by Danny Tuccitto

Welcome back for the sixth and final installment of our anniversary series on individual DYAR and DVOA records since 1991. If you need to get up to speed or would just like to reminisce, here are the links to the previous installments:

Over the course of the series, I've made several observations, both explicitly and implicitly, about the difficulties inherent in football analytics. In "Best Running Backs," I made a purely statistical case for Priest Holmes' Hall of Fame candidacy knowing full well that statistics aren't everything (as many commenters astutely pointed out). In "Best and Worst Wide Receivers," I cited the problem of separating a wideout's value from that of his quarterback and fellow pass catchers. The real issue underlying both of these is one of process versus outcome. Even knowing the strengths and weaknesses of the methods used to come up with a number, we're still often guilty of focusing too heavily on the number itself.

Back when Doug Drinen created Pro Football Reference's approximate value (AV) statistic, he spent several thousand words detailing the methods behind it. Buried in those words, and apparently forgotten over the past five years by those of us who care about process, is a preliminary, admittedly arbitrary, yet nevertheless elegant attempt to assign an average proportion of passing, running, receiving, and blocking for each offensive position.

For tight ends, Drinen allotted 30 percent of their value to blocking, while setting the other stat-driven positions to zero. Admittedly, the impact of a running back's (or wide receiver's) blocking ability on his total value as a player is higher than zero percent -- Goddammit Donald! -- but even if we gave them non-zero blocking value, I think we would still all agree that the proportion for tight ends would remain significantly higher than the other positions. For our purposes today, the specifics aren't nearly as important as the fact that (a) tight ends have much more of their individual value wrapped up in blocking, and (b) blocking isn't in the play-by-play, which is what forms the basis of DYAR and DVOA. Like Walter Johnson said, "You can't hit what you can't see."

I've chosen to wax philosophical here for two reasons. First, it will become apparent very quickly that the extent to which a tight end's responsibilities diverge from that 70-30 split ends up making a huge difference in his DVOA and DYAR. Second, the rankings are so dominated by a handful of predictable tight ends that I could stop the column right now and go straight to a red light challenge in the comments section.

Instead, here are the best and worst receiving DVOA seasons by a tight end since 1991:

Best Receiving DVOA, Season, 1991-2012

(min. 25 targets) Year Player Team Tgts Recs Yards TD DVOA 2010 Antonio Gates SD 65 50 782 10 76.3% 1999 Rickey Dudley OAK 59 39 555 9 62.3% 2008 Martellus Bennett DAL 27 20 283 4 56.3% 1998 Tony McGee CIN 32 22 363 1 54.0% 2010 Jermichael Finley GB 26 21 301 1 51.8% 2010 Rob Gronkowski NE 59 42 546 10 51.7% 2008 Visanthe Shiancoe MIN 59 42 596 7 51.4% 2003 Matt Schobel CIN 30 24 332 2 50.2% 1997 Troy Drayton MIA 50 39 558 4 50.1% 1995 Ken Dilger IND 55 42 635 4 48.3% Worst Receiving DVOA, Season, 1991-2012

(min. 25 targets) Year Player Team Tgts Recs Yards TD DVOA 1998 Howard Cross NYG 29 13 90 0 -78.2% 2010 Daniel Graham DEN 37 18 153 0 -63.4% 1996 Keith Cash KC 33 14 90 0 -62.4% 1992 Ron Heller SEA 29 12 85 0 -58.5% 2009 Daniel Coats CIN 30 16 150 0 -54.7% 1994 Ron Hall DET 25 10 106 0 -54.1% 2004 Tony Stewart CIN 25 10 48 1 -53.2% 2000 Marco Battaglia CIN 36 13 105 0 -53.1% 1992 Mark Boyer NYJ 33 19 149 0 -48.9% 2003 Brian Kozlowski ATL 27 10 87 0 -48.6%

Yes, Antonio Gates was ridiculous in 2010, but no one would mistake him for a great blocker. That's not a slight; it is what it is. Rickey Dudley was a "below average blocker." Tony McGee was "not the best blocker" and only was a blocker because the Bengals often needed him to be a blocker. Jermichael Finley was a poor run blocker prior to this month. Visanthe Shiancoe is "one of the worst run-blocking tight ends in the league." Matt Schobel had the dreaded tag of "finesse blocker." Troy Drayton was a converted wide receiver.

