Grabovski Hypothesis – Regression Refined (offense)

28 Aug

1st Regression and Post

I received a good comment yesterday about whether ‘shots for’ being related to Fenwick and Corsi were messing with the regression.  So, I separated all of that out.

Corsi – Fenwick = Blocked shots (BS)

Fenwick – Shots for = Missed shots (MS)

I re-ran the regression with and without the lockout year from the 07-08 season…..


Missed shots and blocked shots have no statistically significant affect on goals for.  That seems pretty obvious, right?  If a shot is blocked or missed the net, then why would it have an affect?  I think the idea with Fenwick and Corsi “tilting the ice”, or having a lot of possession, does not affect offense statistically according to this regression.  On offense, the only things that seem to matter significantly are shots that actually hit the goalie and shooting percentage.

Again, if a player can individually put more shots on goal or be more accurate than a person is replacing, he would benefit the team.  He could also assist his players by getting them the puck in certain positions to be more accurate or to get the puck on net.  However, it appears the possession portion as defined by Corsi and Fenwick are irrelevant on offense.

More on defense coming soon….


With lockout season….

Estimate              Std. Error             t value Pr(>|t|)

(Intercept)          -98.299082          25.991111            -3.782    0.000218 ***

SF                           0.076925              0.002881              26.704  < 2e-16 ***

SA                           0.003641              0.002532              1.438     0.152307

BS                           0.002288              0.004109              0.557     0.578428

MS                         -0.003707             0.005360              -0.692    0.490186

Sh.                          16.144123            0.307568              52.490  < 2e-16 ***

Sv.                          -0.283125             0.290146              -0.976    0.330600

OZFO.                   0.111255              0.262291              0.424     0.672000

DZFO.                    -0.340800             0.209741              -1.625    0.106112

east                       1.269434              1.335174              0.951     0.343124

west                      1.531076              1.402439              1.092     0.276556

yr13                       0.659509              2.735007              0.241     0.809751

yr12                       -0.013865             1.072697              -0.013    0.989703

yr11                       -0.152273             1.074736              -0.142    0.887503

yr10                       0.352642              0.957111              0.368     0.713017

yr9                          -0.045403             0.849630              -0.053    0.957448

yr8                          NA                          NA                          NA          NA

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Without lockout season….

Estimate              Std. Error             t value                  Pr(>|t|)

(Intercept)          -1.464e+02          1.207e+01           -12.135                 <2e-16 ***

SF                           7.962e-02            1.167e-03            68.241                   <2e-16 ***

SA                          -6.315e-04           1.086e-03            -0.582                    0.562

BS                           2.436e-03            1.658e-03            1.470                     0.144

MS                         -2.519e-03           2.191e-03            -1.150                    0.252

Sh.                          1.827e+01           1.409e-01            129.625                 <2e-16 ***

Sv.                          7.535e-02            1.303e-01            0.578                     0.564

OZFO.                   -9.744e-02           1.195e-01            -0.815                    0.416

DZFO.                    -7.999e-02           9.176e-02            -0.872                    0.385

east                       -1.961e-01           5.760e-01            -0.340                    0.734

west                      -8.845e-02           6.023e-01            -0.147                    0.883

yr13                       NA                          NA                          NA                          NA

yr12                       3.841e-01            4.270e-01            0.900                     0.370

yr11                       3.014e-01            4.280e-01            0.704                     0.482

yr10                       4.671e-01            3.778e-01            1.236                     0.219

yr9                          9.021e-02            3.310e-01            0.273                     0.786

yr8                          NA                          NA                          NA                          NA

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


More on Grabovski – Do advanced stats say anything about a team scoring goals?

28 Aug

An initial disclaimer:

This piece is for discussion.  Statistical operations can be tricky and there can be a number of ways to do things.  I am not claiming to be right or wrong on anything, yet.  If you have some advice, please provide comment.

Round 2

So, after my article on the Caps picking up Grabovski and me not thinking it was as big of a deal as others were making it, the response was brutal.  I take some credit for that by putting out an unpolished piece.  In the end, I stand by my argument that the idea Grabovski would go from a career 45-50 point scorer to a 60-70 point guy was hyperbole.

