Player Comparison Tool/Salary Generator

Every NHL contract negotiation will always feature at least 2 common events: 1) reporters listing off subjectively-determined comparable players to peg a player to a given salary (“He’s going to be looking for Andrew MacDonald money”); and 2) fans picking-and-choosing stats to poke holes in the analysis performed by the media and come up with their own valuation. While the player evaluation tools available to the hockey community have grown over the past few years, the use of these tools to value players has always been somewhat lacking-should we look at a player’s Corsi-Rel, or his raw CF%? How do we include contextual factors like zone starts in our analysis? And what if there’s something that our stats don’t measure, that really should be included in a proper valuation? On the other hand, while finding comparable players is an admirable approach, the comparisons that are often used include such factors as “playing the tough minutes” or “bringing heart into the dressing room” or “he’s not Russian”. While these make for nice storylines (except the last one), they don’t always translate into good decisions (as the Flyers will likely find out with the aforementioned Mr. MacDonald).

As a fancy stats enthusiast and someone generally interested in tinkering in Excel, I wanted to look at whether we could blend the approaches to come up with a way to turn advanced statistics into comparable players. While I used a nearest neighbour analysis to find comparable players in my free agent preview this year,  I found that it was tough to translate the results of a single variable (in this case, xGD20) into a salary, particularly considering that important factors such as usage weren’t included in the analysis. I wanted to put something together that was flexible enough that it could be modified to take different variables into account depending on the kind of analysis that was being undertaken (for example, comparing players on usage or comparing players on performance) to allow any analyst to decide which were the stats that mattered when determining player salary. And so, after the usual few weeks of procrastination, I’ve finally built a working Player Comparables Tool, which I’ve put up for download here.

The underlying spreadsheet that drives the whole tool was put together by the amazing Rob Vollman, who literally wrote the books on hockey analytics (which you should go purchase immediately if you haven’t yet). Pretty much every piece of data you could want to include is in there, including both stats of the fancy and non-fancy variety. The tool is setup to allow you to choose up to 10 stats to include in your analysis, and to weight them as you see fit. All changes should be made to the highlighted cells on the Player Comparables tab for best use-if you’re an NHL exec whose tinkering leads to a bad deal, I’m not giving refunds.

The approach the calculator takes is to find a given player’s “nearest neighbours” across the selected variables, calculating a z-score for each variable to ensure that everything is scaled the same way. I’ll spare you the rest of the nitty-gritty details of the calculations, but if you want to dig into it a bit more, the calculation “steps” are more or less outlined in columns O-AR of the “Consolidated” sheet.

The one piece of data that’s missing is a differentiation between contracts that cover UFA years, versus deals that are only for a player’s RFA seasons. This unfortunately tends to understate the salary of some of the UFA deals that get signed, but with the data at hand it’s a necessary limitation.

A few other things to note:

  • If you choose only a few stats you’re likely to get wonky results and/or errors (this is due to ties in the nearest neighbour ranking).
  • If you want to add your own stats all you need to do is add them onto one of the tables (Main, PP, EV, PK), and they should automatically appear in the dropdowns.
  • If you want to use more than 10 players in the calculation, you just need to add rows below the 1-10 names, and adjust the formulas as appropriate.
  • All of the salaries in the sheet are based on 2013 cap hits. If you want to update, edit the Cap Cost column (CX) of the Main Page.

So how well does the predictor do in actually guessing free agent salaries? I took a very basic approach, equally weighting OZ%, ES CF%-Rel, ES TOI%, PP TOI%, PK TOI%, ES IPP, Total Sh%, ES PenD/60, ES Pts/60 and PP Pts/60, and compared the actual salaries with the nearest-neighbour predicted top 60 free agents from TSN. While this model is obviously a fairly basic one, it does do a decent job, generating an R^2 between predicted and actual of 0.25. With a bit of tweaking of the weights (and ideally, the inclusion of UFA/RFA deal info), it would likely get a lot better.

Actual vs. Predicted Salary for Top 60 Free Agents (salary data from TSN.ca)

Actual vs. Predicted Salary for Top 60 Free Agents (salary data from TSN.ca)

If you have any questions or issues with the sheet (or, if you find any bugs) don’t hesitate to let me know either in the comments or at puckplusplus AT gmail DOT com.

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Posted in Free Agency, Predictions

When should teams attempt to block shots? Looking at the break-even success rate for shot-blocking

The 2013-2014 season was a painful one for Ottawa Senators fans. After reaching the playoffs in both of the previous two seasons, many analysts predicted that the Sens were on the verge of breaking through into the league’s elite. Instead, the Sens struggled to string wins together, and finished the year 11th in the Eastern conference in spite of posting a 52.4% 5v5 Corsi percentage, a number that had them 7th in the league.

