1/52: What is an NHL goal worth?

Context: The audience for this data analysis report is the very general one.  The assumed background is very little statistics but enough to know what a correlation, IQR and standard deviation are.  I have not assumed that the reader has an understanding of hockey beyond a general understanding of sports. Additionally, the analysis here is a fairly straightforward choice since  our interest is in the relationship between these two variables.

Data: whatsagoalworth.xlsx

In this analysis, we will be considering what is the value of a goal to a National Hockey League (NHL) team.  The question of the worth of a goal is motivated by a desire to understand and evaluate goalie save percentages and the impact of those percentages on team performance.  In the NHL, teams receive points for winning games.  Two points are awarded for a team that wins a game in regulation or overtime or by shootout.  One point is awarded for teams that lose in overtime or by shootout.    A team wins a game by scoring more goals than their opponent.  The data that we will analyze here are those for all NHL teams from the previous three completed seasons (the 2007-8, 2008-9, 2009-10 seasons).  For each team and each season we have the total number of points that each team earned and the goal differential.  Goal differential is found by taken the total number of goals that each team scored minus the number of goals that there opponent scored.  The aim of this analysis is to determine the relationship between these two variables.

Figure 1: Histogram of Points

We begin this analysis by summarizing our two variables of interest.First, we consider the distribution of Points.  Figure 1 (at left) gives a histogram of the distribution of Points.  For this graph we can see that the distribution of Points is roughly unimodal and symmetric and does not contain an outliers.   The smallest values in this data is 61 (belonging to the 2008-9 New York Islanders) and the largest is 121 (belonging to the 2009-2010 Washington Capitals).  Both the mean and the median are 91.50.  On average, number of points scored by a given team scored differs from the mean by 12.35.  Figure 2 (below left) summarizes the distribution of Goal Differential.  This distribution is slightly skewed left with a mean of 0 and a median of 3.  The interquartile range here is 41 goals mean that the range of the middle 50% of the data is 41 goals.  There are potential outliers at the upper extreme of this distribution but they seem to fall within the general pattern of the distribution.  The largest of these points is a differential of +86 and belongs to the 2009-10 Washington Capitals. 

Figure 2: Histogram of Goal Differential

The next step in our analysis is to look at the relationship between these two variables.   A scatterplot of these two variables is given in Figure 3 (below).  We can see that the relationship between the two variables is linear, positive and strong.  The correlation between these two variables is 0.942.  Figure 3 also has the regression line, Points =91.5 + 0.3497 x Goal Differential ,  added to it.  From this we can infer that the predicted number of points for a Goal Differential of 0 (zero) would be 91.5.  Further, for each increase of one in goal differential, the predicted number of points that a team would earn would increase by about 0.35.

Figure 3: Relationship between Points and Goal Differential with Regression Line Added

A quick assessment of the model fit show a slight quadratic trend in the plot of the residuals versus the fitted values.  Fitting a regression model with an additional term for Goal Differential squared yields a slightly better plot of residuals versus fitted but the quadratic term is not significant (p=0.32).

The answer to the question: What is a goal worth? is that a goal (either give up or prevented) is worth approximately one-third (0.35) of a point.  This provides a metric for evaluating the performance of both skaters and goalies.  It also provides a criterion for the goal differential needed to achieve a particular target number of points.  For example, for the period covered by these data, the average number of points required to reach the playoffs was 92.  Using our prediction equation, we note that the smallest goal differential that will yield a predicted number of points above 92 is a goal differential of +2.  (NB:  91.50 + 0.3497*(+2)=92.20.)