This is a follow up on the Pythagorean formula discussion, and focuses on the NHL and the Vancouver Canucks. A lot of people have ragged on Luongo (myself included). I wanted to objectively value his worth.
The Pythagorean formula to determine winning percentages has long been used in sabermetrics. The formula is best summarized as:
Wining % = GF^2 / (GF^2 + GA^2)
Where GF = goals for, and GA = goals against.
This article is used to illustrate the value of Roberto Luongo.
Firstly, a goaltender cannot be valued purely based on SV% as this percentage is based on the defensive strength of the team in front of a player, and the offensive capabilities of the opponent. A better metric used is the Defense-Independent Goalie Ratings (DIGR) introduced by Michael Schuckers at the MIT Sloan Sports Analytics Conference in 2011. A discussion of the theory behind the DIGR stat is here: http://myslu.stlawu.edu/~msch/sports/Schuckers_DIGR_MIT_2011.pdf.
For the 2010-2011 season, the DIGR save percentages ratings and salary caps for the following players were as follows (See: http://myslu.stlawu.edu/~msch/sports/DIGR10-11.pdf):
Cory Schneider – 0.9285 (Salary cap $0.9mm)
Roberto Luongo – 0.9269 (Salary cap $5.333mm)
Average Goalie – 0.9133 (Avg Salary cap $3.95mm) [Note 1]
Based purely on DIGR, it would be infinitely beneficial to use Cory Schneider (reduced GA, results in higher winning %, and $4.433mm in additional cap spending). This analysis assumes Cory Schneider does not exist, as it’s only logical to play Schneider as much as possible. Additionally, obviously, these stats are a point in time (2010-2011 season) – consequently, they should not be taken as granted, given that players improve or deteriorate.
Using the Pythagorean formula, we can deduce that based on 30 shots/game on average (assumption), Luongo will save 0.408 goals/game more than the average goaltender. Assuming Luongo plays 60 games a season, that results in 24.5 less GA. In 2010, Vancouver allowed a total of 262 GF and 185 GA (predicted win% of 0.667). Using an average goaltender, there would be 262 GF and 209.5 GA (predicted win% of 0.610). However, the team would also have $1.383mm additional cap space to use.
To get back to the same predicted win% of 0.667, that incremental $1.383mm would have to do one of the following:
a) Increase number of goals scored by 34.5 throughout the season,
b) Decrease goals scored by 24.5 (obviously – to offset the increase in goals allowed)
c) A combination of (a) and (b).
Given that goal scoring is generally valued at a premium, (a) is less likely to happen with an incremental $1.383mm. (b) is easier to do, as traditionally defensive defensemen do not trade at a significant premium (compared to goal scoring).
If we look at the goals versus threshold (GVT), number of goals benefit of a specific player versus that of a replacement, we can see that top defensemen only contribute to approximately 10-14 less goals allowed. (See: http://www.behindthenet.ca/2010/gvt.php?sort=14&mingp=&team=ALL&pos=D).
While clearly not an apples-to-apples analysis for GVT, it becomes apparent that $1.383mm of additional cap hit would not likely help reduce goals scored by 24.5 goals.
Therefore, assuming Vancouver did NOT have Cory Schneider, it would be beneficial to keep Luongo. However, the reality is that Vancouver does have Schneider and the team should likely utilize the addition cap room for other players to increase the predicted win%.
[Note 1] Average 0.9133 was the league average save percentage (unknown whether this is the DIGR or the basic average). For the purpose of this analysis, it is assumed that it is a DIGR. Average salary cap was based on 2010-2011 for the top 30 goaltenders (whereas the average save percentage) was for the top 49 goalies, so therefore the average salary is overstated. This analysis should be revised to properly use DIGR and average salary for the same sample of goalies.