One major reason that the Sens failed to capitalize on their relatively strong possession numbers is that their Corsi advantage failed to translate into recording more shots than their opponents. Much of this had to do with the fact that the Sens blocked shots at a rate that was significantly lower than the rest of the league. While the league average block rate was 25.6% (total blocks/total Corsi attempts against), the Sens only got in the way of 20.5% of the shot attempts directed towards their net. And while some of this may be bad luck, we do know that blocked shots show a reasonably strong repeatability at the team level. Moreover, there’s ample evidence to suggest that this reluctance to block shots was an intentional decision on coach Paul Maclean’s part.

Now there’s definitely an argument to be made that attempting to block shots can be a risky proposition. You may end up screening the goalie or deflecting the puck on your own net, both of which increase the odds that your goalie isn’t going to stop it. Letting the goalie see the puck and staying out of the way is a mantra that’s oft repeated, in particular by a certain Saturday night first intermission hockey host. But there are obvious benefits to blocking a shot too: a successful shot block has a 0.00% chance of going in.

The question then is, how successful do we need to be when blocking shots to make up for the increased risk of a screened or deflected shot. If we consider only two possible outcomes, a successful block that prevents a Fenwick attempt, or a failed attempt that results in either a miss (we’re not worried) or a shot on goal with an increased probability of going in, then we can calculate the rate that we need to be successful at in order to make the attempt worthwhile.

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Posted in Theoretical

What’s a goalie worth these days? Determining replacement level goaltending

The concept of a replacement level player is one of the most important ideas in sports analytics, but one that unfortunately is used relatively infrequently in hockey. Replacement level is meant to represent the level of talent that’s widely available to any team at little or no cost. Comparing players against replacement level is important because it essentially tells us whether a player is worth keeping or not – anyone performing below replacement level should be discarded, since it’s likely that any free-agent or waiver wire pickup would perform better. It’s important to note that this is different than comparing against the average player – when we compare against the average we know whether a player is better or worse than most of the players eating up minutes throughout the league, but it doesn’t give us any indication of whether he’s worth keeping around.

For position players figuring out an appropriate replacement level is extremely difficult – there’s no broad agreement as to what individual statistics should be used, let alone any idea of how to determine who a replacement level player is. For goalies, however, we have a half-decent metric (Even Strength Save Percentage), that’s broadly accepted as being representative of individual talent, even if it is somewhat more variable in the short term than we’d like.

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Posted in Uncategorized

Why is it so hard for good teams to get better? Looking at the value of a marginal goal

We’re now three days into free agency and with most of the marquee names on the market already signed on for the coming year and beyond, teams and fans alike are starting to look over their rosters trying to figure out whether they’re sitting in a better position than they were on June 30th. With some teams the improvement is fairly obvious: after finishing 8th in the West last year the Dallas Stars have added Jason Spezza and Ales Hemsky and looked poised to take a run at the Blues and Blackhawks for Central Division supremacy. The Anaheim Ducks also made a big splash, bringing in Ryan Kesler from the Canucks while only sacrificing Nick Bonino and Lucas Sbisa. Having added a big name to take some of the pressure off of Ryan Getlaf, should we expect a similar bump to elevate the Ducks to President’s Trophy champions next year?

This type of situation comes up frequently not just in the NHL but across professional sports: fringe team adds a few key pieces and turns into championship contenders, while a team that finished the previous year on the edge of winning it all can’t turn their added potential into dominance. Ultimately, what this comes down to is that the value of a given player isn’t the same to each team: adding on additional goals (or allowing fewer goals, depending on which way you look at it), has different effects on a team’s record depending on how good they were before. Adding Brad Richards to the Blackhawks isn’t the same as adding Brad Richards to the Blue Jackets would be. To put it another way, the value of a marginal goal decreases as a team’s goal differential increases (and in a non-linear manner, as we’ll see later).

To illustrate this point, I put together a quick simulation to look at how the value of an extra goal varies based on team strength. I began by generating 82 games, picking a random number of goals for and against between 0 and 5. I assumed that we were only looking at regulation play, and so allowed the game to finish tied in this case (while this isn’t perfect, practically it shouldn’t make much difference). I totalled up the initial goal differential across the 82 games, and then chose one of the 82 games to randomly add a goal to. If the game had initially finished in a tie, or with our simulated team down by 1 goal, I added one point on to their overall point total. Then, I repeated this process 50,000,000 times and counted how many times a team got an extra point by adding an additional goal. If we take that number and divide it by the total number of times we added an extra goal, we can figure out the marginal value of an added goal for a team with a given goal differential.

