## Introducing GAETAN

This Fanpost presents a new stat: Goal Asymmetry Experienced by Team Above Normal. Here's GAETAN in two sentences:

GAETAN tells us how many more or fewer goals a player's team scored and allowed while he was on the ice than we would have expected from an average player. To calculate GAETAN, we first determine how many goals for and goals against would have occurred while an average player played the same number of minutes as a particular player, and then we compare those numbers to the actual goals for and goals against that occurred while the particular player was on the ice.

All of the numbers are available in this spreadsheet.

GAETAN is essentially a reworking of plus/minus. ("Goal asymmetry experienced by team" is another way of saying "plus/minus" - it's the difference between a team's goals for and goals against while a player is on the ice). The stat is named after the late Gaetan Duchesne, a solid 2-way forward whose +68 rating in his career as a Capital ranks ninth among team leaders, and whose career +102 rating makes him #188 all time. To this day, Duchesne, Doug Jarvis, and Bobby Gould may be the best line of defensive forwards the Caps ever iced.

In traditional plus/minus, goals scored by a team on the power play and goals scored against a team killing a penalty are entirely thrown out of the equation. Without this adjustment, the stat would be worthless - power play specialists would be at a huge unfair advantage, and penalty killers at a huge disadvantage. On the other hand, simply throwing out the power play goals for and penalty killing goals against seems like an excessively drastic step. There is good information in those goals, if only there were a good way to put it into context.

The first step in calculating GAETAN is to set baseline goal scoring rates for even strength, power play, and shorthanded situations. These baselines provide the context to permit the inclusion of all the goals scored while a player was on the ice. The baselines tell you how many goals for and goals against an average player would experience in a given amount of time playing for an average team against average competition. The baselines also provide the "normal" portion of "Above Normal" in the stat's name.

The GAETAN baselines are ES, PP, and PK scoring rates per minute. In the 2010-2011 regular season, NHL teams played a total of 149,866 minutes and 52 seconds of hockey. (Half of that -- 74,933 minutes and 26 seconds -- were actually played, since each game involves two teams.) That's 60 minutes and 55 seconds per game. (It's more than 60 because of overtime.) 6,721 goals were scored during the season. That breaks down as 4,944 goals in 121,187 minutes of ES time, 1,571 power play goals in 14,340 minutes of PP time, and 205 shorthanded goals in 14,340 of PK time. (PP and PK TOI are the same because every minute that someone is on the PP is a minute that someone else is on the PK.) Using simple division, the 2010-2011 baselines were .041 goals per minute at ES time (equivalent to a 2.45 GAA), .110 goals per minute on the PP (about a 6.57 GAA, or roughly one goal every 5 full 2-minute power plays), and .014 shorthanded goals per minute on the PK (about a 0.86 GAA, or roughly a shorthanded goal every 35 full 2-minute penalties).

Using these baselines, we can set benchmarks for what to expect out of a player. For example, compare the following expected goals for and goals against for Mike Green and Jeff Schultz ("X" stands for "expected":

 Player TOI ES TOI PP TOI PK TOI XGFON XGAON Mike Green 1234.5 900.9 217.9 115.6 62.3 52.6 Jeff Schultz 1424.0 1,243.0 4.8 176.2 53.8 70.1

Schultz played about 190 more minutes than Mike Green, much of that on the penalty kill. How does that translate to goals scored? Using the baselines, one would expect an average player (on an average team facing average competition) to have been on the ice for 7.5 more goals against if he'd played Schultz's minutes than if he'd played Green's minutes. On the other hand, Green had a lot more power play time than Schultz. For that reason, we'd expect an average player who played Green's minutes to be on the ice for 8.5 more Capitals goals than Schultz, even though Schultz had more minutes overall.