Some people discussed how his Corsi and Fenwick ratings, and that Washington had a lot more offensive zone faceoffs than Toronto (which should lead to more chances), would make him an improvement over Ribeiro.  I basically argued that despite the improved advanced stats, it seemed crazy that any one person’s numbers would jump that high; thus, the Caps roster is at a net loss without Ribeiro, add Grabo.

To that end, I wanted to examine this further.  Here is my idea:  the better Corsi, Fenwick and offensive zone faceoffs a team has, under the “Grabovski hypothesis”, should lead to more team goals (he manes his teammates better argument).  If this is true, we should be able to perform a linear regression and see how a variety of statistics effect the number of goals a team scores (goals for).  In other words, I wanted to see what happens when we regress a team’s “goals for” for a season (y-variable) on a set of variables, including those mentioned above (X-set).

Thus, I went to and grabbed team stats for all teams from the 2007-2008 seasons through the last season.  I added all of HA’s data (see legend below) and added some dummy variable, which is common when analyzing panel data.


TOI = Time on ice
GF = Goals For
GA = Goals Against
GF60 = Goals For per 60 minutes of ice time
GA60 = Goals Against per 60 minutes of ice time
GF% = Goals For percentage = 100* GF / (GF + GA)
SF = Shots For
SA = Shots Against
SF60 = Shots For per 60 minutes of ice time
SA60 = Shots Against per 60 minutes of ice time
SF% = Shots For percentage = 100* SF / (SF + SA)
FF = Fenwick For
FA = Fenwick Against
CF = Corsi For
CA = Corsi Against
Sh% = Shooting Percentage
Sv% = Save Percentage
OZFO% = Percentage of face offs that took place in the offensive zone
DZFO% = Percentage of face offs that took place in the defensive zone

Items in red are in the data table, but were not used in the regression so there weren’t correlation issues between the x-variables.

Dummy Variables

east – Eastern Conference (0=No, 1=yes)

west – Western Conference (0=No, 1=yes)

yr** – year dummy for the year the data was taken (0 = not year **, 1 = year**) – one dummy variable for each of the six years


Looking from the 2007-2008 season through the 2012-2013 season, the regression results only showed statistically significant results (at the 0.05 level) for shooting percentage and shots for (see “regressions results with lockout year” below).

I thought maybe the lockout-shortened season last year might have messed with things a bit, so I removed it and ran it again.  The only thing statistically significant again is shooting percentage and shots for.  Fenwick-for and Corsi-for are statistically significant at the 0.1 level, which is usually not accepted.  Let’s say we do accept the stats at this level.  A team would gain 1.7 goals per season for every additional 1,000 Corsi-for, or 1,000 shots directed at the net, or an one goal per season for every 333 additional Fenwick-for or 333 shots directed at the net (excluding blocked shots).


If I did this correctly, then only those old-fashioned statistics of shots on goal and shooting percentage matter how many times a team scores.  Offensive zone faceoff percentage does not matter.  Corsi and Fenwick are not statistically significant.  Even so, Grabovski and his improvement on other players would have to add 1,000 shots directed at the net to gain an additional 1.7 goals per season (or 333 shots not including blocks).

This does not say whether or not Grabovski will be better or worse than Ribeiro.  But, as it stands, Grabovski’s addition to the team based on the advanced stats do not have a statistically significant affect.  What will matter?  If he can get people the puck to score at a high percentage or put a lot more pucks on net, unblocked.  We know he is not an assist guy, so I think it can be deduced that he will not likely raise the shooting percentage for others (give them good chances).  Ribeiro on the other hand is a distributor based on his higher assist numbers throughout his career.

With the regression, as it is, I think my argument stands….the Washington Capitals roster is worse minus Ribeiro, plus Grabovski.  The boys still have to play this out on the ice….

All files and R script are available upon request.


Regression results with lockout year.