Pts. Per Marginal Goal

Pts. Per Marginal Goal

As we’d assume, what we see is that the number of additional points we expect a team to earn for adding an extra goal decreases as our imaginary team’s goal differential increases, and the relationship isn’t linear. A team that is sitting on a +20 goal differential gets less benefit from adding one additional goal than a team with a -20 goal differential. From a practical perspective, this means that it’s a lot easier for a bad team to improve than it is for a good team.

What’s interesting to note though is that the graph doesn’t actually peak at 0 as you might expect. While a team with just as many goals for and against might expect to each 0.36 additional points from adding one more goal, a team with a -50 goal differential will get about 0.37 additional points. On the other hand, a team with a +50 goal differential is only going to earn approximately 0.32 additional points from scoring once more over the course of a season. This might explain why teams are able to go from the bottom of the league to near the playoff cut-off so quickly while the teams that dominate are often a lot harder to knock of their perch.

Another way to look at this is by considering how many goals you need to add one extra win. While we commonly use a constant goals per win number when discussing player value in the analytics community (usually about 6), looking at the data above we know we shouldn’t expect the number of goals per win to be the same for each team. If we take the inverse of each number above and multiply it by 2, we can translate our marginal goal value into the number of goals needed to add one additional win (or 2 standings points in this case) for different team strengths.

Goals Per Win

Goals Per Win

Looking at it this way makes things slightly more obvious: a team with a -50 goal differential needs to bring on 5.3 additional goals to increase their win total by 1, while a team with a positive 50 goal differential needs to add over 6 goals to achieve the same result.

One thing to keep in mind here is that the values in both graphs above will change depending on the goal scoring environment. While in our model we assumed that each team had an equal chance of scoring and allowing anywhere between 0 and 5 goals, in reality the probabilities are different and while the results should generally look the same, the fitted curves that we generate will be different.

Nevertheless, the implications for teams shopping the free agent market should be obvious: while it might make sense for a team struggling at the edge of the playoff picture to look for one or two big pieces to propel them forward, for a team at the top it’s a lot more difficult to improve their place in the standings by spending money. This is of course complicated by the fact that it’s harder to find pieces to replace on a good team: even if you can go out and add a top line player forward, the player whose minutes they’ll be taking is likely to have been a useful player already. All of which is to say that it’s not all that surprising that teams often fail to strike gold and establish dominance through free agency: it’s not that they’re not getting better, it’s just that the numbers are often stacked against them from the start.

Posted in Theoretical

2014 Free Agent Preview: Forwards

It’s almost free-agent season, the time of year when most fans are salivating over all the possible superstars their team might add, while the analytics fans of the world are mostly hoping their GM’s don’t screw up too badly. In celebration of this most joyous terrifying time of year, Puck++ is proud to present our First Annual Puck++ Players for Purchase at a Premium Price Preview™.

Rather than going through every available free-agent though (since in the time it would take me to write up most of them will end up signing), I’m going to focus on 15 forwards and 10 or so defencemen (to be determined when/if I get around to writing part 2) who are likely to garner significant interest, or at least significant media attention.

For each player I’m going to present 3 sets of data: 1) His traditional stats from the last 3 seasons (G, A, Pts., +/-); 2) His xGF20, xGA20 and xGD20 numbers for the last 3 seasons (the details on how these numbers are calculated can be found here and here); and 3) His 5 most comparable players, using xGF20 and xGA20 for the past 3 years. The comparable players are determined by looking at which players had seasons most similar from an xGF20 and xGA20 point of view over the past 3 years. As an aside, if you want a quick cheat sheet to evaluate xGD20 numbers, here are the average numbers based on ice-time in the 2013-2014 season:

Line xGD20
1 0.09
2 0.05
3 0.00
4 -0.05

All salary data quoted below is from CapGeek. All standard stats from HockeyDB. Blame them (or my poor transcription) for any errors.

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Posted in Free Agency

Context Neutral Player Evaluation: Examining Defence and Calculating xGD20

A few months ago I wrote about xGF20, my attempt to isolate a player’s offensive ability from his teammates abilities and the luck involved in shooting percentages in small samples. At its core, xGF20 is based on 3 reasonably repeatable individual measures:

1) A player’s rate of individual shot generation;

2) A player’s rate of altruistic shot generation (that is, the shots he generates for his teammates); and

3) A player’s individual shooting ability (regressed based on position)

Using these three metrics, xGF20 presents a player’s expected on-ice goals for per 20 minutes of ice-time, assuming his teammates shoot at a league-average rate. While the calculation is slightly more complicated than what I’ve just presented, it does allow us to make comparisons between players without worrying about who their linemates were. If you put Jason Spezza on a line between my brother and I (sorry Ben), you’d expect his on-ice GF20 to drop dramatically through no fault of his own. Although xGF20 is very similar in theory to Relative CF20, taking into account a players own shooting ability allows us to differentiate between those who just throw the puck at the net without purpose (David Clarkson) and those who take more shots because they’re better at it (Alex Ovechkin).

