Updated xSV% - Save Percentage Accounting for Shot Quality

Goalies are voodoo. That should probably be added as the 11th Law of Hockey Analytics. Goaltending analysis is currently one of the most lacking subjects within hockey analytics. Great strides have been made however, with 5v5 SV%, AdjustedSV% and High Danger SV%. A few months back I revealed a statistic I referred to as xSV%. You can click there to read the article but, more or less, I calculated a goaltender's Expected SV% based on the quality of shooter for each shot faced based on a rolling average of the shooter's individual shooting percentage. xSV% is a goalie's actual SV% minus their ExpSV%. A higher (positive) xSV% is good while a lower (negative) xSV% is bad. I have thought more about that specific methodology since posting that article and have eventually decided that with some substantial changes I could greatly improve upon xSV% . Based on factors in my ExpG model combined with regressed shooting percentage for each shooter (same mindset but different process as the original xSV%) I basically started from scratch to develop this latest rendition of xSV%.

Methodology

The basis of a goalie's Expected SV% comes from the same model I used in my latest ExpG model. Here is a quick breakdown of the different variables and a brief explanation of why they are included in the model:

• Adjusted Distance
• The farther a shot is taken from the lower likelihood it has of resulting in a goal 
• Type of Shot
• Snap/Slap/Backhand/Wraparound/etc...
• Different types of shots have different probabilities of resulting in goals
• Rebound - Yes/No?
• A rebound is defined here as a shot taking place less than 4 seconds after a previous shot
• Rebounds are more likely to result in a goal than non-rebounds
• Score Situation
• Up a goal/down a goal/tied/etc…
• It has been proven that Sh% rises when teams are trailing and vice versa
• This adjustment, while only slight, helps to account for a variety of other aspects that we are currently unable to quantify yet have an impact goal scoring 
• Rush Shot - Yes/No?
• Shots coming off the rush are more likely to result in a goal than non-rush shots

Now that we have the structure of our ExpSV% we need to add shooter talent into the mix since the model currently assumes league average shooting talent for each shot, which we know is not the case in reality. Generally, a shot from Sidney Crosby is more likely to result in a goal than a shot from George Parros. So I wanted to make a multiplier for each player in each season to get a best estimation of their personal effect on each shot's probability of resulting in a goal.

Using the Kuder-Richardson Formula 21 (KR-21) I was able to find that 5-on-5 Sh% stabilizes for forwards at about 375 shots while 5-on-5 Sh% for defenceman begins to really stabilizes around 275 shots. Therefore, for each season I added these shots (375 for forwards, 275 for defenceman) to a players total shots. I also added a certain amount of goals calculated as the added shots (375 or 275) multiplied by league average Sh% (forwards and defence had different league average Sh%) for that season. This would then allow me to calculate regressed Sh% based on these new shots and goals totals. I then divided rSh% by the league average Sh% (forwards and defence had different league averages) to give a Shot Multiplier. Then multiply this Shot Multiplier for each shot they took in that season. In case you didn't quite follow that rough explanation, here is an example of how this process played out for Steven Stamkos' 2011-2012 season, the highest rSh% season since 2007-2008:

Repeatability

The big issue with goalie metrics has always been how well they actually represent true ability. Sample size is a frequent issue with goaltenders and it has been shown countless times that the only way to truly get a good idea of a goaltender's ability is to take very large shot samples. These samples typically take multiple years to accumulate. Looking at year-to-year correlations, so far, it seems as though xSV% is on par with 5v5 SV%. The interesting difference I found, with the vital help of @MannyElk, is shown in the graph below. To paraphrase his earlier work, the experiment was done by drawing random samples of n games for each 40+ GP goalie season since 2007 and each sample was compared with the goalie's xSV% over the whole season. Essentially, the graph below shows that xSV% will show us more signal than noise sooner than 5v5 SV%.

**Disclaimer** Manny and I are not 100% sure of the results here so if anyone has suggestions please reach out. 

Data 

Quick review of the stats below:

• xSV% = Actual SV% - Expected SV%
• dGA (Goals Prevented Above Expectation) = Expected Goals Against - Actual Goals Against
• Similar to GSAA

Below is a wonderful Tableau visualization created by @Null_HHockey, as well as a spreadsheet with all of the relevant information. Once again big thanks to the guys at War-On-Ice for all their help (and data). Everything below will also be stored full time on a separate xSV% page. Enjoy!

Corsi Against Doesn't Correlate with Save Percentage

How does a goalie's workload affect their ability to preform?  This question always seems to be bouncing around  and recently has come up again with regards to whether a goalie's workload (the amount of Corsi events they face) has a tangible impact on their save percentage.

Previous Literature 

The first analysis was done by Brodeur Is a Fraud and found little to no evidence of a correlation between the two variables. Another look was done over at Hockey-Graphs and found similar results with a different method:

For the forty active goaltenders to play at least one hundred NHL games over the past four seasons, there is no substantial relationship in them playing better -in terms of save percentage- when facing more or less shots against.

