Height and basketball success are examples of two variables that are known to possessively correlate, but what exactly is the correlation in the general adult U.S. male population? Recently a list was created of the 30 greatest white American basketball players of all time (the top 25, plus 5 honorable mentions). From this list of 30, I identified the 23 who are living, and obtained their listed heights and weights from Wikipedia:

rank name listed height (in cm) listed weight (in lbs)
1. larry bird 206 220
2. jerry west 193 175
3. bob pettit 206 205
4. john havlickek 196 203
5. john stockton 185 175
6. bob cousy 185 175
7. rick barry 201 205
8. dolph schayes 201 195
9. jerry lucas 203 230
10. kevin mchale 208 210
11. david cowens 206 230
12. bill cunningham 201 210
13. bill walton 211 210
14. chris mullin 198 200
15. tom hensohn 201 218
16. mark price 183 170
17. bill laimbeer 211 245
18. tom chambers 208 230
19. cliff hagan 193 210
20. paul westpal 193 195
21. dan issel 206 235
22. jack sickma 211 230
23. kevin love 208 251

As of 2015, there are about 72 million non-Hispanic white males, age 25 or older, in America, according to U.S. census projections. That means the median man on the above list (rank 12) is about one in six million when it comes to basketball performance. That equates to a normalized basketball Z score of +5.13.

The average listed height of the 23 greatest living white American basketball players is 200.61 cm (standard deviation = 8.37). That’s equivalent to about 6’7″ but it could be misleading because blogger Steve Sailer (perhaps the best journalist in America) notes that heights can be listed with or without shoes on. The average listed weight is 209 lbs (standard deviation = 22.09).

By contrast, the average non-Hispanic white American (age 20 or older) has a height of 177.2 cm (standard deviation = 6.44). That means, the average man on the above list has a height Z score of +3.57.

Now recall what we learned from my previous post: assuming a bivariate normal distribution, the correlation between two variables expressed as Z scores is equal to the slope of the regression line when the variables are plotted in a scatter plot.

So if we plotted height Z scores of every white man in America (age 25 or older) on the Y axis and their normalized basketball Z scores on the X axis, then the regression line would have to have a slope of 0.7 to correctly predict that white men with a median normalized basketball Z score of 5.13, have an average height Z score of 3.57:

Regression slope = 3.57/5.13 = 0.7 = correlation of 0.7

A correlation of 0.7 is very similar to the correlation between IQ and academic success in the general U.S. population. Thus NBA players are to height as Nobel prize winning academics are to IQ. Just as NBA players average heights that are three to four standard deviations above the mean, some evidence suggests Nobel level academics average IQs that are three to four standard deviations above the mean (IQ 145 to IQ 160).

And just as there some NBA players who are extremely short, we should not be surprised to find some Nobel level academics are less than brilliant, or even stupid. Yet it seems that every single time an eminent academic claims to have an IQ below 150, let alone below 90, people assume either the test was wrong or that person must have been joking. And yet statistically, we should expect such cases to exist.

NBA player Muggsy Bogues (right) has a listed height of 160 cm (5’3″)

Advertisements