Looking at xGF20 numbers over the past few years was encouraging not only because the results agreed with common intuition (Sidney Crosby had 5 of the top 10 seasons over the past 5 years), but also because it was highly repeatable year-over-year. When we calculate a player’s xGF20 for a given year, it has a strong correlation to his xGF20 in subsequent years, a good sign that we’re isolating an individual ability.

xGF20 did have a major fault as a player evaluation tool though: it only looked at one side of the game. To get a full view of a player’s contribution to his team we need to consider the defensive side-of-things as well. This is, unfortunately enough, where things get tricky. Isolating individual defensive ability is extremely hard to do, as defensive results are influenced by the efforts of each player on the ice as well as any effects a coach might have through his choice of defensive system (see here, for example, where I found that teams had a fairly strong ability to control whether opposing forwards or defencemen were taking the shots against their net).

A lot of effort in the analytics community recently has been put into finding effective ways to evaluate defensemen (who tend to, intuitively at least, shoulder most of the defensive responsibility): Tyler Dellow has looked at using CorsiRel (the difference between a team’s CF% with a player on the ice and off the ice) and found that most “famous” defensemen tend to outperform their teams results, while Garret Hohl looked at defensemen’s effect on both their team’s and opponent’s Corsi %.

We’re going to take a similar approach here on the defensive side of things, but rather than look at Corsi %, we’ll use CA20 WOWY. In an ideal world we’d be able to break down defensive contribution further, but given that there’s a lack of clear evidence to support the idea that on-ice save percentage is repeatable, CA20 WOWY gives us a decent way to measure a player’s shot prevention ability relative to his teammates. Our expected goals against metric simply takes a player’s CA20 WOWY and adds it to the league average CA20 (17.5) to calculate his expected CA20. We then multiply by the league average Corsi shooting percentage to find his xGA20:

xGA20 = (17.5 + CA20 – TMCA20) * lgCSh%

xGA20 shows significantly less repeatability than xGF20, which we would expect given that it attempts to measure something that’s far stronger at the team than individual level. If we look at the year to year correlations in the graph below, we see that that as more years pass xGA20 shows stronger repeatability than unadjusted CA20 for defencemen (interestingly, for forwards raw CA20 seems to show a stronger correlation). While the repeatability isn’t what we’d hope for in an individual stat, it does give us a starting point in measuring a player’s defensive contribution.

xGA20 Year-Over-Year Correlations

xGA20 Year-Over-Year Correlations

One thing that’s important to note is that we see a lot less variance in xGA20 than in xGF20 since we don’t use an individualized save percentage. While this may unfairly penalize a small subset of players who do have an effect on their on-ice save percentage, it allows us to sidestep the difficult issue of trying to seperate out a player’s contribution to on-ice save percentage from his goalie.

Position Mean Std. Dev.
F 0.76 0.057
D 0.75 0.057

Now that we’ve taken care of the defensive side of things, let’s look at pulling everything together into one aggregate metric. After all, what we ultimately care about is whether or not a player is going to help our team outscore our opponents or not. To measure that all we have to look at is the difference between each player’s xGF20 and his xGA20, which we’ll call xGD20.

xGD20 = xGF20 – xGA20

xGD20 shows reasonably good repeatability, with a year to year correlation forbl forwards of 0.62 between subsequent seasons dropping down to 0.51 when we look at comparing one year with 4 years in the future. For defensemen, the correlations are lower as we’d expect, ranging from between 0.41 (year y to y+1) to 0.47 (year y to y+4). What’s important to note though is that it tends to be more repeatable than CF% WOWY for forwards, and at the same level for defencemen (to be expected since the defensive shooting is heavily regressed and they take fewer shots themselves).

xGD20 Year-Over-Year Correlations

xGD20 Year-Over-Year Correlations

From a descriptive statistics point of view, the mean for both forwards and defencemen are right where we’d expect them to be around 0. We again see more variance in the forward’s numbers, driven by the higher variance in regressed shooting percentage.

Position Mean Std. Dev.
F -0.01 0.14
D 0.01 0.10

One of the interesting things that I’ve found is that xGD20 seems to relate fairly well to even-strength ice-time. If we break up the list of forwards from 2013-2014 into 4 groups by ice-time, we see that xGD20 decreases steadily by each group.

Group xGD20 Average
1 0.09
2 0.05
3 0.00
4 -0.05

We also see the same result, albeit to a lesser degree, if we break up the defencemen by ice-time, with first pairing blueliners showing better xGD20 numbers then 2nd and 3rd pairing players respectively.