Estimate              Std. Error             t value Pr(>|t|)   

(Intercept)          -9.013e+01          2.739e+01           -3.290    0.00123 **

SF                           7.776e-02            7.542e-03            10.310  < 2e-16 ***

SA                           9.466e-03            7.945e-03            1.191     0.23526

FF                           -4.715e-03           8.897e-03            -0.530    0.59690

FA                           -3.381e-03           7.771e-03            -0.435    0.66408

CF                           2.919e-03            4.285e-03            0.681     0.49663

CA                          -7.803e-04           3.323e-03            -0.235    0.81466

Sh.                         1.614e+01           3.087e-01            52.269  < 2e-16 ***

Sv.                          -3.527e-01           2.997e-01            -1.177    0.24093

OZFO.                   7.607e-02            2.656e-01            0.286     0.77492

DZFO.                    -3.457e-01           2.135e-01            -1.619    0.10732

east                       1.101e+00           1.352e+00           0.815     0.41634

west                      1.385e+00           1.438e+00           0.964     0.33663

yr13                       6.808e-01            2.779e+00           0.245     0.80681

yr12                       1.468e-01            1.141e+00           0.129     0.89776

yr11                       1.178e-02            1.138e+00           0.010     0.99176

yr10                       4.663e-01            9.894e-01            0.471     0.63808

yr9                          1.853e-02            8.647e-01            0.021     0.98293

yr8                          NA                          NA                          NA          NA

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Regression results without lockout season.

Estimate              Std. Error             t value Pr(>|t|)

(Intercept)          -1.444e+02          1.295e+01           -11.152   <2e-16 ***

SF                           8.331e-02            3.073e-03            27.110   <2e-16 ***

SA                          -2.951e-03           3.277e-03            -0.900   0.3696

FF                          -6.418e-03           3.604e-03            -1.781   0.0773 .

FA                           3.601e-03            3.134e-03            1.149   0.2525

CF                           2.929e-03            1.721e-03            1.702   0.0911 .

CA                          -1.713e-03           1.354e-03            -1.266   0.2078

Sh.                          1.826e+01           1.418e-01            128.81   <2e-16 ***

Sv.                          6.188e-02            1.359e-01            0.455     0.6497

OZFO.                   -1.117e-01           1.214e-01            -0.920   0.3592

DZFO.                    -6.648e-02           9.268e-02            -0.717   0.4744

east                       -2.084e-01           5.782e-01            -0.360   0.7191

west                      -2.127e-01           6.114e-01            -0.348   0.7285

yr13                       NA                          NA                          NA          NA

yr12                       5.828e-01            4.596e-01            1.268  0.2071

yr11                       4.903e-01            4.583e-01            1.070  0.2866

yr10                       5.869e-01            3.926e-01            1.495  0.1373

yr9                          1.635e-01            3.373e-01            0.485  0.6286

yr8                          NA                          NA                          NA       NA

A Response to Peter Hassett and RMNB

25 Aug

It appears my article has gotten a lot of looks today.  A little has been discussed about the substance of my article, but mostly about a couple of small mistakes that in no way take away from the conclusion of my article.  The Russian Machine Never Breaks‘ Peter Hassett took the time to breakdown why my article is incorrect.  I feel that I should give a response to what has been the most intelligible critique of the article.

Here goes (responses in bold):

  1. “Caps Back to Early Playoff Exit Status with Grabovski Signing”
    A fine piece of trolling in the title. The Capitals surely have a reputation for getting bounced from the post-season early, and Caps fans have dealt with bombast like this ever since Tony Kornheiser coined “choking dogs” back in 1987 (or whenever). But I’m not sure that’s a) an actual meaningful status , or b) something the Caps ever lost considering they’ve lost in the first or second round every year since 2008.

Without a doubt people read articles based on the title.  Is it trolling?  You decide.  Mostly local Caps media have lauded this move.  It does make the roster better.  Does it get them to contender status?  I don’t believe so.  The title hopefully catches your eye and then you can read on whether you believe it or not.

  1. “Time to separate the facts from the hyperbole.”
    An author flatly proclaiming to be The Arbiter of Truth is never a good sign.

It does set me up for some heavy critique….though Arbiter of Truth is ironically a bit of hyperbole.  Especially after hammering my title…..

  1. “First, the Capitals cannot re-sign Mike Ribeiro at a decent price and he heads off to Nashville.”
    Ahh yes, the desert paradise of Nashville. The Jewel of Arizona. The Southwest’s own Music City. Powder City, AZ. Athens of the Southwest. America’s least sustainable city. Tennessee’s urban heart. (Ribeiro signed with Phoenix.)

