Marginal Revenue Product and the Effect of Teammates on Player Productivity in the NHL

This paper creates a process for estimating the marginal revenue products (MRPs) of players in the National Hockey League (NHL). Since hockey is a team sport, where a given player's output depends on the abilities of his surrounding teammates, I wanted to include the effect of a player's teammates in my estimates, which previous MRP calculations for hockey players lack. Using detailed play-by-play data from the NHL's real time scoring system (RTSS), I obtained the total number of goals for and goals against for each combination of players on the ice at a time (five skaters and a goalie). I then estimated several linear OLS regressions to create production equations that explore the impact of each individual players' dummy variable on the goals for and goals against per 60 minutes of ice time for every player combination. Afterwards, I estimated a linear OLS regression, examining how a team's cumulative goals for and goals against impacted its revenue. Taking the dummy variable coefficients from the production equations and the goals for and goals against coefficients from the revenue equation, I created MRP estimates for every NHL player. Ultimately, I created very noisy MRP estimates, partly because the large degree of multicollinearity among the dummy variables in the production equations created imprecise coefficient estimates. While my estimates do not include the impact of a players' teammates, they pave the way for incorporating it in the future by including player pair dummy variables that examine how a player's production changes with different teammates.