So now that we know what an average player would have done if he'd skated Green's or Schultz's minutes, let's see how Green and Schultz did. ("^X" means "above expectations")

 Player XGFON XGAON GFON GAON GFON^X GAON^X +/-^X Mike Green 62.3 52.6 58 40 -4.3 -12.6 8.3 Jeff Schultz 53.8 70.1 53 60 -0.8 -10.1 9.3

Fifty-eight Capitals goals were scored while Mike Green was on the ice. Sounds like a good number, but it's actually 4.3 goals lower than one would have expected from an average player. On the positive side, Green was on the ice for just 40 goals against. That's 12.6 less goals than one would have expected from an average player (the lower the GAON^X the better, and ideally you want that stat firmly in the negative). So on the whole, Green was a net positive for the team, but he went about it in an unexpected way - by contributing to the Caps' excellent defensive results while he was on the ice. It's far less of a surprise to see that Schultz's contributions to the Caps were mainly defensive. But it is perhaps a surprise to see this stat suggest that Schultz was more valuable than Green this season.

These two examples show some of the benefits and limits of GAETAN. Using GAETAN, you can compare apples to oranges - you can compare Mike Green to Jeff Schultz even though they're very different players who are asked to do very different things. And you can make that comparison based on everything they contribute on the ice - there's no need to carve out and ignore special teams play.

On the other hand, GAETAN suffers from many of the same limits as +/-. It does not account for team effects. Green and Schultz played an awful lot of minutes at the same time, and both ended up with very favorable goals-against numbers. GAETAN can't separate out the relative contributions of two or more players who are playing at the same time. So GAETAN can't tell us if Green was a victim of a Caps powerplay that was ineffective, or whether he was substantially to blame for its struggles - it can only tell us that Caps goals were scored with Green on the ice than we would have expected from an average player. GAETAN also does not account for quality of competition. So like most other stats, it is still important to add context like "he was paired with Zdeno Chara" or "his qualcomp was the highest on the team."

GAETAN is only as good as the baselines. Going with the league average scoring rates at ES, PP, and PK is just about the simplest way one could approach a stat like this. The possibilities for a GAETAN 2.0 are nearly endless - especially if individual baselines for each player are calculated. For example, one could factor in team effects or quality of competition. Instead of using leaguewide averages, one could use replacement level as the baseline, with all the benefits that come with that modification. One could factor in zone starts. One could replace goals with shots, or Corsi events, or Fenwick events, or chances. Etc. But I'd urge caution. One of the goals of GAETAN is that it be simple and easy to explain (a funny thing to read 1000+ words into an explanation of the thing, I know.) There's something attractive about being able to say "it's a comparison of the goals for and goals against while a particular player was on the ice versus what you'd expect from an average player." That's already a mouthful, and I fear that much of the value would be lost if it gets much more complicated than that. This stat isn't something new or revolutionary so much as a new way to present the data we've all already been using. Simplicity is therefore a virtue.

One more fact that the Green/Schultz comparison illustrates is that this version of GAETAN gives absolute numbers. It's therefore much better as a backwards-looking stat, for use in allocating credit and blame for past results to individual players. For other purposes, a rate might be more useful. It's easy enough to convert these numbers in to rates - all you need is a denominator. But my goal today is to look back at the season and postseason that was. So I'll be looking at those absolute numbers.

To start, here are the best offensive players - the top 10 leaders in goals for above expectations.

 Player Team Pos XGFON XGAON GFON GAON GFON^X GAON^X +/-^X Henrik Sedin VAN C 84.37 57.50 133 52 48.63 -5.50 54.13 Daniel Sedin VAN L 82.19 54.83 130 44 47.81 -10.83 58.64 Lubomir Visnovsky ANA D 102.45 73.82 146 76 43.55 2.18 41.38 Corey Perry ANA R 90.86 76.32 131 92 40.14 15.68 24.46 Ryan Getzlaf ANA C 75.42 55.54 111 58 35.58 2.46 33.12 Ryan Kesler VAN C 83.46 75.14 119 60 35.54 -15.14 50.67 Steven Stamkos TBL C 92.49 59.53 128 70 35.51 10.47 25.03 Jonathan Toews CHI C 80.61 72.02 116 67 35.39 -5.02 40.40 Brian Rafalski DET D 67.47 47.59 100 55 32.53 7.41 25.12 Martin St Louis TBL R 94.65 63.01 127 75 32.35 11.99 20.36

