Principal Components of Talent

This is not a statistics post per se, but it is based on an important mathematical concept: orthogonality (or linear independence). I'm interested in the concept of breaking down players into a set of independent (or orthogonal) "vectors" that describe some important aspect of talent. These would be like the "directions" of talent. The weights or magnitude of the vectors would also be important, but that is a separate discussion (more than one, of course). This is similar in vein to the concept (each factor is theoretically orthogonal to the other).

Here is one set of possible (as an engineer, I tend to think of these as eigenvectors) that make sense to me:

Principal components of basketball talent.

I think these are self-explanatory. What I call "vision" represents one component of passing, which is the ability to see open teammates. You might argue that could be part of BBIQ, too. There are no right answers here. Just an interesting discussion to have that stimulates thought, if nothing else. Would you add principal components that are orthogonal to these (i.e. that cannot be explained by the others)? Would you remove one of these, because you think it is not orthogonal to the others? I'm interested to hear your thoughts.

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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).

Your math >>> my math :)

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.

Is the ability to stop quickly also a separate quality or is that part of agility? Or maybe agility is the combination of starting and stopping ability? Interesting stuff. I appreciate the discussion.

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.

"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." No reason at all. I just didn't know how to break it down into the granularity both you and Eric brought up. But those make sense. Are there tests that can be done to measure each of these independently of the other?

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.

Not tangential at all. That's exactly the kind of thinking I'm interested in hearing, and I tend to agree with you. So, practically speaking, how would you break down "athleticism" into additional orthogonal components (e.g. speed, quickness, etc.)? Additionally, in terms of players like Kidd, couldn't one argue that his combination of ball handling, court vision, and BBIQ enable him to achieve similar outcomes than someone else who might be more "athletic"? Or are there really other physical/mental traits that he possesses that are not captured by these other components?

Some quick thoughts on possible orthagonals... - Muscle strength / max force applied 9could divide upper / lower body, grip strength, etc) e.g. Metta World Peace - Explosiveness aka power output (ability to apply large amounts of strength quickly) - this can also be broken down into "eccentric" or "reactive" explosiveness i.e. running jump or sharp cuts vs. concentric explosiveness i.e. jumping from a standstill, but maybe not here...? Russel Westbrook, Blake Griffin, Nate Robinson - Tendon strength and elasticity (tendons can store energy on impact and then release to aid movement) Michael Jordan - strength relative to weight Kevin Durant? - movement efficiency / form (an oft-overlooked component of good leapers and sprinters) Lebron James, Chase Budinger - hand-eye coordination Steph Curry - latency in reflexes uh, javale mcgee? - accuracy of reflexes Jason Kidd? - height & wingspan Ekpe Udoh - Active range of motion in joints (for example, baseball pitchers tend to be in the top percentile for shoulder mobility, for reasons both nature and nurture, but this also means the ability to apply force at extreme ranges of motion) Javale McGee - Proprioceptive ability - ability to feel the position of one's body/limbs without looking (try standing on one leg, then close your eyes and you're using your proprioceptive sense) Brandon Roy, Monta Ellis - Durability/structural integrity of muscles, tendons, bones, etc. John Stockton - Anaerobic energy storage (creatine for example does not increase peak anaerobic power but can increase the duration of peak power output before switching to aerobic systems) - Aerobic / cardiovascular energy production, both in terms of power output and in terms of time before exhaustion - Ability to read body language and intention Shawn Marion - Muscle memory any good shooter I'm sure I could keep going, but I need to go eat dinner! :)

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?

It seems to me that you can be athletic without being strong. Kevin Durant is athletic, but he's not "strong". You can also be very strong, but not be particularly athletic. Think a big hulking center. I like your other suggestions. Maybe "confidence" is a good one to summarize those. What about "Determination" for the others?

It seems to me that there might be a principal component for "sense" (vision, pattern recognition, other stuff you mentioned) and basketball IQ is maybe more about understanding game strategy? So "sensual" and "conceptual" might be two different aspects of basketball IQ. One is more high-level brain function and the other more low-level. Does that make sense?


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