MLB - Various Proposition Equations

Batter's True Batting Average Against Certain Pitcher:^[1]

     Where:
          BA = Player's Batting Average
          BAA = Pitcher's Batting Average Against
          LBA = League's Batting Average

Total Number of Hits in a Game by Player X:

     Where:
           TBA = True Batting Average
           ^AB/_G = At Bats Per Game

Park Factor:

     Where:
           OBP = On Base Percentage
           OBPA = On Base Percentage Against
           N = Number of Games

Probability of Team Scoring Run in First Inning:[2]

     Where:
           A = Team's Runs/Game

Sources:
[1] Sugano, Adam (2008). A Player-Based Approach to Baseball Simulation (Dissertation). University of California, Los Angeles. p. 50.
[2] Woolner, Keith (n.d.) An Analytic Model for Per-Inning Scoring Distributions (Report.) Baseball Prospectus. pp. 8–10.