Group xGD20 Average
1 0.02
2 -0.02
3 -0.03

Looking at the top 10 forwards from last year we see a lot of expected names, as well as a few players who appear to have had more extremely unlucky seasons. Sidney Crosby unsurprisingly leads the list, while Joe Thornton, Patrice Bergeron, Corey Perry and Jonathan Toews aren’t shocking to see at the top. In contrast, while Alexander Semin and Alex Burrows both had disappointing years, their past shooting ability and their shot numbers last year suggest that they’re due to bounce back next year.

Player Team Position xGF20 xGA20 xGD20
CROSBY, SIDNEY Pittsburgh F 1.12 0.73 0.39
THORNTON, JOE San Jose F 1.01 0.62 0.38
BERGERON, PATRICE Boston F 0.97 0.61 0.36
VORACEK, JAKUB Philadelphia F 1.01 0.65 0.35
NEAL, JAMES Pittsburgh F 1.08 0.73 0.35
PERRY, COREY Anaheim F 0.96 0.63 0.33
SEMIN, ALEXANDER Carolina F 1.04 0.72 0.32
TOEWS, JONATHAN Chicago F 1.03 0.71 0.32
MARCHAND, BRAD Boston F 0.98 0.67 0.30
BURROWS, ALEX Vancouver F 0.98 0.70 0.28

On the blueline, TJ Brodie and Mark Giordano lead the way, although a large part of that is driven by their amazing xGA20 numbers (which are in turn related to Calgary’s awful defence). Upcoming free-agents Matt Niskanen and Anton Stralman look like they could be good value pickups, with their xGD20 rankings outpacing their traditional stats. Interestingly, most of the players made this list by holding their opponents to fewer shots, rather than through their own offensive ability – all of the top 10 defencemen are well below in xGA20, while only one of the top 10 defencemen in xGF20 made the list (Lubomir Visnovsky).

Player Team Position xGF20 xGA20 xGD20
BRODIE, TJ Calgary D 0.81 0.57 0.24
GIORDANO, MARK Calgary D 0.80 0.58 0.23
TIMONEN, KIMMO Philadelphia D 0.83 0.62 0.22
VLASIC, MARC-EDOUARD San Jose D 0.82 0.62 0.20
NISKANEN, MATT Pittsburgh D 0.84 0.64 0.20
STRALMAN, ANTON NY Rangers D 0.81 0.61 0.20
VISNOVSKY, LUBOMIR NY Islanders D 0.88 0.68 0.20
WISNIEWSKI, JAMES Columbus D 0.85 0.66 0.19
DONOVAN, MATT NY Islanders D 0.88 0.69 0.19
GARDINER, JAKE Toronto D 0.82 0.63 0.19

I’ve uploaded a full list of xGD20 for all players in 2013-2014 to a Google Spreadsheet here. If you’re looking for a primer on who your team should avoid come July 1st, the bottom of the list will certainly come in handy.

Obviously there are still improvements to be made-the list of top defencemen above highlights that players on extreme teams can observe extreme results in the short term. If we look over a longer horizon though, xGD20 does seem to provide a fairly consistent view of a player’s talent, and one that intuitively makes sense. All it attempts to measure are things that we know a player has a degree of control over-how many shots he takes, how many shots he sets up for his teammates, how good of a shooter he is, and how well he prevents shots against his own net. Everything else is, generally speaking, too variable to use to evaluate players, and as such we need to take it out of a player’s results to get a true sense of his talent independent of the results in any given year.

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Posted in Statistics

Adjusting Save Percentage for Team Effects

As anyone who’s looked at evaluating goalies before knows it’s not a pleasant task. Even ignoring the inherent extreme variability in game to game or year to year statistics, a goaltender’s numbers can be heavily influenced by the 5 skaters in front of him. While when we look at forwards ordefencemen we can get around this issue by looking at WOWY or Relative numbers, we don’t have that same luxury with goalies. Even if we were to compare a goalie to how his team did when he had the night off our analysis is complicated by the fact that most teams tend to use only a small number of goalies each season. While we may be able to say that a team posted a better save percentage with their starter than their backup that doesn’t give us a good sense of whether the starter was great or the backup was terrible – we’re still stuck trying to isolate the team effect.

One method we can use to get an estimate of the team effect is their skill at shot prevention. Teams that are better defensively are likely to give up fewer shots, although somewhat paradoxically those shots are more likely to go in. But what if we looked at things from a different point of view: what if rather than focusing on a team’s ability to prevent shots in general we adjusted for who was taking the shots? After all, shots by defencemen tend to go in less than half as often as shots by forwards, so it stands to reason that if a team can prevent opposing forwards from putting the puck on net that their goalie would likely experience a higher save percentage because of that.

