A Bayesian Approach to Estimating a National Hockey League Draft Pick Value Chart with Bounds

Abstract

For leagues like the National Hockey League (NHL), that use a draft to allocate players to team, the valuation of draft picks is an important topic. There is a robust literature of approaches to the creation of draft pick value charts (DPVCs). Our focus will be on a DPVC that values picks based upon the performance of past selected players. In this paper we propose two additions to this literature. First, we introduce two new Bayesian methodologies for estimation of the values in a DPVC. Both of these approaches create a flexible monotonic DPVC. These methodologies, along with a traditional LOESS approach, are compared and evaluated via cross-validation. Second, we generate credible intervals to move beyond point estimation for the evaluation of draft picks. Our methods are applied to three different responses variables: games played, time on ice, point shares and games above replacement. We evaluate these techniques using cross-validation on players selected as part of the NHL drafts from 2009 to 2018 and we find that a monotonic Bayesian B-spline model does best based upon cross-validation performance. For the resulting model, we provide tables (with interval bounds) for each of our three responses.