The puck found its way into the opposition's net at a very high rate when these players were on the ice. And did I mention team effects? Because the top six players in this category each play for either Vancouver or Anaheim. The Hart trophy usually goes to the league's "best offensive player," and GFON^X doesn't go very far in settling the debate between Daniel Sedin and Corey Perry, though third nominee Martin St. Louis is pretty far behind them on this rating. But the difference in GAON^X appears significant. Perry's 15.68 team goals allowed above expected is the worst rating on this chart, and Sedin's -10.83 is second best. (Remember, since it's goals allowed, a negative number is good.) That makes Sedin look pretty good in comparison to Perry. And when you see how much worse Perry's GAON^X is than his linemate Getzlaf, and how much better Daniel Sedin's GAON^X is than his brother, you get the sense that Daniel really did play much better defense than Perry this year.

Of course, XGFON and XGAON also show quite how protected the Sedin brothers were this season. You'd expect average player who played Daniel Sedin's minutes to be on the ice for 27.36 more goals for than goals against (82.19 XGFON versus 54.83 XGFON) - a huge spread caused by his extremely PP-heavy ice time. Still, you can't dispute that Daniel came through. In absolute numbers, 86 more Canucks goals than opposition goals were scored while Daniel Sedin was on the ice. That's astounding, and it means that Daniel exceeded his huge 27.36 expected goal differential by 58.64 more goals. He may have been on the ice for fewer and easier minutes than Perry or St. Louis, but he absolutely killed the opposition during those minutes. That 58.64 +/- over expectations was good enough for #1 in the league.

Here are the top 10 in overall +/- above expectations, starting with Daniel Sedin:

 Player Team Pos XGFON XGAON GFON GAON GFON^X GAON^X +/-^X Daniel Sedin VAN L 82.19 54.83 130 44 47.81 -10.83 58.64 Henrik Sedin VAN C 84.37 57.50 133 52 48.63 -5.50 54.13 Christian Ehrhoff VAN D 92.22 81.47 123 59 30.78 -22.47 53.25 Ryan Kesler VAN C 83.46 75.14 119 60 35.54 -15.14 50.67 Lubomir Visnovsky ANA D 102.45 73.82 146 76 43.55 2.18 41.38 Jonathan Toews CHI C 80.61 72.02 116 67 35.39 -5.02 40.40 Dan Hamhuis VAN D 60.80 70.43 75 50 14.20 -20.43 34.63 Ryan Getzlaf ANA C 75.42 55.54 111 58 35.58 2.46 33.12 Kevin Bieksa VAN D 63.63 69.66 78 51 14.37 -18.66 33.03 David Backes STL R 77.31 69.98 106 66 28.69 -3.98 32.67

A lot of Vancouver again here. No matter how their postseason ends, that team deserves a ton of credit for being so dominant at both ends. With that said, when Kevin Bieksa is #9 in the league, it's hard to imagine that something isn't skewing the results - in this case, team effects.

Credit goes to Toews and Backes for being by far the best on their respective teams. The next Hawk on the rankings is Brian Campbell at number 22 (+27.15); the next best St. Louis player is Andy McDonald at 42 (+22.54).

