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The numbers refute this statement. Tyler Johnson's PER was 12.4 last year, 13.8 career (well below average for both). Schroder's PER was 12.7 last year, 14.8 career (well below average last year, but just barely below average for his career). (Meanwhile, just to highlight how horrible of a signing Cory Joseph would be, though I know you don't care about him in this discussion, his PER was 11.0 last year, 12.5 career, which is pretty darn awful for a veteran player getting significant minutes.)
No they don't. Tyler's defense is MUCH better than Schroder's, easily enough to eclipse the small difference in PER. Plus, Tyler, as far as I know, hasn't made a career out of irritating his teammates.