Principal Components of Talent

Nitpick not at all related to the content of the post, which I really like, but orthogonality and linear independence are strictly speaking no the same things. Linear independence is common to any vector space and its really an algebraic notion, but orthogonality on the other hand is a geometric notion which is germane only to a space with a geometry, or inner product. Basically, you can be linearly independent without being orthogonal (think of two lines which are not the same but are not at right angles to eachother).

The simplest definition that I like for agility is a deceleration followed by a reactive acceleration. It depends how detailed you want to get. FWIW, I divide skills into four broad categories: athletic, psychological, tactical and technical. Within each category, there are many skills or qualities.

Some agility tests share a high degree of variance with speed because a straight-ahead sprint is a major part of the test, for instance an Illinois Agility Test. The greater the degree of change, the less variance agility shares with speed, so an Edgren test - which is a lateral shuffle - is distinct from sprinting speed. The longer the sprint distance, the less variance is shared with a vertical jump test. Truthfully, you can subdivide speed into acceleration and speed (maximum velocity) and you can differentiate speed and quickness. Quickness is often used interchangeably with agility, but they are not the same.

Well, since I've been reading these types of papers lately to prepare my dissertation proposal, PCAs have found that speed, agility, and vertical jumping are different qualities. What about balance, hand-eye coordination, etc? The reason that I asked about strength and athleticism was for this reason: if you're lumping everything else together, I wasn't sure why strength would be the one that would be pulled out. Regarding Kidd, he may not be as "athletic" now since he's 38, but when he was 19, he was as athletic as anyone. He is/was super-fast, strong, could jump, had tremendous hand-eye coordination, etc.

Ranting Tangentially - One of my pet peeves is the lumping of all physical gifts into one singular continuum of "athleticism". Do we just know it when we see it? Very few even try to define what athleticism is, exactly, and when they do, I think they get it wrong. Who is more athletic... a power lifter or a high jumper? They would be judged very differently depending on whether you're in a gym or on a track, right? General fitness, or general physical preparedness, takes a back seat to specific physical preparedness when you approach the upper echelon of any sport. So what kind of fitness is required in basketball? It's a combination of lots of things and varies by position. Even then, it varies by play style. Who is more athletic: Ekpe Udoh or Kwame Brown? Do we consider ability to hold position on the block an "athletic" trait? Do we consider ability to go hard in the 36th minute of playing time an athletic trait? The definition gets even fuzzier when you consider the role of the nervous system in athletic ability. Jumping isn't just about having lots of "fast-twitch" muscle fibers or the optimal muscle/tendon geometry... the most overlooked component is the ability to fire all of the relevant muscles quickly, in the right order, as well as RELAXING other muscles at the exact right moment. This is a skill that CAN be trained (though, just like everything else, there is a genetic component). Plyometrics primarily train this neurological aspect, which is why they can effect such large improvements so quickly. The boundary between body and mind is so very difficult to discern, if it can be said to exist at all... So considering the neural aspect of jumping, how different is it from shooting? Shooting may involve more of "fine" motor control in certain ways, and does involve use of an external object (the ball), but I would consider the skills displayed in shooting to be primarily "athletic" skills. Players like Shaq (or lately, Blake Griffin) suggest that there may be a genetic component at play in shooting as well. Which is why it bugs me a bit when I hear people say that so-and-so is a good shooter but a poor athlete, or so-and-so is a great defender in spite of their athletic limitations, or that another guy is a "great athlete" but lacks the coordination to do x y or z basketball task. Obviously jumping, running, and raw strength have value in the game of basketball, but if you equate just a few physical qualities with athleticism, it just makes it that much harder to think clearly about player evaluation. And that isn't just a hypothetical point - see: Thabeet, Biedrins, countless draft busts who in reality showed all the warning signs to those with eyes to see... or on the flip side, Jeremy Lin, Andre Miller, Jason Kidd, or other "unathletic" guys who have demonstrated more than adequate ability to get to their spots, get boards, and play good D in real world basketball situations.

Why is strength separate from athleticism? Vision and IQ would not be orthogonal. Studies have shown that there are no visual differences between elites and non-elites. The differences that we perceive to be visual are really perceptual skills such as pattern recognition, selective attention, etc. What about psychological attributes like confidence, self-efficacy, etc? What about grit, a popular new concept, or mindset, or resiliency?