Here are the defensive rankings

 Player Team Pos XGFON XGAON GFON GAON GFON^X GAON^X +/-^X Jannik Hansen VAN R 44.66 62.54 41 37 -3.66 -25.54 21.88 Christian Ehrhoff VAN D 92.22 81.47 123 59 30.78 -22.47 53.25 Brooks Laich WSH C 73.53 68.10 74 47 0.47 -21.10 21.58 Michael Sauer NYR D 52.12 61.63 53 41 0.88 -20.63 21.51 Dan Hamhuis VAN D 60.80 70.43 75 50 14.20 -20.43 34.63 Ryan Suter NSH D 84.75 75.35 92 55 7.25 -20.35 27.60 Johnny Boychuk BOS D 58.55 66.26 52 47 -6.55 -19.26 12.70 Brian Campbell CHI D 67.06 65.21 75 46 7.94 -19.21 27.15 Logan Couture SJS C 67.13 58.72 70 40 2.87 -18.72 21.59 Kevin Bieksa VAN D 63.63 69.66 78 51 14.37 -18.66 33.03

The name "Brian Campbell" jumps out, doesn't it? I'd be very interested to hear from Chicago fans whether they believe his excellent defensive numbers are due more to the quality of his play this year, or how he was used, or some combination of the two. It's true that Duncan Keith and Keith Seabrook face the Hawks' toughest opponents, but it's still impressive to see that Campbell was only on the ice for 46 goals against in 1,494 minutes of ice time, 113 of those minutes on the penalty kill, when GAETAN predicts that an average player who played those minutes would be on the ice for 65 goals against.

Michael Sauer and Logan Couture are the first rookies to appear on these lists. Sauer flew under the radar this year, and while he may have been protected to some extent behind Staal and Girardi, he got his share of PK time (110 minutes). These are impressive numbers - Sauer is definitely worth watching. Couture is now my pick for Rookie of the Year because his contributions at both ends were so solid. He is best known for his offense (32 goals and 24 assists), but on this ranking his primary contribution appears to have been great defense. He was on the ice for nearly 19 fewer goals against than we would have expected from an average player who played his minutes.

If you're into Schadenfreude, you might notice that Eric Staal is not on this list. In fact he was really not on this list. Really, really not on this list. Like #887 in the league, 6th from the bottom. Staal was on the ice for 93 goals against, which is 22.24 more goals against than you'd expect for an average player who was given his playing time. Ouch!

And this defensive GAETAN chart finally includes something that ought to put a smile on the faces of Caps fans (at least until UFA Brooks Laich joins another team during the offseason). If a typical Caps fan had been asked which Capitals player was most likely to appear on one of these charts, we'd probably have gone through several names before Brooks's. But there he is as the #3 defensive player in the NHL in terms of goals allowed by his team versus an average player playing his minutes. In fact, there are several Caps players in the top 50: Carlson (#13), Alzner (#17), Backstrom (#21), Knuble (#24), Semin (#35), and Mike Green (#47). In comparison, there are zero Caps in the top 50 on the GFON^X leaderboard - Ovechkin was the best with 16.89 GFON^X, good for #54 in the league. Seeing three of the young guns on a list of top defensive players in the league should put to rest any questions of whether the Capitals stars "bought in" to the new system - at least during the regular season.

Here are the Caps' forwards:

 Player XGFON XGAON Team GF Team GA GFON^X GAON^X '+/-^X Nicklas Backstrom 79.4 65.6 93 50 13.6 -15.6 29.2 Alex Ovechkin 93.1 59.8 110 49 16.9 -10.8 27.6 Alexander Semin 60.7 46.6 74 33 13.3 -13.6 27.0 Brooks Laich 73.5 68.1 74 47 0.5 -21.1 21.6 Mike Knuble 67.4 60.3 66 45 -1.4 -15.3 13.9 Marcus Johansson 43.8 45.3 45 40 1.2 -5.3 6.5 Jason Arnott 8.6 6.6 10 3 1.4 -3.6 4.9 Tomas Fleischmann 16.7 12.7 15 8 -1.7 -4.7 3.0 Eric Fehr 33.7 24.0 30 18 -3.7 -6.0 2.3 Jay Beagle 12.6 15.7 7 10 -5.6 -5.7 0.1 Marco Sturm 10.9 11.0 8 8 -2.9 -3.0 0.1 Brian Willsie 0.3 0.3 1 1 0.7 0.7 0.0 Keith Aucoin 0.9 0.3 0 0 -0.9 -0.3 -0.6 Andrew Gordon 3.6 3.0 4 5 0.4 2.0 -1.6 Mathieu Perreault 20.6 15.6 19 16 -1.6 0.4 -2.0 DJ King 3.8 3.7 3 6 -0.8 2.3 -3.1 Matt Hendricks 35.1 42.0 33 43 -2.1 1.0 -3.1 Matt Bradley 26.4 26.2 20 23 -6.4 -3.2 -3.2 David Steckel 24.6 33.5 18 32 -6.6 -1.5 -5.1 Boyd Gordon 28.7 41.1 19 38 -9.7 -3.1 -6.6 Jason Chimera 45.3 47.3 38 49 -7.3 1.7 -9.0

