Hey /r/hockey! I recently had to do a statistics assignment for one of my political science classes. In this assignment, we had to assess a statistical relationship (political or non-political), and I decided to look at the GAA of Vezina Trophy winners in conjunction with their team's playoff wins. I got a decent grade on the assignment (yay!), and so I decided I might share some of my findings with you all. What I have here isn't my actual assignment (since the format of that one is a lot more formal and includes other data analysis not related to hockey), but instead a breakdown of what I found while doing the assignment.

Since the 1986-87 season, the first NHL season to include four best-of-seven rounds in the playoffs, only three goalies went on to win the Stanley Cup during the same season in which they won the Vezina Trophy. In addition, only three additional goalies (six total) went on to even make the Stanley Cup finals during their Vezina-winning season. While this is more than likely due to numerous reasons, including team performance and quality of competition, a goalie's own performance could play a role as well.

While GAA is not a perfect stat, it can still provide a picture of how a goaltender performed. Vezina-trophy winners since '86-'87 have averaged around 2.245 GAA; teams as a whole have averaged around 2.859 GAA during that same period. Vezina winners, however, show a slight increase in their GAA during the playoffs, averaging around 2.659 GAA during the post-season. This difference in performance caught my attention, so I decided to do some analysis of these numbers. Buckle up, because this is going to be a long post.

GAA stats of Vezina Winners

For this analysis, I looked at the season GAA (SGAA) and the playoff GAA (PGAA) of each Vezina winner since '86-'87. I substracted PGAA from SGAA to calculate the difference-GAA (dfGAA) for each goaltender.

Three goaltenders were excluded from the analysis. First, Capitals goaltender Jim Carey, the winner in '95-'96, played for only 97 minutes in the '96 post-season. As a result, his PGAA is unusually high (6.18!), and his minutes are significantly lower than the other goaltenders. Due to his unique circumstance, he is excluded from the data; regardless, his inclusion or exclusion does not change the result of the analysis. Second, Sergei Bobrovsky's '12-'13 data is excluded due to the Blue Jackets not making the post-season that year. Third, Jets goalie Connor Hellebuyck's data for this past season ('19-'20) is excluded, as the Jets failed to make it out of the qualifying round of the playoffs.

Below is the table with SGAA/PGAA/dfGAA data for each goalie included in the analysis. Bold italicized names indicate goalies who won the Stanley Cup that year; bold names indicate goalies who lost in the Stanley Cup Finals that year. Italicized names indicate goalies who lost in the Conference Finals.

Assessing Playoff Success

Now there are several ways to assess a team's playoff success. The simplest way is to assess whether a team won the Stanley Cup or not. However, this may not provide as full of a picture, as a team making the Conference Finals could be considered more successful than a team that is swept in the first round. Looking at a team's total playoff wins for a given season can provide a clearer, though not perfect, indicator of playoff success.

For clarity, here is a chart comparing playoff results with total playoff wins.

With that in mind, here is a chart showing each goaltender's dfGAA in comparison with their team's playoff wins (PGW). Italics indicate a goaltender that lost in the Conference Finals; bold indicates a goaltender that made it to the SCF; bolded italics indicates a team that won the SCF.

Analysis of Data

I ran a few statistical tests on the data. First, I ran a correlation test on dfGAA and PGW. The correlation coefficient helps provide some context into the statistical correlation of two variables. A value of 1 indicates a perfect positive relationship (i.e. as one number goes up, the other goes up as well), while a value of -1 indicates a perfect negative relationship (i.e. as one number goes down, the other number goes up); a value of 0 indicates no relationship between the stats. The correlation test of dfGAA and PGW indicates a correlation coefficient of -0.661, indicating a moderately negative relationship between dfGAA and PGW. In other words, goaltenders with lower dfGAA values were correlated with teams winning more games.

