The Effective Goalie Formula and Its Uses

By Ethan Fasking 

Part 1: Development and Purpose 

    The core idea behind the Effective Goalie Formula (EGF) was to aggregate baseline goalie statistics in a way that directly compares goalies to each other in a manner similar to football’s Quarterback Rating (QBR). To accomplish this, I first determined which statistics best reflect a goalie’s core effectiveness. I determined these to be save percentage (SV%), saves per game played (SV/GP), goals against average (GAA), and shutouts per game played (SHO/GP). SV% was chosen because it is directly proportional to the value a goalie adds to their team, i.e. the higher proportion of shots they save, the more effective they are to their team. SV/GP was determined to be important because, as demonstrated below, a higher SV/GP was associated with higher GAA stats and lower SHO/GP stats. Using SV/GP allows us to account for this phenomenon and better judge a goalie’s effectiveness in context. GAA was chosen to acknowledge what many consider to be the most important statistic for a goalie: how many goals do they let in? This is, fundamentally, a good question to answer when discussing a goalie’s effectiveness, so it was included. Finally, SHO/GP were included to represent the proportion of “very good starts” a goalie has in a given period of time. 

    After the constituent statistics were chosen, the baseline averages were determined by taking the average in each category of NCAA women’s goaltenders between the 2008-09 and 2012-13 seasons. The averages and standard deviations are as follows:  

	Average	Standard Deviation
SV%	0.914	0.020
SV/GP	24.84	4.503
GAA	2.497	0.890
SHO/GP	0.118	0.090

    In each category, a goaltender increases their score by performing above that mean and lowers their score by performing below the mean. These factors were then weighted in a way that reflects a goalie’s influence over each stat (approximately 12 | 8.25 | 7.5 | 6). For instance, a goaltender has a high degree of control over the proportion of saves they make, but less over the gross number of saves. The initial weights were then refined such that the distribution of scores was roughly normal, and that a goalie performing to the “average” in each category would produce a season score of 100. This mark was chosen due to its intuitive measure as a baseline average, a la IQ. This creates a metric where goaltenders who face a high number of shots, make a high number of saves, and let in as few goals as possible score the highest, while those who face fewer shots and let in more goals perform the worst. 

    The core purpose of the EGF is to produce scores that illustrate the relative efficacy of goaltenders over a season. This means there are a few ways to interpret results. The first is to directly compare multiple goalies within the same league and season. This illustrates which goalies are more effective, i.e. which goalies are providing the most value to their teams by their individual effort. The second is to compare goalies to the average score for their year. While the EGF does have “average” metrics, they only reflect the average of the five-year period I used to create the EGF. So, the best way to get an idea of which goalies are above average for a given season is to compare them to the average of that season, rather than the flat 100.00 mark. Finally, the EGF can be used to track the progression of goalie efficacy across seasons by comparing the averages of those seasons. This doesn’t necessarily reflect general talent differences, but it does reflect how much teams rely on their goalies over time. 

Part 2: Predicting Awards 

NCAA Men:  

    As of 2023, the Richter award has been awarded ten times since its inception. The goaltender who achieved the highest EGF Score by the end of the season (and played at least 20 games) has won 5 of them, making it a better predictor of the Richter than any individual stat tracked by the NCAA. Additionally, of the 13 goaltenders in the Richter era to score 130 or higher, all of them became finalists. They spanned 8 seasons, and collectively won 6 Richter awards. Here are the conditions under which the EGF champion has not won the Richter: 

• 2014-15 and 2016-17: The lowest-rated finalist won. 
• 2017-18: Cale Morris (137.65) upsets Colton Point (138.93), overcoming a 1.28 deficit. 
• 2018-19: Cayden Primeau (122.62) Upsets several goalies, but excluding his last game of the season (which voters hadn’t seen at the time of voting), he would have been the league leader. 
• 2020-21: Jack LaFontaine (122.48) upsets Strauss Mann (a tandem goalie) and Spencer Knight (127.37). LaFontaine led in SV%, GAA, and SHO/GP, while Knight led only in SV/GP. 

    Overall, it seems clear that both the “eye test” (represented by the Richter committee) and the EGF agree, generally, on the most outstanding goalies of a given season. 

    By contrast, the EGF is not a good predictor of the Hobey Baker award. Going back to the 1999-2000 season, goalies make up two Hobey winners and 10 finalists. Among these goalies, 3 have been the EGF champion and another 2 have placed second, while the rest are between 4th and 8th in their given year. This limitation lies primarily with the Hobey Baker Committee’s reliance on legacy. This is best exemplified by the 2021-22 season, where Devon Levi became the all-time NCAA EGF single-season champion, won the Richter, and lost the Hobey to Dryden McKay, who recorded an impressive career, but a relatively lackluster season. 

NCAA Women: 

    On the women’s side of NCAA, the EGF’s power as an awards forecast is much stronger. Of the past three Women’s Goaltender of the Year awards, EGF has predicted all three (excluding tandem goalies). Additionally, the EGF is also a great predictor of finalists and winners of the Patty Kaz award (NCAA Women’s Player of the Year). Of the ten Patty Kaz finalists who have played goalie since 2000-01, 7 were the EGF champion that year, and the remaining three were second. Overall, high EGF scores are among the strongest, if not the strongest, indicators of which goalies will win national awards in a given season. 

NHL: 

    I haven’t done any multi-season study into the NHL, but for the 2022-23 season, the top regular season goalies are as follows: 

Name	EGF Score
Linus Ullmark (BOS)	121.82
Filip Gustavsson (MIN)	118.44
Ilya Sorokin (NYI)	112.56
Alexander Georgiev (COL)	108.60
Connor Hellebuyck (WPG)	108.27

    Linus Ullmark won the 2023 Vezina Trophy. Ilya Sorokin was second in voting, followed by Connor Hellebuyck, Juuse Saros, and Jake Oettinger. Saros and Oettinger were 6th and 7th in EGF respectively this season, meaning voters passed on Gustavsson (who played far fewer games than the others on this list) and Georgiev (whose defect isn’t readily apparent). 

Part 3: Conclusion 

Potential Limitations: 

    The first limitation I have considered here is how strength of schedule influences these results. After all, it would make sense that facing better teams would generally depress your season statistics. I believe that the prioritization of SV% and SV/GP sufficiently mitigates this, since SV% does not appear to be strongly influenced by SV/GP and the best teams tend to put more shots on goal. Similarly the effect of the defensive scheme of a given team is similarly mitigated by emphasizing SV/GP, as the best defensive schemes tend to allow the fewest shots. 

    The next limitation considered is quality of shot faced. This limitation is the strongest among those I have identified. This is because the quality of shot faced is only dealt with by relying on the large number of shots faced per season producing roughly even amounts of different-quality shots per goalie. That is to say, each goalie who faces enough shots will end up with a roughly normal distribution of shot quality centered around the national average. 

Applications: 

    The EGF is a robust statistical aggregator with flexible applications across high-level hockey leagues. It is best used as a measure of which goalies are most effective relative to others across one season but can be used to gauge historical data and the relative efficacy of goaltenders across different timeframes. As a predictor of awards, it is highly effective and shows a strong ability to correctly predict winners given minimal external limitations. 

Award	Winner top EGF Score	Winner Top-5	Winner Top-10
Richter Award	50%	80%	80%
Hobey Baker Award	50%	50%	100%
Women’s GotY	100%	100%	100%
Patty Kaz Award	100%	100%	100%

Proportion of the time the winner of each award has had the top EGF score, a top-5 EGF score, or a top-10 EGF score at the end of each season.