The first thing we should check before we get into this is whether the claim I just made (that teams can control whether shots against their net come from opposing forwards or defencemen) is actually true. The easiest way to verify whether something is more talent than luck is to check what the split half correlation is between even and odd games (in simpler terms we’re looking at whether the results we observe in the even games are a good predictor of the results in the odd games). There are two ways to look at this talent in our case and fortunately enough for us they both give similar results. The first way is to look at what percentage of a team’s even strength shots against come from forwards vs defencemen. In this case our split half correlation is 0.74, which is high enough to say that we’re likely on to something. The other stat that we can test is the total number of shots against per 20 minutes of even strength ice time that a team gives up to forwards and defencemen (fFA20 and dFA20, we’re using shot attempts here since I have the numbers handy but the results should hold generally for shots on goal). Under this method, our correlations are 0.80 and 0.72 for forwards and defencemen respectively, again good enough that we can feel confident that this is at least a team level skill*.

So now that we’ve established that teams can generally control where their opponents’ shots are coming from (positionally, at least) it naturally makes sense to adjust our goalie statistics (in this case 5v5 save percentage, which we’ll be using throughout the rest of this article) to take this fact into account. After all, if I post a 0.960 save percentage you’d likely be impressed, but if I told you that I only ever faced shots from the point your appreciation of my netminding skills would probably decline significantly. To do this we’ll start by looking at how many shots each goalie faced from forwards and defencemen, which we’ll call fSA and dSA respectively. After that we’ll calculate how many goals we’d expect our goalie to give up given their shots against distribution by position:

xGA = fSA * lgFSh% + dSA * lgDSh%

Where lgFSh% and lgDSh% are the league average forward and defencemen shooting percentage in each season, as given below:

Season lgDSh% lgFSh%
20082009 3.96% 9.18%
20092010 4.32% 9.15%
20102011 3.98% 9.03%
20112012 3.94% 9.19%
20122013 4.12% 9.24%
20132014 4.12% 9.12%
2008-2014 4.07% 9.15%

Once we’ve calculated our expected goals against, we can turn this into an expected save percentage by simply dividing by the total shots each goalie faced:

xSv% = 1 – (xGA / SA)

We can then look at how each goalie actually performed against their expected value to come up with a relative team-adjusted (and in actuality also season-adjusted) save percentage:

adjSv% Rel = Sv% – xSv%

Which we can turn into adjusted save percentage by adding on the league average save percentage in the appropriate season (as shown in the table below):

adjSv% = adjSv% Rel + lgSv%

Season lgSv%
20082009 92.05%
20092010 91.99%
20102011 92.21%
20112012 92.17%
20122013 92.09%
20132014 92.24%

So now that we have our new stat defined, let’s take a look at the results. The table below has the standard 5v5 Sv% as well as the 5v5 adjSv% for each goalie who faced more than 500 5v5 shots over the past season. I’ve also included a column at the end which shows the delta between the traditional save percentage and our adjusted save percentage.