Chris Boyle in his own study at SportsNet did seemed to find a quite strong relationship yet I have some serious doubts as to the validity of his methodology. Essentially by looking at the raw shot counts and save percentages posted in individual games while removing goalies who didn't play the full game you result a very serious issue of survivor bias. Why do goalies in this study who see a large amount of shots against only post high save percentages? Most likely it is because if a goalie faces a large number of shots and doesn't post a high save percentage they will allow a large number of goals which leads to them being pulled from the game and therefore they are removed from this study. This removal doesn't happen for goalies who face a low number of shots while posting a low save percentage because they can still allow only a low number of goals against giving their coach no incentive to pull them. Example, a goalie faces 20 shots against and lets 2 in. That's a .900 save percentage which in the big picture isn't good but in an individual game only allowing two goals against is just fine. Therein lies my issues with this study.

Finally, we arrive at the most recent post by David Johnson at Hockey Analysis who can summarize his own methods best:

In my opinion, the proper way to answer the question of whether shot volume leads to higher save percentages is to look at how individual goalies save percentages have varied from year to year in relation to how their CA60 has varied from year to year. To do this I looked at the past 7 seasons of data and selected all goalie seasons where the goalie played at least 1500 minutes of 5v5 ice time. I then selected all goalies who have had at least 5 such seasons. There were 23 such goalies. I then took their 5-7 years worth of CA60 and save % stats and calculated a correlation between them. 

Basically, he found the individual correlations for each goaltender and then averaged these individual correlations. A few issues I noticed starting with the fact that correlation coefficients aren't additive. You need to first convert them to Fischer z values which are additive. This issue is minor as I ran his test again the results don't alter too much with this adjustment.

The second issue I take is with the claims made based on this study. Starting the use of word "boost" in the title implying that there is not only causation here which I am not convinced of (we simply see a correlation via his methodology) and also that there is only a positive correlation, meaning that an increase in CA/60 results in an increase in SV%.  Examine the data closer you find that 8/23 goalies saw the inverse effect (more shot-attempts against lowered their SV%) while another two saw essentially zero change in SV% in relation to their shot-attempts faced. This leaves us with only 13 goalies who we can see to have a positive correlation. This leads to my issue with the author making a general assumption about the impact of CA/60 boosting Save Percentage as a uniform result that can be applied across the board to all goalies, when he is really only talking about a specific subgroup. Later on in this post I will reveal my doubts with regard to his methods and how I believe he simply found a false positive for a relationship that doesn't exist. 

My Findings

I tweeted this graph out earlier when this question was first raised on Twitter. It is a very basic graph that took me a few minutes to put together but you can see a team allowing more shot-attempts against having a noticeable impact on their save percentage to be essentially zero.

These next few charts look at the individual goalie level. I set different cut offs in each graph just to see if we could weed out some goalie talent since better goalies tend to play the more minutes (unless your team is located in Winnipeg) and we still aren't able to find any strong evidence (the correlation does actually increase as we narrow the sample jumping from about 0 to 3%). 

This graph below is the same as the ones above but only using the data included in the Hockey Analysis study.

Since none of the graphs I managed to produce were able to find any correlation I decided to try my own blind recreation of the method used at Hockey Analysis. Below are two graphs very similar to the graphs first produced at Hockey Analysis that seemed to demonstrate the correlation between CA/60 and SV%. I have removed the titles of these two to add an element of surprise. Take a quick look at both before finding their titles below. 

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 Surprised? This is my basic way to suggest that the results shown in Hockey Analysis' study could be the result of simple random variation. Pekka Rinne's chart is to show how one of these samples can be pretty much out of wack on the individual level while the Niemi vs. Howard chart shows that even when picking two variables that we know for a fact should have zero correlation to each other, when dealing with such small samples in this case only 5 seasons (or data points), it can be pretty easy to discover a relationship that doesn't actually exist.

The chart below shows the data on the correlation's found by Hockey Analysis. I took the liberty of converting it to Fisher z-values and then the Inverse of that which is the real correlation that he was looking for. So in actuality his correlation was higher than he first reported. To make things simpler I have stared* the important column here with the true correlation. 

Average Correlation	Average Fisher	Average Fisher Inverse*
0.183	0.215	0.212

The issue as you may have seen above in the Niemi vs. Howard chart is that it is very easy with this data set and this method to find correlation's that we know for a fact shouldn't exist. Below I calculated 23 correlations and their subsequent Fisher values in my blind test. I simply put the goalies in alphabetical order and compared the CA/60 for goalie A with the SV% of goalie B. 

Correlation	Fisher
-0.292	-0.301
0.098	0.098
-0.098	-0.098
0.730	0.930
0.631	0.743
-0.407	-0.432
-0.726	-0.919
0.116	0.117
0.536	0.599
0.117	0.118
0.126	0.127
-0.230	-0.234
-0.131	-0.132
0.338	0.351
0.586	0.671
0.468	0.507
-0.631	-0.744
-0.383	-0.403
-0.616	-0.718
-0.708	-0.882
-0.213	-0.217
-0.095	-0.095
Average	Average Fisher
-0.784	-0.916
	Fisher Inverse*
	-0.724

We know from common sense and logic that the number of shot-attempts faced by Evgeni Nabokov will have no effect on Henrik Lundqvist's save percentage but the number's actually show a correlation (.73). This is obviously a false positive showing a correlation that doesn't truly exist. Simply stated, correlation doesn't always prove causation. Based on what I have found here and the earlier research done on the subject, I feel confident in stating there is still little to no evidence relating the Corsi Against a goaltender and their Save Percentage.

