For one brief moment in the late 1990s, Microsoft stock reached ridiculously high levels, and the media reported that Bill Gates was worth $100 billion USD making him the World’s first centibillionaire. So freakish was Gates’s achievement that It would take nearly 20 years years before another centibillionaire would appear when Jeff Bezos made the cut in 2017 (I’m ignoring Putin in this analysis because there’s no reliable info about his individual wealth).

However by circa 2020, Bezos was eclipsed by Elon Musk who became the first multi-centibillionaire (someone worth several hundred billion) when his net worth briefly his $340 billion.

Thus it’s interesting to ask who was richer? Gates in the late 1990s or Musk circa 2020. At first glance it would appear to be Musk because if you adjust for inflation, $100 billion in the late 1990s equals almost $163 billion circa 2020, which is less than half of Musk’s fortune of $340 billion.

However adjusting for inflation is just a crude way to compare buying power across time. It doesn’t really tell you the respective economic status each man had at his respective peak. For example, in 1982 Daniel Ludwig was the richest American with a net worth of $2 billion but adjusted for inflation that would be less than $6 billion circa 2020, which is less than 2% of Musk’s then fortune. And while it’s true that a 43% increase in U.S. population meant Musk had more competition to become the richest American than Ludwig did, that comes nowhere near explaining the 50 fold difference in wealth,

Commenter Philosopher once suggested using percentile ranks to compare wealth across time which is a good idea, but since both Gates and Musk were each the richest person in their respective eras, by definition they were both at the 100th percentile so this can’t break the tie.

Z scores

What is needed is the wealth Z score of each man: the number of standard deviations (SD) each man was from the mean of his era. A standard deviation is just a measure of inequality (a small standard deviation means most people cluster closely around the average while a large one means they are spread quite apart). It’s quite literally the standard amount people deviate.

It’s a fascinating statistic because it allows you to compare apples and oranges. For example if a weight lifter and a sprinter wanted to compare who was better at their respective sports, this would be hard to do because one sport measures success in weight lifted and the other measures success in seconds spent running. But if performance in both sports is converted into Z scores, such comparisons can be made. Or for example, if the average Canadian man and woman are 5’10” and 5’5″ with SDs of 3 and 2 respectively, a 5’9″ woman can claim to have a higher sex adjusted height than a 6’1″ man because the former is +2 SD for her sex (Z score = +2) while the latter is only +1 SD for his sex (Z score = 1).

When variables are normally distributed (a bell curve) Z scores can be directly converted into percentile ranks, so for example:

For those who are new, the IQ scale is simple Z score * 15 + 100.

Natural logs

Now when it comes to net worth, there are problems with calculating Z scores because the distribution is so abnormal. For example in 2017, the three richest Americans had more wealth than the bottom 50% of the country. Thus it’s almost impossible to calculate how much the average American is worth because unless you do a census of the entire country, the inclusion or omission of just one centibillionaire will skew you’re sample’s average by orders of magnitude and unlike a normal curve where the mean and median are the same, the average American is actually orders of magnitude richer than the median American.

Now one solution statisticians use to deal with this problem is they transform net worth into its natural logarithm using calculators like this. Natural logs tend to fit the bell curve far better than raw wealth data. Let’s apply this concept to Gates and Musk.

The next step is to transform these natural logs into Z scores. To do this we must estimate the mean and SD for U.S. wealth natural logs in the years when Gates and Musk made wealth history. If we assume that natural wealth logs are roughly normally distributed, at least within 3 SD from the mean, then we simply assign the natural wealth logs at the 50th and 99th percentile the Z scores they would have on a normal curve: 0 and +2.33 respectively.

On a normal curve, a Z score of 0 is by definition the mean and by dividing the difference between the mean wealth log and the 99th percentile wealth log by 2.33, we can estimate the SD.

From here we can estimate that Gates, who had a natural wealth log of 25.33 in the late 1990s had a wealth Z score of +8.32 (8.32 SD above the mean) while Musk who had a wealth log of 26.55 circa 2020 had a wealth Z score of +7.65.

While both men have freakishly high Z scores, Gates was clearly far richer for his time than Musk was for his. To put it in perspective, Musk would need $1.25 trillion to be as rich circa 2020 as Gates was in the late 1990s.

Recently Musk’s SAT scores were reportedly revealed and while they equated to an extremely high IQ, like 99.9% of Americans, he was still in the biologically normal IQ range of 50 to 150 which is why he has lots of worshipful fan boys who can relate to him. Outside this range, people tend to be mutants.

Lucky for us normal humans, the high IQ mutants have their own freaky interests and so the richest and most powerful people tend to come from the pinnacle of the normal range (IQ 135 to 150): Musk, Bezos, Buffet, Soros, etc.

However once in a while, one of the 170 IQ mutants gets bored writing computer programs in his mom’s basement and with enough luck and hard work, decides to compete with the mere mortals and like an invasive species entering an eco-system not evolved to them, even the brightest normal humans are no match for the mutant who absolutely slaughters them at their own game because his IQ is just so much higher, and that is what we saw with Gates in the late 1990s, allowing him to become a centibillionaire nearly two decades before anyone else and be the richest American for 23 years .