Paired comparison models, such as the Bradley-Terry model and its variants, are commonly used to measure competitor strength in games and sports. Extensions have been proposed to account for order effects (e.g., home-field advantage) as well as the possibility of a tie as a separate outcome, but such models are rarely adopted in practice due to poor fit with actual data. We propose a novel paired comparison model that accounts not only for ties and order effects, but recognizes that the probability of a tie may be greater for stronger pairs of competitors, and that order effects may be more pronounced for stronger competitors. The model and several variants are evaluated on games outcomes from all US Chess Open tournaments from 2006 through 2016, events consisting of players of wide-ranging abilities. The models are fit in a Bayesian framework with informative prior distributions based on pre-tournament ratings. Model comparisons are performed by leave-one-out cross-validation.