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Unfortunately I’m not sure there’s much of one. Somewhat interestingly he posted two of his highest BB% in his walk years (2000 and 2007), each of which were immediately followed by fairly steep declines, from 14.9% in 2000 to 10.2% in 2001, and from 13.4% in 2007 to 10.9% in 2008. In the first instance the decline in BB% also came with a drop in K%; however, in 2008, his K% soared over 200 basis points from 20.6% to 22.9%. The only larger increase in K% in Alex’s career came in 1999, which saw him go from 17.6% to 21.7%.
A-Rod’s 9.9% BB% from 2010 signified a 510-basis-point drop from 2009′s career-high 15.0%, which was the most significant dip of his career. His K% also fell in 2010, from 21.8% to 18.8% — Alex’s lowest K% since 1998. As discussed in detail in the aforelinked OBP post, there is good analytical reasoning to expect an A-Rod bounceback in OBP and, correspondingly, his BB%, but looking at it graphically makes a return to at the very least his career average (11.0%) if not higher (Bill James likes A-Rod at 12.2%) seem that much more likely.
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