Implicitly Defined Baseball Statistics

Major League Baseball uses statistics to determine awards every season. The batting champion is given to the player with the highest batting average. The Cy Young Award is given to the top pitcher which is determined by many different statistics including earned run average (ERA). Batting average and ERA have been used for many years and are major statistics in baseball. Neither batting average or ERA consider the skill of the opposing pitcher or batter. Thus, every pitcher and batter is considered to have the same skill level. We develop an implicitly definded statistic that determines the skill or value of a player. The value of a batter and the value of a pitcher is based on the skill of the oppposing pitcher and batter respectively. We use linear algebra to find eigenvector solutions to the eigenvalue problem, Aλ = λx, which generates each player’s statistical value.