Actually, its not. IQ is normally distributed because it is a statistic explicitly transformed to be normally distributed with respect to the population.

But intelligence itself is more like exponentially distributed. Think of a chess grandmaster versus a range of people of various ability. What does the distribution of winning odds look like?

Normal distribution has an exponential term in it. Your intuition is mostly correct for the >100 part of IQ but thats totally in line with it being normally distributed.

Intelligence is not exponentially distributed. That would mean that the density is monotonically decreasing which its not. There are more “average people” than extremely low intelligence ones.

No, you are missing the point. The point is the scaling is all wrong. The IQ distribution, normally distributed by design, is what people think of when talking about intelligence. But it does not give proper intuition as there is no evidence that _intelligence itself_ is normally distributed.

More concretely, someone with 140 IQ is not 40% more intelligent than someone with 100 IQ. It would be more correct to say that 140 IQ person is orders of magnitude more intelligent than the average person.

Perhaps a better analogy is the decibel scale. 100 dB vs 110 dB is only a difference of 10% on the scale, but in actually represents an order of magnitude change. A similar effect goes on with intelligence and how we measure it.

Take height for example, which largely follows a normal distribution. The 7 ft tall person can reach items on the shelf that are simply inaccessible to someone who is 5ft tall. This represents an infinite difference in "raw capability" yet the underlying distribution is still normal.

Height may be normally distributed but that doesnt mean intelligence is. IQ is normally distributed because its transformed to be so; similarly, "being able to reach things" is not a natural transformation with sufficient explanatory power of what could be considered the "underlying distribution". Like IQ its a transformation of height.

If you look at any intellectual skill or ability, the most raw and natural measuremnt is not normal. Going back to chess, if you look at ELO, you might be persuaded that chess ability is normally distributed. But thats wrong because ELO, like decibel, is a log transformation of the underlying measurement. We take logarithms when the the raw thing we are looking is so variable it spans orders of magnitude. So in reality the underlying distribution of chess ability is extremely skewed with a heavy right tail. It spans orders of magnitude.

I think the mistake you are making is transforming the distribution to another one and drawing conclusions from that. For instance, the win rate in the shelf reaching game becomes a Dirac delta function at the right tail of the normal distribution.

I think either you are not reading my post or I'm not explaining myself well.

What Ive been trying to do is make the argument why an exponential-like distribution is a more natural representation of intelligence and therefore what the "underlying distribution" looks like.

Clearly, a delta function against a shelf game is not a natural or useful representation of height so I think that counterpoint to your argument is obvious.

According to you, what is the underlying distribution of intelligence and why?

>> According to you, what is the underlying distribution of intelligence and why

I think intelligence is normally distributed, like all other human characteristics. When transformed to win rates based on intelligence that becomes a different distribution. Your argument is centered on the 2nd distribution.

> I think intelligence is normally distributed, like all other human characteristics.

My question was why do you say it is normally distributed? where is your evidence?

> When transformed to win rates based on intelligence that becomes a different distribution.

You dont have to look at just competition, but other mental skills too. Most any application of intelligence is not normally dostributed. Why is this fact not a natural reflection of the underlying distribution?

I am struggling to see any support for your position. Help me out.

>> What does the distribution of winning odds look like?

This is effectively casting the distribution into a different space. Taking the right tail of a normal distribution and applying a test on it converts it to a Dirac delta distribution.