

Well, no. Not really. Because Barber and Shockey weren't that great to begin with.
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This meme has the same funadamental flaw as many barstool sportsman arguments, which is that it incorrectly conflates correllation (i.e., the loss of Barber and Shockey coming at roughly the same time as the Giants Super Bowl run) with causation (i.e., the loss of those two players is the reason why the Super Bowl run has happened). This is large in part because the media has underestimated the relative effectiveness of Barber and Shockey versus their replacements. Here are the invaluable Football Outsiders DVOA rushing ratings for Barber and his replacement:
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8.0% (21st in the league)
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'07 Brandon Jacobs:
16.3% (14th in the league)
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Briefly, DVOA measures the per-play effect of a player on his team's chances to succeed. By that measure, Brandon Jacobs was nearly twice as valuable this year as Barber was last year. So the simplest explanation here is not that Barber's personality was hurting the team; it's that his play wasn't doing as much to help the team as Jacobs's does. What about Shockey, you ask? Let's look at the DVOA receiving ratings:
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1.8% (25th in the league)
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'07 Kevin Boss:
50.9 % (not enough playing time to qualify for rankings)
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Let's acknowlege up front that this comparison is slightly unfair--Kevin Boss's rankings are grossly inflated by his TD catch against New England in week 17, and it's tough to imagine that he could keep that pace up for a full season. That said, Shockey's numbers are mediocre enough that it's likely not a tough a job to improve on him. These numbers also don't take into account blocking, where my admittedly amateur eye thinks Boss has an additional advantage. So again, it's not that Shockey's attitude sucks; it's that his play sucks.
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For further proof of the relative importance of talent versus character, by the way, look no further than the Patriots, who have assembled recent teams around noted malcontents such as Corey Dillon and Randy Moss, and come through the experience looking pretty darn good indeed.
So the writers of the world don't need to try to peer into the walnut-sized brains of our nation's sporting elite to try to explain away the absences of Barber and Shockey. All that's needed is an accurate valuation of of their relative worth and an understanding of the bedrock principle that teams with good players are better than teams with bad players. For all of the above, give this meme a 7.5 on the hype scale.