthholders by Size of Net Worth: 2001
http://www.irs.gov/pub/irs-soi/web_table_2.xls

The table with the age breakdowns starts at the $675,000 level, not
even into the millions, so it is even less helpful. I think an
extrapolation from super-high income levels for the proper age group
using Pareto's Law of wealth distribution is a reasonable way to
proceed.

leapinglizard

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Request for Answer Clarification by gapgapgap-ga on 10 Apr 2006 09:58 PDT

Can you use Pareto's Law of wealth distribution to arrive at a close answer?

---

Clarification of Answer by leapinglizard-ga on 11 Apr 2006 16:10 PDT

I did apply Pareto's Law in my calculations above to arrive at an answer 
by extrapolating from the number of billionaires no older than 43. The
IRS figures start at a net worth of $675,000, which does not qualify as
super-rich. Pareto's Law works only for the top 3% of the population, 
and there are almost 4 million males with a net worth of at least
$675,000. That's 4% of the 100 million American males who are no more
than 43 years old. 

    In 1897, a Paris-born engineer named Vilfredo Pareto showed that 
    the distribution of wealth in Europe followed a simple power-law
    pattern, which essentially meant that the extremely rich hogged
    most of a nation's wealth (New Scientist, 19 August 2000, p
    22). Economists later realised that this law applied to just
    the very rich, and not necessarily to how wealth was distributed
    among the rest.

    Now it seems that while the rich have Pareto's law to thank, the 
    vast majority of people are governed by a completely different 
    law. Physicist Victor Yakovenko of the University of Maryland
    in College Park and his colleagues analysed income data from 
    the US Internal Revenue Service from 1983 to 2001. They found
    that while the income distribution among the super-wealthy -
    about 3 per cent of the population - does follow Pareto's law,
    incomes for the remaining 97 per cent fitted a different curve -
    one that also describes the spread of energies of atoms in a gas.

New Scientist: Why it is hard to share the wealth
http://www.newscientist.com/article.ns?id=mg18524904.300

The IRS gives an age breakdown only at the $675,000 level and not the $20
million level, so we can't use these figures to arrive at an accurate
answer. Working from the number of billionaires, however, Pareto's
Law predicts odds of 1 in 12 million, assuming no relationship between
wealth and dropout status. This figure can be multiplied by some factor
depending on what kind of relationship one sees between dropout status
and net worth. 

leapinglizard

Awesome answer!  That was fascinating to read through and see your
analytical approach.

ipfan or anyone else might be interested in some of the earlier
question asked, quite similar to this one:


http://www.answers.google.com/answers/threadview?id=408852


http://www.answers.google.com/answers/threadview?id=412186

Very interesting calculations in all three question answers.
The question here was about "the odds...".  Gapgapgap's earlier
question was about a specific male born in 1963, suggesting that there
is, indeed, such a person, if not several.

This list of persons born in 1963 suggests a few candidates:
http://en.wikipedia.org/wiki/1963#Births

Johnny Depp certainly looks like a good one: dropped out of highschool
for sure, and other sites suggest that he is in the money.  Whitney
Houston may have dropped out of high school, as may have Julian
Lennon.
Athletes could be expected to have graduated from high school, whereas
stage and music stars could be more likely to have dropped out to
pursue their careers.

Of course, the Wikipedia list is not comprehensive in any way.  There
could be quite a few drop-outs who inherited 50 million or more, and
some who married into such wealth.

If we assume that Johnny Depp has accumulated that much  - a site says
he earns 5 million per year -  he certainly beat the odds and would be
the person sought in Gap's first question.

I wonder who many others have.