Was a simple mixup with Hendricks and I glossed over it on proofread.  As I stated elsewhere, Riberio could be on the moon.  Doesn’t take away from the main point of the article?

  1. “The Capitals problem was never scoring goals.”
    The Caps were shut out eleven times in 2010-11Their goals per game fell from 3.27 in 2008-09 to 2.67 in 2010-11. I write recaps of about 75 Caps games a year; don’t tell me scoring goals was never a problem.

They were still middle of the pack, but it is difficult to say it was a “problem”.  It was not as good as other teams.  Defense has been a longer, persistent problem and Grabovski won’t help much here.  Last year, scoring was not a problem….in the context of Ribeiro vs. Grabo, which is the point here.

  1. “It is a stretch if Schultz and Hendricks roles will be adequately replaced.”
    I love Matt Hendricks, but replacing a fourth line grinder is about as tough as finding  a spare $800K in Uncle Ted’s wallet. Schultz was scratched for almost half of last season, so I’d consider him replaced since the beginning of April.

They are using farm guys as call ups to fill these spots.  Maybe they will be okay here.  Kind of a minor point…that’s why it was such a small piece of the article.  Just pointing out the Caps lost more than Ribeiro and didn’t sign anyone of equivalence.

  1. “Washington did re-sign defensemen Karl Alzner and Tomas Kundratek, which made the offseason not a complete coup for free agents.”
    And thank goodness. If the Caps not did not re-sign Karl Alzner (which they did on July 10), I’d be picketing outside the McPhee house, and I would not be alone there. Though I doubt the extent to which the market was clamoring for Kundratek.

Seems like we agree, if Azner wasn’t re-signed, it would have been a free agent exodus.

  1. “But again, the problem in Washington is defense and nothing was done to shake up the old guard.”
    I actually agree with this point. I feel dirty.
  1. “The Capitals just have a hard time with the salary cap and likely for other reasons (which could be discussed at length) attracting big time free agents.”
    The whispering campaign continues: Surely, with its comfortable suburbs, cosmopolitan city center, the team’s focus on offense, and a player-centric coach in Adam Oates, DC is a toxic anathema to free agents. No. At this point, innuendo about the Caps locker room is more damning for the speaker than the subject. When you read a line like that, you know to doubt everything surrounding it.

I don’t think the Caps locker room is cancer-ridden.  Not my insinuation.  Who are the big free agents that come to DC though?  Ribeiro and Grabovski?  DC just doesn’t have the allure, for whatever reason you want to plug in, as other NHL teams.  Players at times take less and go elsewhere.  Maybe because other teams seem a lot closer to the Cup than DC?  I don’t know, but they’re not flocking here like they do to other teams.

  1. “. . . His Corsi-in and Corsi-out and other advanced stats show that he will make his teammates better.”
    I think the writer means Corsi On and Corsi Off– measurements of how the ice “tilts” when a player is on or off the ice based on shot attempts. You’d think with eight years experience as a statistician, Mr. Bourcier would be bothered to look up the names of the stats. Or at least copy them accurately from the source articles (which include RMNB! Yay! Thanks for the link!).

It was -on and -off.  A mistake.  It was corrected earlier.  Using Corsi wasn’t to highlight any advanced stats, but to illustrate how a basic look at Grabovski’s numbers and tenure in Toronto are not a clear cut win for the Caps.  Toss in some locker room issues in Montreal and Toronto and off-ice issues elsewhere, there is a lot of prima facie evidence that more is being made of this signing than what it really will happen on ice.  Statisticians like yourself are using more exotic/advanced metrics to show how he could be a great addition.  Truth is, he is a career lower point scorer than Riberio with no proven playoff experience.  Will his efficiency shine through and he ends up a 70 point scorer as some are predicting?  Maybe.  Will he bite another player?  Maybe.  He has done one of these in his career….

  1. “Oh, and puck possession—Grabovski really can possess that puck.”
    The writer says this right after the line about Corsi, which makes me wonder if he understands that Corsi is already a measurement for possession or that we’ve been talking about shot attempts this whole time.

It was written after, because it wasn’t meant to be the same thing.  Puck possession was another thing mentioned where he was better than Ribeiro and how he would better the Caps because of this.  

