In our last entry below we looked at the non-signing of Antti Niemi and the signing of Marty Turco by the Chicago Blackhawks.  At the end of that discussion we highlighted Roberto Luongo and his skill.  (Yes, yes, I hear the complaining from Western BC about his playoff performance.)  The question that we wondered about was what does it mean that Luongo saves you about eight and a half goals over what Niemi saves for you?  What does 8.5 goals mean or extrapolating to a full season what does 17 goals mean to your team over the course of a regular season.
What's a Goal Worth?
There are a bunch of ways that we could be quantifying this but we decided to see what the impact of those goals was on team points.  So we built a linear regression of points on goal differential and we used data from the last three NHL regular seasons: 2007-08, 2008-09, and 2009-10.  We used goal differential because a goal saved is worth a goal scored when you look at differential.  This can help us assess value of both goalies, defenses and scorers.The relationship between points and goal differential is plot at left.  The linear equation of the red line is

Points = 91.5 + 0.350 *Goal Differential.

The line well characterizes the relationship between the two variables.  We might have expected that the relationship would be more logistic (s-shaped) but that is not what the data suggests.  The relationship (Some other details.  A look at the residuals suggests that the relationship is indeed linear and the relationship is quite strong (R^2=0.89).  The p-value for the slope coefficient is significant, p<0.001.)  Another way to think of this is that no matter what your goal differential is the relationship between points and goal differential is constant. 

The relationship is that a goal — saved or scored — is worth about 1/3 of a point.  So if we think about how much a player adds to a lineup, every 10 goals is worth between 3 and 4 points over the course of 82 games.  So now we’re back to Luongo.  He’s worth 17 goals and 17*0.350=5.95 or about 6 points over Niemi.  He’s worth about 2*(8.5+3.7)*0.35 = 8.54 points over Turco (see Turco/Luongo numbers).  Eight points in the standings was the difference between 1st and 5th in the 2009-10 Western Conference or between 5th and 8th in that same conference. 

Similarly, Turco would be expected to cost the Blackhawks 2*(3.7)*0.35= 2.6 or about 3 points over playing Niemi.  That is, if Turco played the full season rather than Niemi playing the full season (assuming that the Blackhawks give up the same distribution of shots and those two individuals perform as they have done in the last two season).  Oh, andTurco saves you about $1.45 million. 
 

This begs the question though.  Luongo costs you $10 million, Niemi will cost you $2.75 million but Turcocosts you $1.3 million.  That seems like a lot to pay for 9 points. Money a GM could be spending to add defense or scoring.  A more thorough analysis would be necessary to assess what is the cost in terms of $$$ for a goal differential.  That should be fun.