We present a quantitative analysis of throwing ability for major league outfielders and catchers. We use detailed game event data to tabulate success and failure events in outfielder and catcher throwing opportunities. We attribute a run contribution to each success or failure which is tabulated for each player in each season. We use four seasons of data to estimate the overall throwing ability of each player using a Bayesian hierarchical model. This model allows us to shrink individual player estimates towards an overall population mean depending on the number of opportunities for each player. We use the posterior distribution of player abilities from this model to identify players with significant positive and negative throwing contributions. Our results for both outfielders and catchers are publicly available.