Only one of the links you provided deal with innings increases year over year, and that study finds no evidence that increasing innings too quickly causes injury. The relevant findings: "RESULTS: A total of 161 starting MLB pitchers met the inclusion criteria. With the exception of total innings pitched from 2010-2011 being significantly associated with DL placement in 2012 (no DL, 310.5 ± 97.5 innings; DL, 344.7 ± 85.9 innings; P = .040), no other finding for starts, pitch counts, innings, or pitches per start in the cumulative years from 2010-2014 had a significant association with pitcher placement on the DL for any musculoskeletal reason or for an upper extremity reason between 2011 and 2015. CONCLUSIONS: In this study, we demonstrate that there is no association between preceding years of cumulative pitches, starts, innings pitched, or average pitches per start and being placed on the DL for any musculoskeletal reason." Again, as far as I'm aware of, and I've looked, there are no studies that show that arbitrary limits on inning increases year over year have any bearing on preventing injury. If Graterol is healthy, he should be allowed to throw as many innings as he is able to until his body tells him it's enough. Not some arbitrary number they decide on beforehand.