Goalie Sv% xGA xSv% adjSv% Rel adjSv% Delta
RASK, TUUKKA 94.2% 99.6 92.2% 2.0% 94.2% 0.0%
HARDING, JOSH 94.2% 41.1 92.2% 1.9% 94.2% 0.0%
KHUDOBIN, ANTON 93.6% 69.4 92.2% 1.4% 93.6% 0.1%
JOHNSON, CHAD 93.4% 41.5 92.2% 1.2% 93.5% 0.0%
PRICE, CAREY 93.4% 109.3 92.2% 1.2% 93.4% 0.0%
VARLAMOV, SEMYON 93.5% 118.7 92.4% 1.1% 93.4% -0.1%
KUEMPER, DARCY 93.4% 43.0 92.3% 1.1% 93.3% 0.0%
BOBROVSKY, SERGEI 93.3% 99.5 92.2% 1.1% 93.3% 0.0%
BISHOP, BEN 93.2% 101.5 92.3% 0.9% 93.2% 0.0%
SCRIVENS, BEN 93.2% 70.6 92.3% 0.8% 93.1% -0.1%
HOLTBY, BRADEN 93.0% 86.3 92.2% 0.8% 93.0% 0.0%
BERNIER, JONATHAN 93.0% 105.5 92.3% 0.7% 92.9% -0.1%
ENROTH, JHONAS 92.9% 51.4 92.2% 0.7% 92.9% 0.0%
QUICK, JONATHAN 92.8% 67.9 92.2% 0.6% 92.8% 0.1%
LUNDQVIST, HENRIK 92.9% 108.7 92.3% 0.5% 92.8% -0.1%
CRAWFORD, COREY 92.7% 94.8 92.2% 0.5% 92.7% 0.1%
BRYZGALOV, ILYA 92.8% 52.2 92.3% 0.5% 92.7% -0.1%
SMITH, MIKE 92.7% 108.4 92.2% 0.5% 92.7% 0.0%
MASON, STEVE 92.6% 108.0 92.1% 0.4% 92.7% 0.1%
ANDERSEN, FREDERIK 92.8% 48.5 92.4% 0.4% 92.6% -0.1%
LUONGO, ROBERTO 92.6% 96.8 92.2% 0.4% 92.6% 0.0%
LEHTONEN, KARI 92.8% 108.4 92.4% 0.4% 92.6% -0.2%
HILLER, JONAS 92.4% 80.0 92.1% 0.3% 92.5% 0.1%
HOWARD, JIMMY 92.5% 87.1 92.2% 0.3% 92.5% 0.0%
LACK, EDDIE 92.5% 63.9 92.3% 0.2% 92.5% 0.0%
MONTOYA, AL 92.5% 45.3 92.2% 0.2% 92.5% 0.0%
ELLIOTT, BRIAN 92.3% 42.2 92.1% 0.2% 92.5% 0.1%
SCHNEIDER, CORY 92.4% 64.4 92.2% 0.2% 92.4% 0.0%
ANDERSON, CRAIG 92.5% 96.3 92.3% 0.1% 92.4% -0.1%
HALAK, JAROSLAV 92.3% 80.7 92.2% 0.1% 92.3% 0.0%
MILLER, RYAN 92.0% 110.6 92.1% -0.1% 92.1% 0.2%
REIMER, JAMES 92.2% 65.2 92.4% -0.2% 92.0% -0.2%
EMERY, RAY 91.8% 42.5 92.1% -0.3% 92.0% 0.2%
RAMO, KARRI 91.7% 69.0 92.0% -0.3% 91.9% 0.2%
FLEURY, MARC-ANDRE 91.9% 103.9 92.3% -0.5% 91.8% -0.1%
HUTTON, CARTER 91.7% 63.1 92.2% -0.5% 91.8% 0.0%
NIEMI, ANTTI 91.8% 102.3 92.4% -0.6% 91.7% -0.1%
WARD, CAM 91.6% 49.3 92.2% -0.6% 91.7% 0.0%
NABOKOV, EVGENI 91.5% 67.0 92.2% -0.7% 91.5% 0.0%
LEHNER, ROBIN 91.5% 64.7 92.3% -0.8% 91.5% 0.0%
MAZANEC, MAREK 91.0% 41.5 92.1% -1.1% 91.2% 0.2%
MCELHINNEY, CURTIS 91.4% 39.3 92.5% -1.1% 91.2% -0.2%
GUSTAVSSON, JONAS 91.3% 41.8 92.4% -1.1% 91.1% -0.1%
THOMAS, TIM 91.0% 82.4 92.3% -1.3% 91.0% -0.1%
BERRA, RETO 90.5% 54.3 91.9% -1.4% 90.8% 0.3%
PAVELEC, ONDREJ 90.9% 96.7 92.3% -1.4% 90.8% -0.1%
BRODEUR, MARTIN 90.4% 57.7 92.2% -1.8% 90.5% 0.0%
DUBNYK, DEVAN 90.2% 56.5 92.2% -2.0% 90.2% 0.1%
POULIN, KEVIN 90.2% 51.5 92.2% -2.0% 90.2% 0.0%
RINNE, PEKKA 89.9% 41.2 92.1% -2.2% 90.0% 0.1%

The way to interpret the delta is this: a positive delta means that a goalie’s adjusted save percentage is greater than his observed save percentage, or in other words that his defense cost him points by allowing more shots from forwards than we’d expect. As you can see, the deltas aren’t huge, but there are goalies for whom it does seem to make a difference in our evaluation. Reto Berra, for example, seems to have played behind the worst defence in the league, costing him roughly 3 points of save percentage over the course of the season (sorry, Flames fans). Over the 672 shots he took that works out to roughly 2 goals, or a third of a win that he was cost due to team defence alone.

On the other hand, both Jonathan Bernier and James Reimer’s save percentages seem to have been boosted by the Leafs’ defensive efforts (yes, you read that right). While the Leafs did give up a ton of shots, a greater percentage of those came off the sticks of opposing defencemen than we’d expect given the league-wide numbers.

While most of the deltas are relatively small, the raw differences don’t quite tell the whole story, as they don’t take into account the number of shots against a goalie faces. Rather than looking at raw Sv% and adjSv%, we can instead look at Goals Saved Above Average (GSAA) which attempts to measure how many extra goals a given netminder prevented over a league-average goalie:

GSAA = (Sv% – lgSv%) * SA

If we look at the delta in GSAA and adjGSAA, we see that the differences become more significant.

