In honor of Super Bowl Sunday, I thought I’d ask whether physical abilities have a general factor (g), the same way cognitive abilities do? For those who don’t know, Charles Spearman famously discovered that all cognitive abilities are positively correlated, suggesting they all are influenced by some general ability, and thus the most efficient way to measure someone’s overall cognition was to test the most g loaded abilities (since these best predict all other abilities).

The existence of a physical g factor would be useful (though not necessary) for assigning people an AQ (athletic quotient), the same way IQ tests assign folks an IQ (intelligence quotient).

Cognitive and physical abilities are both forms of voluntary goal directed behaviors that can be objectively graded on a scale of proficiency, but because cognitive abilities are more prestigious (at least after high school), we increasingly see athletes trying to claim their abilities are mental instead of physical. And so we have commenters claiming that weight lifting requires not just physical strength, but coordination, and terms like kinesthetic intelligence have emerged in the literature.

We all have our biases, which is why I love factor analysis, which allows us to objectively decide what category or sub-category different abilities fall into. Factor analysis is a technique where you look at the intercorrelation between a large number of traits, and notice that some intercorrelate better than others, allowing you to infer sources of variance that are common to some traits but not others, allowing you to group traits into different clusters.

When you control for these common sources of variance, you find that some traits still intercorrelate better than others, allowing you you to infer higher sources of common variance. This allows for a hiearchy of categories and sub-categories that is wholly objective, requiring no judgement or decision on anyone’s part, and yet still agrees with common sense.

As the late Arthur Jensen noted, when you factor analyze hundreds of clothing measurements from every body part dimension imaginable, you find almost all of the variance can be explained by just three factors: general body size, body length, and body width analogous to how every location on Earth can be explained by just three data points (latitude, longitude, and altitude).

When we give people an extremely diverse series of tasks, we find that most tasks that are commonly thought of as physical (running, jumping, lifting) are more positively correlated with each other than with tasks commonly thought of as mental (repeating numbers, defining words, solving jig-saw puzzles). To be sure, there are certain hybrid abilities that load equally on both domains.

When the 11 subtests on the WAIS-R were factor analyzed, it turned out that even though David Wechsler thought he was measuring 11 different parts of intelligence, most of the variance in scores could be explained by just four factors: general intelligence, verbal knowledge, spatial ability, and short-term memory.

Similarly, when ten different physical tests were factor-analyzed, it was found that most of the variance could be explained by just five factors: general athleticism, strength, running ability, coordination, and balance. I find it interesting that measures of physical strength (hand-grip, chinning) have negative loadings on both coordination and balance, suggesting an evolutionary trade-off between muscle and control as we marched up the evolutionary tree.

It’s interesting to note that just as vocabulary was the single best measure of cognitive g in the cognitive battery, 100-yard dash was the single best measure of athletic g in the athletic battery. So just as people who score at the one in a billion level (relative to Western norms) on g loaded cognitive tests are said to have IQs of 190+, people who would score at the one in a billion level on the 100-yard dash can claim an AQ of 190+. That doesn’t mean their athletic g is truly at the one in a billion level (even the 100-yard dash is an imperfect measure of athletic g) but it’s about as close to a perfect measure of athletic g as the best IQ tests are to perfect measures of cognitive g.

Of course the best measure of athleticism would be to give people the full battery of physical tests and calculate the composite score, but if you wanted a short-form, you would just take the 100-yard dash, just like when psychologists wanted a short-form for IQ, they would just test Vocabulary, though more recent research suggests that g loading of Vocabulary has declined or was never as high as once thought.

Which brings us to another key point: The factor structure of any correlation matrix is sensitive to what tests you include, so skeptics might want to see a similar factor structure replicated in several diverse random selections of tests before accepting the factors and their loadings on various tests.