Belated Two O'clock Numbers: 0, 18
Scott Hartnell has a +/- of +18.
Claude Giroux has a +/- of 0.
Does anyone want to make the case that +/- is a valuable stat?
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Me!

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by Chase W on Jan 27, 2012 3:03 PM EST reply actions 11 recs
^Love
And all I've done for want of wit, To mem'ry now I can't recall.
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by PyropenguinX on Jan 27, 2012 3:13 PM EST up reply actions
so good.
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by Travis Hughes on Jan 27, 2012 3:14 PM EST up reply actions
Seriously rec’d for the Nathan Fillion.
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Ian Laperriere (EE-an luh-PAIR-ee-YAIR), proper noun. Definition: Bad-assery on skates
Kesler is +12 so…
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by JaredL on Jan 28, 2012 1:39 PM EST via mobile up reply actions
Well Scott Hartnell’s agent would.
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For those wondering how this is even possible for two guys who spend 75% of their ice time together, notice that Giroux’s on-ice Sv% is .905 and Hartnell’s is .932.
So if the goalies are stopping about 91.5% of the shots when both guys are on the ice, that’d mean they stop 87.5% for just Giroux and 98.3% for just Hartnell.
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Just out of curiosity, is there a way to separate the plus/minus from just even strength ice time as opposed to even strength, powerplay, and penalty kill combined?
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If I’m not mistaken, raw +/- is only measured at even strength. If you’re on the ice for a PP or SH goal, no + or – for you.
by Georgia_Flyer on Jan 27, 2012 3:50 PM EST up reply actions
Short handed goal goes againist +/- Power play does not.
-bob
by Rrainone on Jan 27, 2012 3:53 PM EST via mobile up reply actions
Yup. And it’s not simple to look up how many SHGs a given player was on the ice for, but…
Here are the Flyers stats at 4 v 5. Hartnell hasn’t been on the ice for any goals for, so no impact on his +/-. Giroux has been on the ice for 0.55 goals for per 60 minutes, and given his ice time (2.47 mins per game, 44 games), he was on the ice for one SHG for.
Here are their stats at 5 v 4. Hartnell has seen 0.81 SHGA/60, which works out to 2 SHG against. Giroux has seen 1.71 SHGA/60, which works out to 5 SHGA.
So Giroux’s +/- seems to break down to -5 on the PP, +1 on the PK, and +4 at ES. Hartnell’s is -2 on the PP, 0 on the PK, and +20 at ES.
@BSH_EricT
Writer at Broad Street Hockey
I don’t think Giroux is a -5 on the PP, mostly because the Flyers have only given up 4 shorties this year:
Patrick Dwyer 11/14 (Giroux was on the ice)
Patrick Dwyer 11/14 again (penalty shot, and I don’t know if the NHL counts those in +/-, but Giroux wasn’t on the ice when the penalty was committed)
Jim Slater 11/19 (Giroux was on the ice)
Josh Bailey 1/19 (Giroux was on the ice)
-3.
As for our own shorties:
Talbot 10/29 (Giroux was on the ice)
Couturier 11/3 (Giroux was not on the ice)
Read 11/13 (penalty shot, but Giroux was not on ice for penalty)
Couturier 1/17 (Giroux was not on ice)
+1.
So he’s -2 on special teams and +2 at even strength, not including any empty-netters for or against. I would have to check those but I believe we’ve had three for and three against, so they might make a difference, too.
by everybodyhitswoohoo on Jan 27, 2012 6:00 PM EST up reply actions
Hm. BtN definitely has him as being on the ice for 5 (after I hit post, I noticed the link I gave gives the raw total, so I didn’t have to do the arithmetic on ice time).
Part of the discrepancy probably comes from Seabrook’s goal on 1/5 — Sharp took a 4-minute high-sticking penalty at 10:15 and Seabrook scored at 14:15. The NHL play by play was sufficiently confused to list it as a SHG, but with Sharp back on the ice when it was scored. And I bet you’re right about the penalty shots being part of it too.
I think empty-netters count for plus/minus though. For example, see this game,
@BSH_EricT
Writer at Broad Street Hockey
Oops, misclick.
see this game, in which three people were a +2 when the Flyers scored two PP goals, one EN goal, and one ES goal.