Meanwhile, Howard Cross was "probably the best of all tight ends in the league at blocking." Daniel Graham was "one of the best pass-blocking tight ends in the NFL" in 2010. I could go on.

By my count, outside of total packages like Rob Gronkowski, Martellus Bennett, and Ken Dilger, two of whom -- spoiler alert! -- rank among the best 22 tight ends since 1991, these lists are loosely based on Stealers Wheel lyrics: Receivers to the left of us, blockers to the right.

I wonder if this changes when we switch from DVOA to DYAR. The relevant table is displayed below:

Best Receiving DYAR, Season, 1991-2012

(min. 25 targets) Year Player Team Tgts Recs Yards TD DYAR 2011 Rob Gronkowski NE 125 91 1,329 18 459 1993 Shannon Sharpe DEN 110 81 995 9 358 2010 Antonio Gates SD 65 50 782 10 358 2000 Tony Gonzalez KC 150 93 1,203 9 357 2009 Antonio Gates SD 114 79 1,157 8 336 2004 Tony Gonzalez KC 148 102 1,258 7 335 2004 Antonio Gates SD 114 81 964 13 309 1996 Shannon Sharpe DEN 117 80 1,062 10 303 2012 Tony Gonzalez ATL 124 93 930 8 286 2012 Rob Gronkowski NE 80 55 790 11 279 Worst Receiving DYAR, Season, 1991-2012

(min. 25 targets) Year Player Team Tgts Recs Yards TD DYAR 2011 Marcedes Lewis JAC 85 39 460 0 -162 1998 Freddie Jones SD 111 57 602 3 -158 2010 Daniel Graham DEN 37 18 153 0 -139 2004 Boo Williams NO 75 33 362 2 -139 1997 Jamie Asher WAS 99 49 474 1 -132 1996 Keith Cash KC 33 14 90 0 -125 2004 Stephen Alexander DET 76 41 377 1 -124 1998 Howard Cross NYG 29 13 90 0 -124 2012 Brandon Pettigrew DET 102 59 570 3 -123 2007 Bo Scaife TEN 78 46 421 1 -120

Why yes, yes it does, but the reason is obvious: DYAR depends on volume, so the best blockers (i.e., the worst receivers) will tend to get fewer targets. It takes a legendarily awful performance over a small sample of targets for a blocking tight end to produce an all-time awful DYAR. Hence, only Graham and Cross show up on the list of worsts.

Otherwise, it's a who's who of tight ends that you will recognize from fantasy football waiver wires of years gone by -- and Brandon Pettigrew (and Freddie Jones, but more on him later). Pettigrew's 2012 season in Detroit was the tight end version of Chris Chambers' 2006 season in Miami. The only way a player that inefficient gets that many targets in the pass offense is if (a) he's coming off a big year, and (b) his team is basically forced to keep throwing him the ball due to a dearth of competent pass catchers. Obviously, Detroit had Calvin Johnson last season (and, thankfully for Lions fans, still have him), but when a quarterback shatters the record for most pass attempts in a single season, Megatron can't be the only one on the receiving end. (Of course, it also doesn't help when your No. 2 receiver turns into "The Lifeguard" midway through the season.)

That said, it's tough to absolve Pettigrew of much blame for last year. Although his 58 percent catch rate (10th-lowest among qualifying tight ends) was actually higher than the 49 percent posted by teammate Tony Scheffler's (second-lowest), Pettigrew's average target was 6.3 yards downfield (sixth-lowest), while Scheffler led all qualifying tight ends with an average target 12.5 yards downfield. Catching that few passes on that many short targets translates to a receiving plus-minus of -8.1, which was the worst at his position. What's more, as mentioned in Football Outsiders Almanac 2013, Pettigrew has dropped more passes over the past three seasons than any other tight end. In other words, the best explanation for Pettigrew's appearance on this list is that he was treating a ton of Matthew Stafford passes as if each one was the "Deadliest Catch."

