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:
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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