@BSH_EricT
Writer at Broad Street Hockey
OH YEAH. I remember seeing that and being confused because the PBP said it was a shortie but the box score said it wasn’t (it sure looked like one, IIRC).
The NHL itself says the Flyers have given up 3, so it’s clearly not counting the Seabrook goal or the Dwyer penalty shot goal.
But even if BTN is counting both of those as 5v4 goals against Giroux, that still doesn’t make sense because he wasn’t on the ice for the penalty that forced the penalty shot (19-48-68-25-44-35).
by everybodyhitswoohoo on Jan 27, 2012 6:27 PM EST up reply actions
Also, I know +/- includes empty net goals, but I’m pretty sure BtN does, too (as 5v5 goals). Which seems wrong.
by everybodyhitswoohoo on Jan 27, 2012 6:30 PM EST up reply actions
Yeah, I can give BtN a pass on a play where the PBP contradicts itself, but I have no idea how it got the fifth. Maybe there’s another one somewhere that came right when a penalty ended?
@BSH_EricT
Writer at Broad Street Hockey
Should of traded Giroux instead of Carter
Do you see what happens when you find a stranger in the Alps?
He hasn’t gotten the pre-NMC promise yet.
/s, more often than not
by flyersfaninchicago on Jan 27, 2012 6:34 PM EST up reply actions
I'm confused...
…and not necessarily because Hartnell’s +/- is higher (when most people would assume Giroux’s would be since he certainly seems to be the more talented and defensive player). I don’t understand how they even had the opportunity to distance themselves so much. Aside from the first 7 or 8 games where they were on different lines and the 4 where Giroux was out with his concussion, I don’t seem to remember too many times when they are on the ice without each other since they obviously play on the same line. The exception would be when Claude plays on the PK, but those goals don’t count towards +/- anyways.
The only thing I can think of is that maybe Giroux is always out there when the Flyers are losing at the end of their games so the empty netters count against him. Is that what’s largely making up the difference, or what am I missing here?
No, you’re exactly right - this is remarkable. People will sometimes argue that +/ is OK but just (like any stat) needs some context, but here we’re talking about two guys on the same team, on the same line, with wildly divergent numbers.
We’ve discussed a little of this above. They’ve been on the ice together about 75% of the time at even strength. The team has only had a couple of empty netters for and against, so that wouldn’t explain it. What it comes down to is goalie performance — the goalies have stopped 90.5% of the shots when Giroux was on the ice and 93.2% when Hartnell was, which means that in the 150-200 minutes they were apart, the goalies had to be much worse for Giroux than for Hartnell.
@BSH_EricT
Writer at Broad Street Hockey
I’m sorry for being so thick about this sometimes, but how do you know it’s goalie performance? As opposed to, say, Giroux’s defensive shortcomings being exposed when Hartnell isn’t there to support him?
I’m not asking that question based on what I believe to be true. It’s just an alternative hypothesis. I’d like to know what the fact is that makes the save percentage difference only about the goalie. Is it that it has been statistically proven that save percentages are independent of the skaters on the ice? That, rather, the skaters determine the number of chances against, and that even if Hartnell without Giroux leads to fewer chances against than Giroux without Hartnell, the difference is still too small to explain an 18-unit gap (much the same way empty net goals fail to explain it).
Did that make sense?
/s, more often than not
by flyersfaninchicago on Jan 27, 2012 8:12 PM EST up reply actions
Last year, Giroux’s on-ice save percentage was 0.919. Hartnell’s was 0.916.
Eric’s not saying the only reason is goalie performance, he’s saying that’s the big reason. When you dig deeper – why is the goalie doing that – you have to then look at scoring chances against, shots against, competition, teammates, etc.
But there has been no evidence that skaters can consistently suppress shooting percentage, so until that happens, the evidence suggests it’s goalie performance much more than anything the skaters are doing.
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by Geoff Detweiler on Jan 27, 2012 11:39 PM EST up reply actions
Got it. Thanks for the link, too.
/s, more often than not
by flyersfaninchicago on Jan 28, 2012 1:25 AM EST up reply actions
No problem. It’s a legit question that isn’t completely settled. And Eric sent me a link from Pass It To Bulis that shows the Canucks might think players can suppress shooting percentage, which goes against the current information.
