The distribution of the number of batters faced and the number of runs scored in an inning is fundamental to modeling pitcher performance in major league baseball. Until 1984 sufficiently detailed data on a play-by-play basis were available only for special games, for example, World Series games. Play-by-play data have become available for each league beginning with the 1984 season, and we use them for the 1990 American League season. We found that a minor change from the negative binomial model provided an adequate fit to the distribution of the number of batters faced. However, the distribution of the number of runs scored is complex and involves a convolution of the distribution of the number of batters faced and the conditional distribution of the number of runs scored given a specific number of batters faced. We modeled the latter by a truncated binomial distribution where the probability of a run scoring was a logistic function of the number of batters faced. The goodness of the fit of each of the models was tested on 77 starting pitchers who pitched in the first three innings of enough games to total at least 30 innings, all cumulating for these pitchers to 5,639 innings during the 1990 American League season.