Because of it's discrete, start-and-stop nature with finite set of possible outcomes, the game of baseball lends itself well to study via Markov chain simulations. Although this framework for baseball simulation has been widely discussed in academic literature for decades, actual and realistic implementation of this model has been sparse due to former time prohibitive computational capabilities, as well as the lack of availability to modern sabermetric baseball statistics. In this study, teams are broken down to their true component parts-individual players-and various estimates are used to predict any given player's current level of ability while also adjusting for an assortment of situational affects. The role and informational value of batter-pitcher matchup data is given particular attention through use of a hierarchical beta-binomial model. The accuracy of this player based approach is measured by profitability of wagers versus the daily betting lines offered on individual games throughout the 2007 Major League Baseball Season. Natural applications for this method also include the cost-effectiveness of potential free-agent signings for major league teams, optimal batting lineup orderings, strategic in-game decision making, and a benchmark for teams, players, agents, and Major League Baseball in salary arbitration hearings.