  1. “Here is what we know about Grabovski in facts.”
    I like the use of italics here, as if all the shot-attempt statistics before were somehow counterfactual. As if any statistics except the ones shown on an NBC Sports chyron are myth. But that’d be a curious opinion for a fellow with an nigh-PhD in economics and nearly a decade in statistics experience.

Grabovski is a 45-50 point scorer a season.  10 to 20 points more a season because of greater puck possession, better efficiency, more faceoffs in the offensive zone?  Another .25 points per game?  Advanced stats show he is better in some areas than Ribeiro.  I agree with those measures.  But, how can you disagree that Ribeiro is a better career scorer and has a better playoff record?  It is not that the other things are mythological, but 10% more faceoffs in the offensive zone leading to one player getting that many more points a year?!?

I guess that is my problem.  I have read that Grabovski could score 10 to 20 more points a year under Oates.  Then I see these advanced stats.  But where is the tying these advanced stats to more points?  We should be able to come up with a range of points with these advanced stats.  I didn’t take the time to do it, but I would be interested in seeing it.  I also am not the one claiming a 45-50 point career scorer is going to put up 20-25 more points than usual.  I would be interested in seeing the data connecting the percentage increases to higher production for this one guy.

  1. “Could it be argued Toronto was better when Grabovski was playing less?”
    Sure, you could argue that. But you’d lose that argument. By a lot. Toronto Maple Leafs blog Pension Plan Puppets basically killed a small pixelated forest on this topic (alsoalsoalso,also).

It is maybe oversimplified, but Toronto made the playoffs for the first time since Grabovski was there when he was relegated to 15 minutes a game in a more defensive role.  Toronto obviously found it favorable to buy this guy out.  Montreal didn’t deal with him for long either.

  1. “In the last playoff year, Grabovski put up two assists in their seven game series.”
    Mike Ribeiro had just one goal and one assist in his seven-games playoff series. So what? A seven-game sample during which Grabovski was used exclusively as a defensive player is not convincing evidence of anything. As a measure of either player in the long run, it’s nearly worthless.

If he had more playoff experience, like Ribeiro, we could see what is a trend or if he is a playoff choke artist.  

  1. “They picked up a guy way down the list from who they were really going after and someone no one else really wanted.”
    Grabovski was the object of a bidding war (with 7-12 teams in the running depending on whom you ask) throughout the offseason– a war won by Washington based on the coach’s appeal. Yes, Grabovski was bought out by Toronto (“the opposite of smart” according to Steve Dangle), but he was far from unwanted.

While I think most of your arguments are sound, this is the poorest.  Grabovski was in a bidding war and got only $3m a year and a one-year contract?  People wanted his services, for sure…but they weren’t willing to pay more than $3m for it.  He sat for a long-time and no one scooped him up.  If he was so wanted, he would have gone sooner, for more money and a longer deal.  They were out of good options.  Some credit, they didn’t get desperate and overpay.

  1. “At times Grabovski has score more goals than Riberio, but he has little, unproductive playoff experience and he is now on a team that needs a lot of playoff help.”
    The best predictor of playoff success is regular-season success– John Druce in 1990 excepted. Actually, Druce is a pretty good example of how tiny samples of playoff performance don’t tell you much about the player overall.

Might be the best predictor, but doesn’t mean it is cause and effect.  Maybe Grabovski can do better, maybe he can’t.  Truth is no one knows.  For a team that can’t get over the playoff hump, a guy with no playoff experience, on a losing team his entire career and only 2 assists in limited playoff action….it is a huge question mark.  Grabovski is far from a sure thing that will get the Caps to the next round or make them a contender.  He has a lot of question marks.

  1. “Two years in a row, Laich is getting demoted for two one-year contract guys that are basically patching holes in the roster.”
    Laich played nine games last season. He was not demoted, he was injured. And further, I’d argue that getting an assignment as a defensive forward with lots of special teams work is not a demotion; it’s playing a crucial role. Laich’s boxcar stats will suffer, but he’ll be helping his team win games. Knowing Brooks’ attitude and reputation as a team player, I bet he’ll be cool with that. He’s already got that steady paycheck after all.