Goalie GSAA Adj GSAA GSAA Delta
MILLER, RYAN -3.74 -1.36 2.37
BERRA, RETO -11.88 -9.68 2.21
RAMO, KARRI -4.68 -2.95 1.73
MASON, STEVE 4.56 5.98 1.42
HILLER, JONAS 1.87 3.03 1.16
EMERY, RAY -2.51 -1.52 0.99
MAZANEC, MAREK -6.36 -5.52 0.84
ELLIOTT, BRIAN 0.41 1.19 0.78
KHUDOBIN, ANTON 11.71 12.44 0.72
CRAWFORD, COREY 5.15 5.84 0.69
RINNE, PEKKA -12.44 -11.76 0.68
HOLTBY, BRADEN 7.85 8.34 0.49
QUICK, JONATHAN 4.47 4.93 0.46
DUBNYK, DEVAN -14.93 -14.48 0.45
NABOKOV, EVGENI -6.38 -6.03 0.36
BRODEUR, MARTIN -13.61 -13.28 0.33
SCHNEIDER, CORY 1.06 1.37 0.31
ENROTH, JHONAS 4.11 4.39 0.28
WARD, CAM -3.99 -3.72 0.26
JOHNSON, CHAD 6.26 6.51 0.25
SMITH, MIKE 6.11 6.36 0.25
HUTTON, CARTER -4.10 -3.90 0.20
PRICE, CAREY 16.19 16.33 0.14
POULIN, KEVIN -13.66 -13.54 0.12
HALAK, JAROSLAV 0.58 0.69 0.11
MONTOYA, AL 1.21 1.31 0.09
BOBROVSKY, SERGEI 13.42 13.49 0.07
LUONGO, ROBERTO 4.79 4.84 0.06
HOWARD, JIMMY 3.09 3.15 0.05
RASK, TUUKKA 25.58 25.63 0.05
HARDING, JOSH 10.10 10.13 0.02
LACK, EDDIE 1.98 1.87 -0.11
KUEMPER, DARCY 6.27 6.03 -0.25
BRYZGALOV, ILYA 3.58 3.22 -0.36
LEHNER, ROBIN -5.93 -6.30 -0.37
BISHOP, BEN 13.06 12.49 -0.57
THOMAS, TIM -13.02 -13.64 -0.62
ANDERSEN, FREDERIK 3.25 2.55 -0.70
GUSTAVSSON, JONAS -5.42 -6.24 -0.82
SCRIVENS, BEN 8.50 7.62 -0.89
FLEURY, MARC-ANDRE -4.99 -6.13 -1.14
PAVELEC, ONDREJ -17.13 -18.28 -1.15
MCELHINNEY, CURTIS -4.52 -5.70 -1.19
BERNIER, JONATHAN 10.71 9.51 -1.20
ANDERSON, CRAIG 2.64 1.35 -1.29
LUNDQVIST, HENRIK 9.05 7.73 -1.31
REIMER, JAMES -0.30 -1.79 -1.48
NIEMI, ANTTI -5.85 -7.69 -1.85
VARLAMOV, SEMYON 19.91 17.70 -2.21
LEHTONEN, KARI 7.82 5.40 -2.43

Looking at the delta column, the differences become a little clearer: both Ryan Miller and Reto Berra were cost about 35-40% of a win by their defences, while the defensive prowess of Colorado and Dallas likely added more than 1/3 of a win to each of Semyon Varlamov and Kari Lehtonen’s totals.

While these are still relatively small differences for many goalies, over the course of a career these can start to add up. Since 2008, the Rangers defensive play has saved Henrik Lundqvist roughly 8 goals, or about 1.5 per year. If we look solely at John Tortorella’s years behind the bench, the average delta works out to be more at almost 2 goals per year.

Expanding our sample back to 2008 also reveals larger discrepancies between GSAA and adjGSAA: both Jaro Halak (2010/11) and Craig Anderson (2009/10) were cost more than 3 goals by their team’s defensive play. Given that most goalies GSAA fall between -10 and +10, differences of even 1 goal can represent a fairly large difference in a goalie’s valuation. And it’s these differences in valuation that can shed light on some of the more difficult to measure aspects of the game, allowing us to get a better sense as to what’s within a goaltender’s control, and what we can lay at the feet of their teammates.


*Based on some initial analysis I’ve done this seems to be primarily a team/system level skill. If you look at it at the individual level and take into account how a players teammates did the dFA20 and fFA20 metrics show little year over year repeatability. But all that’s a topic for another post.

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