This chart shows further proof of "buy-in" - almost all of the Caps' forwards were on the ice for fewer than the expected GAON (which is good), and nobody who played more than 100 minutes was on the ice for more than 2 GAON above average. Even Ovechkin appears to have bought in - his GAON^X is bound to be low because he played so much on the power play, where it's almost impossible to be on the ice for many fewer goals against than average because the shorthanded goal scoring rate is so low. (To see what I mean, compare Ovechkin's XFGON and XGAON to Backstrom's. You might think of them as having been on the ice together a whole lot, but in reality they were asked to do very different things.) Ovechkin's -10.8 GAON^X is certainly a good number for him on this table. And it's striking to see the worst GAON^X rating on this table belong to DJ King, who hardly played. Though the sample size was certainly small, this chart illustrates why he could not break the lineup.

For those asking where Nicklas Backstrom was this year, all he managed was to be the Caps' best forward (and to ruin the suspense of the defensemen chart coming up, their best player overall), at least by +/-^X. With more results like these, Backstrom should start getting some attention for the Selke Award for "best offensive player who is also very good defensively." Put simply, Backstrom tilted the ice in the Caps' favor more than any other player.

It'll be no surprise to many to see David Steckel down at the bottom of the list. Boyd Gordon's presence near the bottom can be explained in part by the high quality of competition that he faced, though it would certainly be nice to see some more offense from the fourth line. And then there's Jason Chimera, who had the most disappointing season among Caps' forwards. We should not let playoff OT heroics mask his true talent level. Chimera had a bad year.

 Player Team GF Team GA XGFON XGAON GFON^X GAON^X '+/-^X John Carlson 93 66 83.2 84.1 9.8 -18.1 27.9 Karl Alzner 60 62 64.5 78.1 -4.5 -16.1 11.7 Jeff Schultz 53 60 53.8 70.1 -0.8 -10.1 9.3 Mike Green 58 40 62.3 52.6 -4.3 -12.6 8.3 Dennis Wideman 20 13 16.1 15.4 3.9 -2.4 6.2 John Erskine 36 41 41.9 50.6 -5.9 -9.6 3.7 Scott Hannan 34 42 42.5 54.3 -8.5 -12.3 3.7 Sean Collins 3 2 2.3 2.6 0.7 -0.6 1.2 Brian Fahey 3 4 3.7 3.3 -0.7 0.7 -1.3 Tom Poti 16 20 16.3 18.6 -0.3 1.4 -1.6 Tyler Sloan 11 19 16.5 17.6 -5.5 1.4 -7.0

I'm not sure we really needed more evidence that Carlson had a great year, but here it is. In fact, the defensive corps as a whole had a great year. It would have taken a brave analyst to predict last year that the Caps' cores strength would soon be its depth of quality defensemen, but that's exactly how things are shaking out.

