Pitches Against Starter Metric

It is common baseball wisdom that the earlier you get a starter out of the game, the better chance you have to win. So here I will try to establish a metric that shows how good a team or player is at accomplishing this feat. A team needs to get at least 6.67 pitches per out to get the bullpen after 6 innings (assuming the starter goes 120 pitches). So of course we have to factor pitches per plate appearance, but we also have to factor OBP. Usually the relief pitchers are not as good as the starters, except the set up man and closers for most good teams. So the goal would be to not let the starter go more than 6 innings. You can use this metric to grade players by seeing how many pitches it takes them to get out 18 times. For example, for Robinson Cano, you take his .349 OBP and multiply it by 18. This gives you 6.282, meaning in 18 plate appearances, he will reach 6.282 times. So you add that to 18 to get 24.282. Then multiply it by his pitches per plate appearance (3.34 for Cano). This is only 81.1, meaning it would only take a starting pitcher 81 pitches to get through 6 innings of a Cano only lineup (and the pitcher would clearly still be in the game). Matt Kemp would cause a pitcher to be at 99 pitches through 6 innings. This is also a way to judge the quality of lineups. For example, the Brewers lineup in game 4 of the ALCS Morgan (.357 OBP, 3.69 Pit/PA), Kotsay (.329 OBP, 3.58 Pit/PA), Braun (.397 OBP, 3.93 Pit/PA), Fielder (.415, 3.79), Weeks (.350, 3.84), Hairston (.348, 3.86), Betancourt (.271, 3.16), Kottaras (.311, 3.81), and Wolf (.177, 3.56). This gives you a 2.955 OBP and 33.22 pitches. Because it is 18 outs, multiply both numbers to get 66.44 pitches and 5.91 OBP. Because the OBP is 5.91 you multiply that by the average Pit/PA for the 9 batters (3.69) to get about 21.81. Add that number to the 66.44 pitches to get 88.25 pitches as the final number through 6 innings. So the Brewers lineup is better that Robinson Cano but not as good as Matt Kemp, according to this metric. This pitches against starter metric I really like and will keep using.