Does it make sense to say that some people are more athletic than others? Or do we need to break athletic ability into separate traits like strength, speed, coordination, endurance, and balance?

At one level, we obviously can break it down. A sprinter and a weightlifter are not the same. But when researchers give large groups of people many different physical tests, an interesting pattern appears: performance on different tests is usually positively correlated. People who do well on one test also tend, on average, to do well on others.

At first this may seem surprising. You might expect upper-body strength to trade off against running speed, or hand-grip strength to have little to do with a short sprint. Yet across many datasets, countries, time periods, and tests, the same broad pattern appears: physical abilities are not independent.

This matches ordinary experience. We can usually tell that some people are broadly more athletic or physically capable than others. But can we describe that more precisely?

PCA

One way to do that is with principal component analysis. PCA asks a simple question: when many measured traits are correlated, how much of the variation can be summarized by a small number of dimensions? Do many dimensions matter equally, or does one broad dimension capture much of the pattern?

The process

1. Organize data from test

Create an MxN matrix, where:

• M = number of people
• N = number of tests

Each entry is one person’s score on one test.

2. Normalize the scores of the tests

Different tests are measured on different scales. A grip-strength score and a sprint time are not directly comparable. So we standardize each column by subtracting its mean and dividing by its standard deviation.

Now each column has:

• mean = 0
• variance = 1

This ensures no test dominates just because of its scale.

3. Build a correlation matrix

Compute an NxN correlation matrix, where each entry gives the correlation between two tests. This tells us how strongly each test is related to the others.

4. Extract the factors

Perform an eigendecomposition of the correlation matrix: R = QΛQ^T where R is the correlation matrix, Q is the matrix of eigenvectors, and Λ is the diagonal matrix of eigenvalues.

The first eigenvector gives the direction of greatest shared variance across tests. The first eigenvalue tells us how much variance that factor explains. If the first eigenvalue is much larger than the others, that means one broad dimension captures a large share of the differences between people.

5. Compute the score for each person along this dominant axis

We can then project each person’s standardized test profile onto the first principal component. That gives a single score representing where they fall along the dominant axis of overall performance.

Intuition

Imagine each person is a point in high-dimensional space.

• One axis is speed
• One axis is strength
• and so on, for any number of dimensions

If these abilities were unrelated, the points would look like a round cloud. But they do not, they look like a cigar. Long in one direction, skinny in the others. There is a dominant axis. We interpret this axis as general athletic ability.

It's not one magic ability in their body. It means if you want to summarize the pattern across many tests, one number does a pretty good job. After that, narrower traits still matter. Someone may be especially strong, especially fast, or especially coordinated. But those differences sit on top of a broader common dimension.

Intelligence

This is interesting because something similar happens with cognitive tests.

Verbal ability, memory, spatial reasoning, and processing speed are all distinct abilities. But performance on them is typically positively correlated. When researchers analyze large batteries of cognitive tests, they often find a strong first dimension: a general factor, usually called g.

In fact, this general factor is usually more prominent in cognitive testing than a comparable broad factor is in physical testing. A person’s g score is informative about how they will perform across mental tasks in the same way their general athletic ability is informative on how they would perform at phsyical tasks.

Do the tests create the score?

In one sense, yes. g is extracted from the correlations among tests, so it depends on the tests. But that does not make it arbitrary. Even when researchers use broad and different sets of cognitive tests, they still tend to recover a similar general factor.

So g is best understood as a stable statistical summary of what broad cognitive tests share in common. Its exact form depends somewhat on which tests are included, but it is not merely a measure of one narrow skill.

It also predicts outcomes commonly associated with cognitive ability, such as educational attainment, job performance, and performance on other broad cognitive measures.

Does g matter?

If this pattern is so robust, why do many people believe it doesn't measure something that matters?

Part of the reason is conceptual. People want to imagine that the existence of g implies intelligence must be one simple thing in the brain. But many scientific concepts are real as stable patterns before their mechanism is fully understood. g is not the claim that the mind is simple. It is the claim that there is hard evidence that all mental tasks are correlated.

Another reason is moral and political discomfort. Many people hear claims about cognitive differences and worry that they threaten moral equality. But equal dignity and equal ability are not the same claim. A society can believe that every person deserves the same rights and respect while also recognizing that people differ in memory, reasoning, attention, or learning speed.

A third reason is range restriction. Most educated people do not see the full spread of cognitive ability in everyday life. Schools, professions, and social circles are already filtered. Within a selective university, a hospital, or a technical workplace, most people have already cleared a fairly high threshold. Inside that narrower band, other traits like conscientiousness, charm, ambition, knowledge, luck, and so on, explain more of the remaining differences. This can create the illusion that intelligence does not matter much. But that is like studying only NBA players and concluding that height is not very important for basketball. Among already tall people, height matters less. In the general population, it matters a great deal.

A fourth reason is that raw reasoning is often hard to observe directly. In ordinary life, people judge through proxies: credentials, fluency, accent, grooming, confidence, and conformity to the local culture. Most patients cannot directly assess a doctor’s diagnostic reasoning, so they infer competence from bedside manner, the degree on the wall, and the calmness of the performance. Those signals are not meaningless, but they are not the same thing as underlying cognitive ability. When direct talk about intelligence feels rude or taboo, people do not stop sorting one another. They simply sort by noisier signals. The hierarchy still exists, but it becomes more opaque.

That opacity has another effect. If ability is assumed to be basically equal and fully malleable, then failure is more easily moralized. People are told that anyone could become a doctor, engineer, or physicist if they only worked hard enough. So when someone cannot do it, the explanation shifts toward laziness, lack of grit, or bad character. In that sense, denying cognitive variation can make judgments harsher, not kinder.

For the same reason, direct measures can be more honest than holistic judgments. Standardized tests are imperfect and partly gameable, but they are often less gameable than the bundle of signals that replace them: polished self-presentation, cultural fluency, expensive extracurriculars, strong recommendation letters, and elite credentials. If society is going to sort people for cognitively demanding roles, imperfect direct measures are often preferable to a the proxies.

So the point is not that intelligence is one simple thing, any more than athleticism is. The point is that when you measure many different cognitive abilities, they share a common dimension. People who do well on one broad class of mental tasks tend, to a meaningful extent, to do well on others. That common dimension does not explain everything, but it is real, it matters, and pretending otherwise mostly pushes judgment onto cruder and less honest substitutes.