If you needed more evidence that Tyler Sloan does not belong in the NHL, here it is. If you prefer to focus on the positive, think about the fact that the Caps' top four defensemen on this measure are each home grown and each under 26 years old. The top six in this measure are under contract or RFA. Every one of them was on the good side of +/-^X. And the best among them were Alzner and Carlson, the two youngest. This should be a position of strength for a long time.

We've said a lot of nice things about individual Caps players, but obviously the end result of the season was not what we'd desired. So what the hell happened? Here are the playoff stats.

 Player XGFON XGAON GFON GAON GFON^X GAON^X '+/-^X Jason Arnott 7.6 5.2 10 3 2.4 -2.2 4.6 Alexander Semin 8.6 6.2 12 6 3.4 -0.2 3.6 Marco Sturm 5.6 5.9 6 3 0.4 -2.9 3.3 Eric Fehr 3.7 2.4 5 2 1.3 -0.4 1.6 Scott Hannan 7.7 11.2 6 8 -1.7 -3.2 1.5 Jeff Schultz 7.0 9.4 5 6 -2.0 -3.4 1.4 Mike Green 8.7 6.9 10 7 1.3 0.1 1.2 Mike Knuble 6.2 5.4 5 3 -1.2 -2.4 1.2 John Erskine 4.8 5.3 7 7 2.2 1.7 0.6 Boyd Gordon 4.1 6.6 0 2 -4.1 -4.6 0.5 Sean Collins 0.3 0.3 1 1 0.7 0.7 0.0 Alex Ovechkin 11.6 7.5 11 7 -0.6 -0.5 -0.1 Nicklas Backstrom 10.0 9.2 9 9 -1.0 -0.2 -0.8 John Carlson 9.6 10.1 6 8 -3.6 -2.1 -1.5 Matt Hendricks 2.6 2.8 0 2 -2.6 -0.8 -1.7 Brooks Laich 9.4 9.5 8 10 -1.4 0.5 -1.9 Jason Chimera 4.7 4.9 4 7 -0.7 2.1 -2.8 Matt Bradley 3.4 3.2 0 3 -3.4 -0.2 -3.2 Marcus Johansson 8.0 7.3 8 11 0.0 3.7 -3.7 Karl Alzner 8.1 9.8 4 10 -4.1 0.2 -4.2

I thought hard about the baselines for this chart, before deciding to use the 2010-11 regular season baselines again. We all believe that goal scoring is tighter in the playoffs, but I'm not sure how to properly quantify that. The playoffs themselves provide too small a sample size, in my opinion, to justify recalculating the baselines. In the end, I think the regular season is a pretty good proxy for the playoffs, at least in a relative sense.

Now let me cut to the chase (too late!) - I was shocked to see those two names at the bottom of the chart. My lyin' eyes told me that Karl Alzner and Marcus Johansson were two of the Caps' best playoff performers. And yet here they are at the bottom of this table, having been on the ice for more opposition goals than Caps goals. And then up near the top, that's Jason Arnott and Marco Sturm, who to my eyes were almost absent through the playoffs. But there they are, having been on the ice for more Caps goals than opposition goals. More than that, this chart seemed to show a real trend:

The Y axis is +/-^X, and the X axis is age. Nobody under the age of 25 exceeded expectations. Five out of the seven players who are 30 or older who did exceed expectations. Maybe the Caps' problem this postseason was inexperience. Maybe that's what the problem has been each of the past few years. Maybe the Caps' playoff hopes were actually dashed on March 29 when Tuomo Ruutu wrecked Dennis Wideman's leg and took away one of the team's more experienced defensemen.

I hope this has been useful, and not just one more stat in a sea of them. I know I’d been looking for a way to translate TOI and goals for/goals against into something more meaningful. I’ve probably done about as much as I’m going to with this topic, but others are welcome to run with it however they like. The numbers in the spreadsheet and the methodology are available to all. And if you do something interesting with it, I'd love to hear about it.

If this FanPost is written by someone other than one of the blog's editors, the opinions expressed in it do not necessarily reflect those of this blog or SB Nation.