We extend the Bayesian skill rating system of TrueSkill to accommodate score-based match outcomes. TrueSkill has proven to be a very effective algorithm for matchmaking – the process of pairing competitors based on similar skill-level – in competitive online gaming. However, for the case of two teams/players, TrueSkill only learns from win, lose, or draw outcomes and cannot use additional match outcome information such as scores. To address this deficiency, we propose novel Bayesian graphical models as extensions of TrueSkill that (1) model player’s offence and defence skills separately and (2) model how these offence and defence skills interact to generate score-based match outcomes. We derive efficient (approximate) Bayesian inference methods for inferring latent skills in these new models and evaluate them on three real data sets including Halo 2 Xbox Live matches. Empirical evaluations demonstrate that the new score-based models (a) provide more accurate win/loss probability estimates than TrueSkill when training data is limited, (b) provide competitive and often better win/loss classification performance than TrueSkill, and (c) provide reasonable score outcome predictions with an appropriate choice of likelihood – prediction for which TrueSkill was not designed, but which can be useful in many applications.