Composing a team of professional players is among the most crucial decisions in association football. Nevertheless, transfer market decisions are often based on myopic objectives and are questionable from a financial point of view. This paper introduces a chance-constrained model to provide analytic support to club managers during transfer windows. The model seeks a top-performing team while adapting to different budgets and financial-risk profiles. In addition, it provides a new rating system that is able to numerically reflect the on-field performance of football players and thus contribute to an objective assessment of football players. The model and rating system are tested on a case study based on real market data. The data from the case study are available online for the benefit of future research.