### Did Adrian Peterson really Outgain Eric Dickerson?

A couple years ago, I wrote about how rounding errors affect yardage gains in football.  The general rule was that, assuming the rounding error on each play is independent, the total rounding error follows a normal distribution with parameters mean = 0 and SD = sqrt(number of plays/12).

I began thinking about this again for two reasons.  One, Adrian Peterson just came within 9 yards of Eric Dickerson's season rushing record.  With 348 rushes for Peterson and 379 for Dickerson, that comes out to a standard deviation for the combined rounding errors of 7.8 yards, and about a 12% chance that the 9 yard difference is entirely due to rounding errors.

The other reason is that Brian Burke pointed out in the comments of the original article that the rounding errors of plays in the NFL are not independent.  The total yardage gain for each drive has to round off to the correct figure.  From Brian's comment:

"One other way to state this is that if a team has 2 plays in a row, and one goes for 4.5 yards but is scored as 4, and the next goes for 5.5 yds, it can't be scored as 5. It must be scored as a 6 yd gain because the ball is very clearly 10 yds further down field, not 9."

I wanted to try to account for this constraint and see how much difference it would make.

Note: the following is mostly dry and math-related, so if you want to skip it, I estimate the chance of rounding errors covering the 9 yard difference between Dickerson and Peterson at about 14%.

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### THE EMPTY SET: Reflecting on Cooperstown’s Lost Year

A sea of people stretched across the field and masked the green grass with Cardinal red.  There was Bob Feller mingling across the fence beside the stage.  There was Frank Robinson.  There was Stan Musial.  Somewhere, on our side of the fence, was Tug McGraw.

We were all there for Ozzie.  There were a few scattered Phillie fans there for Harry Kalas, that year’s Frick Award recipient, if you looked carefully for the different insignias on their caps.  Every here and there you'd see a maroon Mike Schmidt throwback.  Other than that, it was just thousands of red-clad fans fixated on the wizard of a shortstop standing at the podium before us.

"This is awesome."  It was the first my dad, uncle, brother, and I had seen of Induction Weekend.  "We've got to come back in five years."

Five years is, of course, the waiting period for retired players before they become eligible for the Hall of Fame.  Three of my generation's great players had just retired.  And one was another beloved Cardinal.

**********

The BBWAA announced the results of their Hall of Fame balloting last Wednesday.  No one got in.  Barry Bonds didn't get in.  Roger Clemens didn't get in.  Not Biggio, not Bagwell.  Not Jack Morris.  Not Piazza, Trammell, Raines, Schilling, Martinez, Walker (either one), or Lofton.  Not McGwire or Sosa or Palmeiro.  Not even Shawn Green.

Someone will get in.  In 1996, the last year no one met the 75% threshold, there were six players on the ballot (Niekro, Perez, Sutton, Santo, Rice, and Sutter) who would get in eventually.  That's how it always is; every ballot has several candidates who will get in someday.

Biggio will get in.  Every player who has ever gotten Biggio's level of support early in his candidacy has had no trouble getting elected sooner rather than later.  Bagwell is at that high early level of support where almost everyone gets in eventually.  Piazza even more so.

Jack Morris will probably get in as a Veterans Committee selection someday.  Schilling will probably get in someday.  Eventually, as the electorate gets a bit younger, Tim Raines will probably find the remaining votes he needs to get in, barring a complete disaster with the current and upcoming logjam that might never clear up before he falls off the ballot.

Maybe they won't all get in.  But some of them will, and maybe some of the others as well.  Trammell is the type of guy who could finally get his due when the Hall puts together a VC for his era.  Edgar Martinez could pick up some support as the voters begin to accept that the DH is now part of the game.  The voters, or the Hall, might someday come around on Bonds and Clemens.

Someone is going to get in.  Definitely Biggio.  Very likely Jack Morris.  They're just going to have to wait.  So too will Cooperstown, which swells up with tens of thousands of tourists (and their wallets) every July except this one.

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