A Shot Quality Adjusted Plus-Minus for the NHL

We explore two regression models for creating an adjusted plus-minus statistic for the NHL. We compare an OLS regression models and a penalized gamma-lasso regression model. The traditional plus-minus metric is a simple marginal statistic that allocates a +1 to players for scoring a goal and a -1 for allowing a goal according to whether they were on the ice. This is a very noisy and uninformative statistic since it does not take into account the quality of the other players on the ice with an individual. We build off of previous research to create a more informative statistic that takes into account all of the players on the ice. This previous research has focused on goals to build an adjusted plus-minus, which is information deficient due to the fact that there are only approximately 5 goals scored per game. We improve upon this by instead using shots which provides us with ten times as much information per game. We use shot location data from 2007 to 2013 to create a smoothed probability map for the probability of scoring a goal from all locations in the offensive zone. We then model the shots from 2014-2015 season to get player estimates. Two models are compared, an OLS regression and a penalized regression (lasso). Finally, we compare our adjusted plus-minus to the traditional plus-minus and complete a salary analysis to determine if teams are properly valuing players for the quality of shots they are taking and allowing