It’ll be in Monday’s Fly By, but if you’re interested, you can find it (no link as I’m on my phone) easily. Search “mike gillis pass it to Bulis suppress shooting percentage”. Should pop right up.
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by Geoff Detweiler on Jan 28, 2012 9:39 PM EST via iPhone app up reply actions
What about…Corsi?
While I am a bit late to the party, I will be the sucker who bites on the tempting low hanging fruit.
Let me start this post by making two of my beliefs very clear: (1) Claude Giroux is a much better hockey player than Scott Hartnell and (2) plus/minus has significant limitations and drawbacks as a statistic.
With that being said, in 5vs5 situations this year, Hartnell has a better Corsi per 60 than Giroux: 5.50 versus 1.91. Further, this difference is magnified a small bit if you look at Relative Corsi: 6.80 for Hartnell versus 1.20 for Giroux. As a caveat, Giroux has faced better quality of competition than Hartnell so these numbers should be considered within this context (as should the plus/minus numbers).
To play the Devil’s Advocate, couldn’t this article have easily have been the following:
"Belated Two O’Clock Numbers: 1.91, 5.50
Scott Hartnell has a 5vs5 Corsi of 5.50.
Claude Giroux has a 5vs5 Corsi of 1.91
Does anyone want to make the case that Corsi is a valuable stat?"
Based on my relative lurking on BSH, I think that most members of this community (especially the stat guys such as Eric T., Geoff Detweiler, etc.) believe that Corsi is indeed a valuable stat (while plus/minus generally is not). However, if one is going to use the fact that Hartnell has a higher plus/minus than Giroux to highlight the limitations of the plus/minus stat (as Giroux is clearly a better player than Hartnell), shouldn’t one also note this mirror fact that Hartnell has a higher Corsi than Giroux to highlight the similar limitations of the Corsi stat?
I realize that I may have just opened up a Pandora’s box with the BSH community by suggesting the limitations of Corsi by drawing parallel arguments in this case to plus/minus. Let me be clear, I do think that Corsi has some advantages (just like plus/minus has some advantages), but I also think that it has some limitations (just like plus/minus has some limitations). Thus, if one sets up an argument to highlight the limitations of plus/minus (as was done with this comparison of Giroux to Hartnell in the original posting), shouldn’t one also apply this same test to other supposedly better (at least more "advanced") stats such as Corsi? The problem is that this argument reaches the same conclusions with the more "advanced" stat of Corsi as it does with the traditional stat of plus/minus.
So is this a case of limitations with the stats or limitations with the arguments?
Just some food for thought – I am sure that the “Advanced” stats crowd will unite to highlight the error of my ways given that I have suggested the limitations of Corsi and put it on par with plus/minus in this instance given the original arguement (albeit for the sake of a Devil’s advocate perspective).
Not participating in the argument (as I know too little about these things to be a major participant in such an argument) but going to add that Corsi should be looked in the context of O-zone start % which you forgot to note. Hartnell has 49.3% O-zone start and Giroux has 45.9% O-zone start. Using my Balanced CorsiRel formula, Hartnell’s balanced CorsiRel is 7.12 (his expected CorsiRel is -0.32) and Giroux’s balanced CorsiRel is 3.37 (his expected CorsiRel is -2.17). Therefore, while looking at zone start gives us a bit of context to why that difference exists, Hartnell’s balanced CorsiRel is actually also higher than Giroux’s.
It’s also interesting to note however that Giroux’s Balanced CorsiRel – which was once elite (at the time I wrote that fanpost I linked above) – is now not actually at a top quartile level. He’s gone down from 6.82 when I wrote that article to 3.37. His actual CorsiRel has gone down from 5.0 to 1.2…
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by PursuitOfLappyness on Jan 28, 2012 7:49 AM EST up reply actions
Good points – You are definitely correct that I didn’t include zone starts, which I understand does have an main impact on Corsi. Thus, I appreciate you highlighting the Balanced CorsiRel . As you note, Hartnell still does have a much higher Balanced CorsiRel than Giroux, so this would support my Devil’s advocate arguement in my prior post…while also taking into account zone starts.
To this end about considering alternative explanations, one thing that isn’t included (although I do mention it as a caveat) is quality of competition. G faces higher quality of competition than Hartnell. Thus, is this difference in competition the thing that is driving the difference between the two in terms of plus/minus, Corsi, Corsi Relative, Balanced CorsiRel?
