The Value of Pitches Taken

[TwentySeven]

I am trying to make a formula to assign a run value to every pitch taken over the average major league player per at-bat.

I am assuming that the average starter will give up three runs over 6 2/3 innings, throwing 98 pitches and facing four batters per inning (on average, in reality the pitcher might face six batters in one inning and just three in another). I am also assuming the average four-batter inning results in 14 pitches thrown, and the average batter makes the pitcher throw just over three pitches per at-bat. Finally, I am assuming that the average bullpen pitcher in the sixth and seventh inning will give up between 1 and 2 runs, and the average bullpen pitcher for the eighth and ninth will give up between 0 and 1 run.

However, those were my guess values for the formula, and I would appreciate some more information on these averages. I need to know the following:

[*]The number of innings the average starting pitcher pitches in

[*]The average number of runs given up by a starting pitcher

[*]The average number of pitches thrown by a starting pitcher

[*]The average number of batters face by a starting pitcher

[*]The average number of pitches thrown in an average at-bat

[*]The average number of runs given up in the sixth, seventh, eighth, and ninth innings by pitchers from the bullpen only

If you guys can help me get this info, I will appreciate it a lot.