I also ran a bivariate regression on the data. This test helps to further assess the relationship between dfGAA and PGW. The results of this analysis provided a R² value of 0.437, indicating that dfGAA explains about 43.7% of the variation in PGW. The data's p-value, which determines the statistical significance of the relationship, was 0.000069. A p-value of less than 0.05 usually indicates that a statistical relationship is likely not due to the chance; with a p-value of 0.000069, we can conclude that dfGAA and PGW are linked by more than just chance.

"But What Does This All Really Mean?"

The statistical relationship of the two variables is all fine and dandy, but I believe there are some other interesting aspects of this data that one could find that provide some interesting insights into Vezina winners and their playoff success.

Not a single goaltender with a positive dfGAA (indicating a worse GAA in the post-season) made it out of the second round of the playoffs. In fact, only one goaltender (Pekke Rinne in 2018) won more more than 6 games while posting a positive dfGAA, though Nashville's 7 post-season wins that year isn't much better than 6. This includes goaltenders who posted an above average GAA when compared to the average SGAA across the league. Some examples:

*indicates the average GAA across the league for that season

**goalie's PGAA minus League Average GAA

***dfGAA still refers to a goalie's PGAA minus SGAA

Only Vezina winners with negative dfGAA numbers made it to the Conference Finals; from there, success tends to become more up in the air. Even still, posting a negative dfGAA does not always equate to success. Dominik Hasek had negative dfGAA numbers for five of his six Vezina winning seasons, but the Sabres only made it to the Conference Finals or better in two of those seasons. Braden Holtby posted the second best dfGAA of all Vezina winners (-0.48, only behind Grant Fuhr's -0.52 in '87-'88), yet the Washington Capitals only won 6 post-season games that year.

What does this all mean then? Well, comparing a Vezina winner's season GAA with their playoff GAA can provide some context regarding their team's playoff success (or lack thereof). Vezina winners almost certainly need to improve upon their already impressive regular season numbers in order to achieve success in the post-season. However, improving their GAA in the post-season may not be enough, as seen with numerous goaltenders demonstrating improvement while still losing in the second round or earlier.

In general, the quality of competition will be much higher than usual in the post-season, and goaltenders will be facing against the same team for multiple games in a row. These factors could explain the potential decline in GAA during the post-season for a Vezina winner. I'd love to hear some of your theories on why winning the Vezina doesn't always lead to winning the Stanley Cup!

Some more fun insights I noticed while working on this:

• Only two Vezina winners since '86-'87 went on to win the Conn Smythe Trophy the same year that they won the Vezina: Ron Hextall (PHI) in '86-'87 and Tim Thomas (BOS) in '10-'11.

• Since 1986-87, the average playoff GAA for Stanley Cup-winning goaltenders is an absolutely bonkers 2.11. Only 12 times since the '86-'87 season has a Vezina winner had a post-season GAA better than this average: Braden Holtby ('15-'16 1.72), Tuukka Rask ('13-'14, 1.99), Henrik Lundqvist ('11-'12, 1.82), Tim Thomas ('10-'11, 1.96; '08-'09, 1.85), Martin Brodeur ('02-'03, 1.65), Dominik Hasek ('00-'01, 2.09; '98-'99, 1.77; '97-'98, 2.03; '96-'97, 1.96; '93-'94, 1.61), and Patrick Roy ('88-'89, 2.09). 5 of those 12 occurrences were by Dominik Hasek. In addition, only two of those occurrences resulted in a Stanley Cup win (Thomas in '10-'11 and Brodeur in '02-'03).

UPDATE: So I ran a quick analysis with SV% instead of GAA, and the results are pretty interesting there as well. Improvement on SV% is very much correlated with playoff wins (the correlation coefficient was 0.63!), and the data is pretty significant (p-value of 0.00016). I'm going to look some more at this and see if I can find any other trends, but so far using SV% instead of GAA turned out results that are much more compelling. If y'all are interested, I can post an analysis with SV% in place of GAA if that would be more interesting!