Twins Video
The above graph shows OPS (on-base percentage plus slugging percentage) against each starting pitcher separated by times through the order. So for example, it shows that hitters have a 0.786 OPS when hitting against Joe Ryan for the second time in a game. The size of the points indicate fraction of pitches. Chris Archer has only pitched to 10 hitters for a third time in a game (mercifully, it seems).
The pattern for most pitchers is clear: the scales tip toward the batter with each successive time through the lineup. So for Rocco Baldelli, the urge to call on the bullpen should strengthen each time opposing lineups turn over.
For comparison's sake, consider the group of middle relievers comprised of Tyler Duffey, Caleb Thielbar, Emilio Pagán, Jovani Moran, and Trevor Megill. That group has an OPS against of 0.636. So while turning to the bullpen often has not been pretty, it's still a much better option than having the likes of Chris Archer, Dylan Bundy, or Devin Smeltzer face a hitter for a 3rd time.







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