Thanks again for bringing up zone starts – This is indeed an important point that needs to be considered, so I appreciate you doing so.
No stat is going to give perfect rankings. But it’s a lot easier to point to usage to explain away a small difference of Corsi (2.5 shots is the difference between 92nd best forward with 30+ games and 140th best) than a huge difference in +/- (where Hartnell is 11th in the league and Giroux is somewhere around 200th).
In other words, the point isn’t “any stat that ranks Hartnell ahead of Giroux is a pile of crap.” It’s “a stat that purports to be a measure of someone’s all-around value that ranks Hartnell miles ahead of Giroux deserves a big helping of skepticism.”
@BSH_EricT
Writer at Broad Street Hockey
Thanks for your thoughts and response. Your comment about how you can "explain away a small difference of Corsi" got me thinking about whether this is indeed true.
As such, I took a stab at testing this claim with some back of the envelope calculations. In particular, I attempted to "explain away" the Corsi difference between Hartnell and Giroux by taking into account two key variables often mentioned as factors that may influence Corsi: Quality of competition and zone starts. While I won’t bore anyone with the technical details of this calculation, it essentially entails (1) determining the effect of "Corsi Quality of Competition" and "offensive zone starts" on Corsi in terms of the relationship between these constructs, (2) determining the difference between Hartnell and Giroux in these two factors, (3) and then extrapolating this data to the difference in Corsi between Hartnell and Giroux.
When you do this calculation, the Corsi gap between Hartnell and Giroux definitely decreases, but there is still a fair difference between the two – By my calculations, the difference in Corsi per 60 is reduced from 3.6 to approximately 1.6. Thus, even when factoring in situation and quality factors, Hartnell still exceeds Giroux in Corsi and this difference cannot be "explained away" by the external factors. You could do the same calculations with plus/minus to show that the difference between the two decreases when you factor in these other variables.
I agree that the standardized difference (i.e., difference of z-scores) between Hartnell and Giroux is larger for plus/minus than it is for Corsi. Indeed, as I noted in my original post, I think that there are significant limitations and drawbacks to plus/minus. However, my main point was that when critiquing one stat, the same critique should be applied to all stats…and especially to the ones that are purported to me more "advanced".
When you do so, a similar conclusion is still reached: Hartnell is more favorable than Giroux (whether it is Corsi, CorsiRel, Plus/Minus). Further, even when factoring in the quality of competition and zone starts, these results still hold (although they are definitely reduced in magnitude across all of these variables).
Thus, the statistics of both Corsi and plus/minus tell us that Hartnell is better than Giroux (albeit differences in magnitude of the "better") even when factoring in situation and competition explanations, while our eyes (at least my eyes) tell me the opposite that Giroux is much better than Hartnell. In my opinion, this discrepancy is very interesting and suggests two things to me: (1) the limitations of both plus/minus and Corsi as statistics, and/or (2) the limitations of my eyes in evaluating performance.
While I won’t bore anyone with the technical details of this calculation, it essentially entails (1) determining the effect of “Corsi Quality of Competition” and “offensive zone starts” on Corsi in terms of the relationship between these constructs,
The technical details are key here. Simple regression typically points to quality of competition having little impact on Corsi, because better players tend to face better competition. But if you set it up so that the player quality is normalized out, where you’re not asking “does the average player with high QoC have a low Corsi” but “does the average player’s QoC drop in the minutes where he faces strong QoC”, I believe you’ll see a much stronger response.
Moreover, the point wasn’t really that QoC and zone starts explain the difference. It was that the difference is small, and so it doesn’t require much of an explanation. Whereas the difference in plus/minus is enormous, the difference between perfectly average and 11th best in the whole league, and is therefore much harder to brush off if you believe +/- is meaningful.
@BSH_EricT
Writer at Broad Street Hockey
Another Argument…To Be Torn Down by the "Advanced" Stats Crowd
My prior post motivated me to dig a bit deeper. Instead of just playing the Devil’s Advocate and suggesting inconsistencies of arguments, I decided to pull up my sleeves and do some quick and dirty (with extra emphasis on the dirty) analysis in order to compare the supposedly faulty plus/minus statistic with the supposedly better "advanced" statistic of Corsi.
