Batting order (i.e., lineup) optimization for professional baseball teams has been analyzed for decades using various models and assumptions. In general, while optimization is useful -even with minimal benefit- it yields only small fractions of a run per game in improvement, mainly due to the interchangeability of most professional baseball players. Youth baseball, on the other hand, is a prime candidate for lineup optimization as it addresses large talent disparities and creates substantial improvements. In addition, a typical youth lineup is comprised of the same batters throughout a season, while this is not even approximately true for most major league teams; thus, finding "a lineup" for a youth team is more meaningful and useful in that sense. Here, the optimal lineup is considered to be the one which produces the highest number of runs per game. A probabilistic algorithm finds this optimal lineup by simulating many games with each possible lineup, allowing for more detailed statistical analysis. In addition, we see how run limits affect game outcomes and how individual players contribute to a team`s performance. A study of a major league lineup is used for comparison.
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