Many have said this and I agree he plays a crucial role.  At the end of the day, would he rather be 2C?  Does it suck to keep thinking you are the next 2C and then they replace you?  I don’t know what Laich’s goals are, but if he wants the limelight or a bigger contract near the end of his term in DC, this has to be painful.  It seems the team doesn’t have the confidence in him playing 2C…maybe a shot to the ego.  I don’t know, just food for thought.

  1. “At the end of the day, even with the Grabovski signing, the Caps offseason has been a net loss.”
    Except when measured by, ya know, measurements.

Ribeiro is a better career scorer with better career playoff numbers, who was scooped off the market quickly because there is no doubt to his talent and leadership.  Grabovski sat there until now and we need advanced stats to show how he could be better.  They also have two-way contracts and farm guys replacing guys who were role players, but with valuable NHL experience.  Easier holes to fill, but not yet proven filled.  In my mind, based on really basic measurements, Caps are still net loss for the offseason.

  1. “Defense is their main issue.”
    And the broken clock has now been correct twice today.

Looks like cute sayings, like my title, are an author’s best options ;).

P.S.  I hope the poor numeration isn’t hammered on too hard.  I realize they are all ones.  I didn’t care about this mistake.

New happenings

2 Jul

I have a few new sports related things I am doing.  Not sure if I mentioned it before, but I am now a contributing writer for the Washington Capitals and for European hockey over at The Hockey Writers.  If you go to my ‘Articles‘ link you can see everything I have written so far.  Out of the six articles, I have already been featured twice!  I am on the front page right now with my Washington Capitals Draft Grades column.  If you like it, leave a comment and/or please spread the word.

Also, I started an English language blog providing news, analysis and roster information for the KHL club in Zagreb, Croatia.  Take a look at my Bears Blog.  The team mascot is a bear.  The KHL is based out of Russian, but there are teams everywhere.  However, the club only posts news in Croatian and it is a bit hard to find.  So, there it is…a new undertaking with a focus on one club.  I have three people ready to contribute, which is nice!  If you are interested in hockey or any of the guys on the team (a lot of North American NHL players), let me know if you are interested in putting in a column.

More fun stuff to come soon!

KHL’s Interesting Take on Expansion Draft

12 Jun

A quick note about an inquiry I made today with the KHL staff concerning the June 17th expansion draft for Vladivostok.  All of the players available for Vladivostok to choose from was supposed to be determined by each team today (see my article over at  However, a KHL spokesman said the names of those available players in the expansion draft would not be made public.

It made me wonder (and follow-up with the league) whether Vladivostok will know who is available prior to the 17th or if the players even know they might be moving a 3.5 hour drive from the North Korean border.

This could be a really great thing for fans, wondering if their favorite players would be moving or Far East Russian hockey fans wondering what talent might be available for them.  Yet, this has to be crazy nerve wracking for players…even if they know they might be Asia bound.  At least North American players will be closer to their continent :)…

***UPDATE – The KHL spokesperson responded and said Vladivostok and the player’s (or their agents) are aware informed of the transfer list.  Now that we know the players know, I wonder how the players feel about the move:  new opportunity or exile across Russia?


Washington Capitals Mock Draft

10 Jun

In my second article for The Hockey Writers, I examine current roster needs and predict a draft pick for the Washington Capitals (article here).  It wasn’t the easiest thing to do, because really you need to know who would be available–the first 22 selections in this case.  You also need to look at team needs while also predicting what the Caps management might do.  Will new Coach Adam Oates have more power or will they continue down the path of selecting offensive-minded European players as they have done with first-round picks in recent history.

There are also a million rankings out there, but none combine North American and European skaters into one category.  It makes it very hard to compare and contrast talent across multiple leagues.  Nevertheless, it was a fun exercise and I hope everyone enjoys the piece.


Check me out at The Hockey Writers

10 Jun

I am now contributing to The Hockey Writers about all things Euro hockey and for the Washington Capitals.  Here is my first piece about KHL expansion.  I’m looking forward to a lot of fun, hard work over the next few months.  Check out the site and give me a follow.  I will be writing a follow-up soon about the World Championships and my complete failure on semifinal winner predictions.  Stay tuned!