My main goal in this analysis was to take the bait (I am sure foolishly) from Eric T. and try to "make the case that plus/minus is a valuable stat". While it is difficult to determine how valuable one stat is in isolation (given the subjective nature of "valuable"), it is possible to say that one stat is more valuable than another by comparing the two together (rather than in isolation) in relation to some meaningful outcome. Thus, I ran some regressions to compare the value of plus/minus and Corsi.
My first assumption was to determine a criterion of interest. While there are lots of possible choices, for simplicity sake, I choose points per 60 minutes (P60). That is, I am assuming that most people would believe that P60 is an indication of a good hockey player. I understand that this has limitations (as would any dependent variable), but P60 is a fairly common metric and useful evaluation of a player all things considered.
To compare plus/minus to Corsi, I regressed P60 onto plus/minus and Corsi with several iterations: (1) regressed P60 on to plus/minus and Corsi simultaneously, (2) regressed P60 onto plus/minus first and Corsi second in a stepwise fashion, and (3) regressed P60 onto Corsi first and plus/minus second in a stepwise fashion. The data is from this year (2011-12) in terms of all NHL forwards who have played more than 20 games. As this is just a quick and dirty analysis, I didn’t add in control variables and I recognize that there is a dependency issue (given certain players play on the same line) with the data which may minorly bias estimates. Further, I completely understand that there is an endogeneity issue by looking at plus/minus and points in the same regression, which has implications for the findings. With these caveats in place, here are the results:
When entered simultaneously, plus/minus and Corsi account for 42% of the variance in P60. Both are significant predictors, but plus/minus is a much stronger predictor (standardized Beta of .55 for plus/minus versus .17 for Corsi).
When entered stepwise, both account for a significant amount of unique variance over one another, which is a good thing as this indicates that they are non-redundant measures. However, plus/minus accounts for much more variance in the second step of the regression than Corsi does. When Corsi is entered first, it accounts for 17% of the variance in P60 and plus/minus accounts for 25% of the variance in the second step. However, when plus/minus is entered first, it accounts for 40% of the variance whereas Corsi only accounts for 3% of the variance in the second step.
Ultimately, these analyses show that plus/minus is a much more "valuable" in predicting P60 than Corsi. The amount of variance that Corsi adds over plus/minus (3%) is very small (albeit significant). Thus, if you already know plus/minus, knowing Corsi doesn’t get you very much understanding of P60. However, plus/minus does get you a lot of understanding (25% of the variance) of P60 even if you already know Corsi. Thus, this traditional stat of plus/minus is much better than the "advanced" stat of Corsi in understanding this criterion of P60.
Thus, here is my case for the value of plus/minus – It is a much better predictor than the "advanced stat" of Corsi in predicting an important outcome of P60. While there are definite limitations of plus/minus, these analyses indicate that it is far more valuable in understanding P60 than Corsi. If an individual only looks at plus/minus in predicting a player’s P60, it is not a big deal to exclude Corsi. However, if an individual only looks at Corsi in predicting a player’s P60, it is huge loss to exclude plus/minus.
Again, I understand that there are some model specification problems with these quick stepwise multiple regression analyses (interdependence of some data, endogeneity, etc.), but these results highlight the utility of plus/minus over Corsi in predicting P60. If one believes that Corsi is a valuable stat for evaluating a player (in terms of his point production), then one also has to think that plus/minus is a valuable stat…and, in fact, these results show that it is actually much more valuable (than the "advanced" stat).
My case has been made (albeit with a number of assumptions, leaps, and statistical misspecifications) – I look forward to having the "advanced" stats crowd (and others) tear it down.
Interesting argument.
Couldn’t you turn this around and say that what you’ve shown is that +/- is redundant with P/60, whereas Corsi adds something new? And if +/- is often cited as a measure of defensive skill, then its redundancy with an offensive measure seems like a bad thing.
The redundancy isn’t really that surprising either, since every time a player gets a point, that also counts as a + in +/-, and a reasonably large fraction (something like 25%) of the events that count in +/- will also count as a point. The question is whether correlation with points really proves that the stat is valuable.
@BSH_EricT
Writer at Broad Street Hockey
Thanks for your thoughts. Given your response, I think we might have different approaches or goals with statistics. My goal is from an inferential sense in order to best be able to predict an outcome of value (with the smallest confidence interval around that prediction) based on potential predictors.