You can reach me via email me here: DTMAboutHeart@gmail.com or via Twitter here: @DTMAboutHeart

NHL Goaltending - Best Friend or Worst Enemy

“Goaltending is 75 percent of your hockey team, unless you don't have it. Then it's 100 percent.” – Harry Neale

Goaltending can make or break a hockey team. Every season there will be a handful of men between the pipes dragging their teams into the playoffs and typically just as many who will will cost their teams an invite to the big dance.

For those of you who are unaware, goalies can be wildly inconsistent. A goalies SV% tends to vary quite largely from year-to-year. Even better evaluators of true talent such as ESSV% or RoadSV% will rise and fall from year to year.

Ottawa Senators are possibly the most recent poster boy for the reality of goaltending inconsistency. The Senators have seen their goalies SV% plummet from an absurd .935 to a below-average .908. How could this happen? Did Anderson and Lehner suddenly forget how to play goalie? Probably not. What probably did happen however was a brutal form of regression. Essentially, Anderson and Lehner's stats came hurling back to earth. So how good are they really then? Are they .935% goalies? Probably not. Are they .908? Probably not that either. The answer most likely lies somewhere in the middle. 

In this analysis, I hope to show what the league would have looked like this year had some goalies not played as amazing as they did (ex. Varlamov) or not as poorly as they did (ex. Dubnyk). 

The method for my research came from the idea posted by Phil Birnbaum:

Roughly speaking, that means you can expect 25% of a goalie's difference from the mean to be repeated next year. Put another way, you have to regress the goalie 75% towards the mean.

Yes, that's not as much as you'd expect. By that calculation, if the average save percentage is .904, and goalie X comes in one season at .924, you'd expect next year he'd be at .909 -- one quarter of the distance between .904 and .924.

The basics of what I did was look at every NHL goalie who had faced about 900 shots (or about 35 games played), and regressed their save percentage 75% towards the mean. The reason I chose to do this and not just set everyone at league average is because I believe this is a better reflection of what a team should realistically expect from them their individual goalie.

I then calculated how many more goals you would expect a goalie to either surrender or save for the given season. Finally, I gave a team 1 point for every 3 more goals saved and vice-versa.

Here are my results...

Team	Official Points	Goalie Regression Points	+/- PTS	Original League Standings	Regressed League Standings	+/- Standings
WINNIPEG	84	89	5	22	17	5
EDMONTON	67	71	4	28	28	0
OTTAWA	88	90	2	19	15	4
NY ISLANDERS	79	81	2	26	24	2
FLORIDA	66	68	2	29	29	0
DETROIT	93	94	1	14	12	2
NEW JERSEY	88	89	1	19	17	2
NASHVILLE	88	89	1	19	17	2
ANAHEIM	116	117	1	2	1	1
SAN JOSE	111	112	1	4	3	1
CALGARY	77	78	1	27	27	0
NY RANGERS	96	96	0	12	10	2
WASHINGTON	90	90	0	17	15	2
LOS ANGELES	100	100	0	9	8	1
PHOENIX	89	89	0	18	17	1
BOSTON	117	117	0	1	1	0
MINNESOTA	98	97	-1	11	9	2
PITTSBURGH	109	108	-1	6	5	1
CHICAGO	107	106	-1	7	6	1
VANCOUVER	83	82	-1	24	23	1
ST LOUIS	111	110	-1	4	4	0
PHILADELPHIA	94	93	-1	13	14	-1
DALLAS	91	89	-2	16	17	-1
BUFFALO	52	49	-3	30	30	0
TORONTO	84	81	-3	22	24	-2
CAROLINA	83	80	-3	24	26	-2
COLUMBUS	93	89	-4	14	17	-3
TAMPA BAY	101	96	-5	8	10	-2
MONTREAL	100	94	-6	9	12	-3
COLORADO	112	105	-7	3	7	-4

As you can see, Varlamov and Price both had huge season for Colorado and Montreal respectively. These new league standings have Montreal sliding down to a wildcard spot and Colorado sliding down to 3rd in the Central. While Winnipeg once again suffered a severe case of Pavelectricity keep them out of a potential 4 way tie for the final wildcard spot in the West.

The results show what I think many would agree with, some teams benefited highly from their goalies while others really suffered. While this helps us more or less neutralize the effects of a particularly strong or weak season by a particular goalie it doesn't totally level the playing field, keeping individuality live and well.

***Notes***

• I only chose goalies fitting my 900 shots or about 35 games played just to eliminate as many small sample sizes as possible
• I didn't run this regression for Henrik Lundqvist and Tuukka Rask, simply based on the fact that these two have yet to post non-elite numbers so I felt it unfair to hurt either of them on the basis that we shouldn't expect much regression at all
• Minnesota didn't have any goalies who fit my minimum requirement therefore I simply ran the regression for their team average