Let me also toss a question into the mix regarding this point: "Shooting/offensive efficiency is actually far more impacted when a player changes teams than when he changes roles. This suggests that a team's system, coaching effects, and teammate interactions play a much bigger role in determining shooting percentages than "skill curve" effects." This seems very important if true, and may well be right. But I worry that significant changes in a player's role could be the result of, rather than cause of, changes in their shooting efficiency. If improving players are allowed to increase usage, it will mask a "usage tax" on their efficiency. If declining/aging/hurt players reduce usage, the reverse would happen. So I think isolating the impact of usage requires looking at essentially involuntary changes in usage. (Which is what Eli Witus tried to measure in his lineup study.) All that said, your evidence seems pretty strong.

I also wonder whether correlations are the best way to compare your four groups. Because the 4 groups presumably vary in terms of sample size, average age, and, most importantly, the talent variance within each group, correlations might differ for multiple reasons. I think it might be better to measure the average absolute change in each stat (e.g. does TS% change less for role changers than team changers?). And (still in the category of suggestions for "work someone else should do") it might be fruitful to divide role changers into two groups: increased role and reduced role. If sample size permits, that might clarify the picture a bit.

This may be true, but the lower correlation for scoring may just reflect the much lower variance in the statistic. If you measured the average absolute y-t-y change in each stat, measured in point value, is it really true that scoring efficiency changes more? It could be that scoring is just as stable, but because players cluster so closely together the correlation is lower.

Aren't skill curves based on the assumption that your team/coach is "maximizing" your skill set within the offense? It would make sense that changing teams causes the model to break down in this regard since the player and the team are still making adjustments to make it all work.