Thus, whereas you suggest that plus/minus is "redundant" with P60, I see it as "predictive"…and much more predictive than Corsi. Indeed, plus/minus and P60 share much less than 50% of the variance together, so they are far from redundant (at least by my definition of redundant…and probably by most statisticians’ definitions of redundant as well). Further, while you might say that Corsi is not redundant with P60, I would say that it is not predictive of this valuable (to me) outcome. If I wanted something that was not-redundant or not predictive, I could examine other variables (besides Corsi) such as shoe size or eye color as these also would be non-redundant and non-predictive (when factoring in plus/minus).
If one doesn’t think that P60 is valuable, then this point is moot. However, if one does value P60, then knowing that plus/minus is far more predictive of it than Corsi (when considered in conjunction) should indeed be of significant use. Given Corsi is nonredundant (doesn’t predict) basically suggests that knowing Corsi is like knowing shoe size or eye color (and these things don’t really matter all that much for P60 if you already know plus/minus).
With that being said, I definitely agree with your point about the measurement overlap of plus/minus with P60 – I noted this issue in my original post when I mentioned the problem with endogeneity. While Corsi would also have an endogeneity issue, it wouldn’t be as large as plus/minus in my estimation. However, based some quick calculations, I don’t think that this issue is driving the results. When I get a bit more time, I plan to do some more complex analyses in order to more fully address this issue. My hunch is that it will have a fairly small impact on the results, but I look forward to seeing if this is a statistical artifact (due to endogeneity) or a "true" relationship.
Along these lines and to your last point, I am curious as to what people see as a "valuable" criterion. I choose P60 as this is of value to me (I think P60 is a good indicator of performance for a forward), but I would be curious as to what others think are useful outcomes. With this information, I can run different models in order to more fully answer the question of "value" of plus/minus and Corsi in conjunction (as value is subjective based on how one evaluates it). I have a few ideas for other constructs to use as criterion (GVT, etc.) and will also definitely add in a host of control variables (i.e., zone starts, quality of competition, etc. as suggested above), but if anyone has any good ideas for other outcomes, I would love to hear them.
If you show that +/- is a better predictor of future P/60 than current P/60 is, then I could understand why you are interested in calling +/- predictive of P/60. But I don’t believe it is, so if you want to predict someone’s P/60, you’re not going to look at +/-; you’re going to look at P/60. Which is why the substantial correlation seems more like redundancy than value to me.
Corsi has been shown to be a better predictor of future goal differential than current goal differential is at the team level. And I believe Corsi has been shown to be more consistent (split half reliability or year-over-year correlations) than +/- at the individual level. The natural conclusion is that Corsi, as a more reproducible measure of an individual talent and as a more important team metric, is a more valuable individual metric.
@BSH_EricT
Writer at Broad Street Hockey
by Eric T. on Jan 29, 2012 6:36 PM EST up reply actions 1 recs
Disagreed if I want to predict future P/60, I would use current P/60. If I was using using current P/60 I would probably not include +/- due to potential multicolinearity issues. Further, if I’m simply trying to fit to current P/60 I’d try to find more meaningful insights than other scoring stats that P/60 drives (such as +/-).
being obnoxious and self righteous while ignoring the point since 9/29/11
Every time we have one of these conversations about +/-‘s “value” as a stat, it never fails that I start laughing because I remember a story from Keith Jones’ book where he ended up being minus-7 and it wasn’t his fault. I can’t find the box score from that game, but I did find a site that has the excerpt from the book with the story. Even if we assume the story is embellished for laughs in the book, it’s probably still accurate enough to illustrate the point:
“I’m ****ing minus 7!” which, mind you, has to be close to an AHL record."
The next day we’re having a meeting, and coach [Barry] Trotz addresses the team. He says, “Guys, there was a guy on our team last night who was a minus 7 on the stats sheet last night against Utica. I’m going to show you guys all of the goals on the video and I want to show you something about hockey.”
Barry, of course, is talking about me. He shows all seven goals scored while I was on the ice. He shows the tape, stops, and says, "Jonesy had his man on every goal.
I was in the right position for every goal and I was a minus 7.
Warning: Arguing the NHL CBA with me could be hazardous to your mental health. Proceed at your own risk.
by DragonGirl0583 on Jan 28, 2012 10:51 AM EST reply actions 2 recs

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