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Any statistic is on an unrelated scale from PER. That seems obvious, doesn't it?
It should also be obvious that dividing two numbers that are on different scales from one another has very little chance of being meaningful. Having two statistics or metrics on the same scale is far from unusual or impossible. Assist Rate and Turnover Rate are on the same scale: percentage of a team's possessions. Thus, there's a much more compelling case for multiplying or dividing those two numbers.
You were wrong on your 1.0 Usg/PER ratio assumption, but that's not a big deal to me.
Generous of you, but it wasn't anything so large as an assumption, just a wondering. The fact that three wildly dissimilar players all happened to come out to within 1.0-1.2 was interesting, but I didn't research it much further. A 1:1 ratio was unlikely (since they're on different scales) but there's still a pretty good chance that there's some kind of mean that players don't vary too widely from. What constitutes "too widely" would be based on the standard deviations from the league (or starter) mean.
but I do feel that there is value in looking at the components of an equation, and how they may impact the answer of that equation.
Sure, I do too. That's what we do all the time when we reference Usage, Rebound Rate, Assist Rate, pace, etc. These are all components of PER. I'm not sure that there's an inherent value in simply dividing the result of a formula by one of its constituent parts. I'm open to it, but I'd like to hear a logical case for why it's meaningful. Not just "Here are a few players' Usage/PER...maybe this means something."
I'm not saying that usage is or is not a valid statistic; I am saying that it may seem to play a role in PER inflation
And I said/agreed with that in my first response to you. PER and Usage are definitely correlated to some extent; that higher Usage will usually yield a higher PER, because PER does reward gross production, not just efficiency. So using more possessions will result in more shot attempts, points and assists. Of course, if the player is not very good, this will only have limited effect because more shots put up and more possessions used (by an inferior player) will result in worse scoring efficiency and more turnovers, both of which hurt PER.
