A mathematical optimization framework for expansion draft decision making and analysis

Abstract

Abstract In this paper, we present and analyze a mathematical programming approach to expansion draft optimization in the context of the 2017 NHL expansion draft involving the Vegas Golden Knights, noting that this approach can be generalized to future NHL expansions and to those in other sports leagues. In particular, we present a novel mathematical optimization approach, consisting of two models, to optimize expansion draft protection and selection decisions made by the various teams. We use this approach to investigate a number of expansion draft scenarios, including the impact of “collaboration” between existing teams, the trade-off between team performance and salary cap flexibility, as well as opportunities for Vegas to take advantage of side agreements in a “leverage” experiment. Finally, we compare the output of our approach to what actually happened in the expansion draft, noting both similarities and discrepancies between our solutions and the actual outcomes. Overall, we believe our framework serves as a promising foundation for future expansion draft research and decision-making in hockey and in other sports.