Now, if we've learned anything thus far in this series, I hope it's that the good players can have horrible games. Do you think that trend applies to tight ends? Well, here are the 10 best and worst games since 1991 (box scores linked in the "Week column; asterisk means the team won):

Best Receiving DYAR, Game, 1991-2012 Year Week Player Team Tgts Recs Yards TD DYAR 2010 4* Antonio Gates SD 7 7 144 2 85 1996 6* Shannon Sharpe DEN 13 13 153 3 84 2008 16 Visanthe Shiancoe MIN 7 7 136 2 77 1995 12 Pete Mitchell JAC 11 10 161 1 75 1993 5 Johnny Mitchell NYJ 8 7 146 3 74 2011 16* Jared Cook TEN 8 8 169 1 74 2004 10 Jason Witten DAL 11 9 133 2 72 2009 12* Antonio Gates SD 7 7 118 2 70 2002 4* Tony Gonzalez KC 10 6 140 3 68 1991 12* Ethan Horton LARD 7 7 123 1 68 Worst Receiving DYAR, Game, 1991-2012 Year Week Player Team Tgts Recs Yards TD DYAR 2006 8* Jeremy Shockey NYG 10 3 15 0 -53 2007 11* Dallas Clark IND 10 3 15 0 -51 2008 3 Kellen Winslow CLE 13 2 14 0 -49 2005 14 Kyle Brady JAC 5 5 43 0 -48 2005 9 Todd Heap BAL 8 4 28 0 -48 2006 16 Jeremy Shockey NYG 7 2 -3 0 -46 2007 13 L.J. Smith PHI 9 3 21 0 -46 2011 8 Jason Witten DAL 12 4 28 0 -46 1993 15 Charles Arbuckle IND 10 8 36 0 -45 2004 1 Boo Williams NO 7 3 13 0 -45

Why yes, yes it does. Exactly half of the bottom 10 tight end receiving DYARs in a game came from players who you will see in our table of best careers, probably the least shocking of which is Jeremy Shockey. Here's the thing about his pair of all-time bad performances in 2006: He actually finished the year above replacement. In the two games featured in the table, he had -99 receiving DYAR; in the other 13 games that year he amassed 121 DYAR. Why? Well, aside from the fact that Shockey had already proven himself to have multiple personalities as a rookie in 2002 playoffs, Eli Manning and offensive coordinator John Hufnagel gave him 98 other opportunities to redeem himself. And unlike, Chambers and Pettigrew, he did. (In case you're wondering why Shockey beat out Dallas Clark despite an identical stat line, it's mainly because Clark's game came against the 14th-ranked Chiefs defense, while Shockey's came against 21st-ranked Buccaneers.)

The list of bests is mostly what we've seen so far: a handful of great tight ends figuring prominently. So, let's take a trip to Whoville and admire Ethan Horton. In 1991, Horton had 57 catches for 650 yards and five touchdowns, which means that he averaged 3.3 catches for 35.1 yards and 0.3 touchdowns in his other 15 games. In 1991, Horton had 133 DYAR; I'll leave the absurd math to you on this one. In 1991, Horton made the Pro Bowl.

How did that happen? Well, it's because 1991 was arguably the worst year for tight ends in our database. Horton's DYAR ranked third; in 2012, it would have ranked sixth. DYAR's most valuable tight end in 1991 was Eric Green, with 170. Only four of the past 22 seasons have seen the No. 1 tight end fail to eclipse 200 DYAR, and Green's was the lowest DYAR of them all. But if you really want a crystallization of how irrelevant the tight end position was back then, here are PFR's yardage rankings for tight ends in 1991. Pro Bowlers Horton, Marv Cook, Jay Novacek, and Steve Jordan ranked second through fifth -- behind Oilers slot receiver Ernest Givins. (Rivers McCown would vehemently disapprove if that was [redacted].)

Next up, the worst career receiving DYARs according to a simple sum, a weighted sum, and an average of the player's six best seasons (asterisk means the tight end is still active):

Worst Receiving DYAR, Career

(Debuted 1991 or Later) Player Years DYAR Freddie Jones 8 -270 Robert Royal 8 -247 Marco Battaglia 7 -242 Greg DeLong 6 -197 Terry Hardy 4 -188 Bo Scaife 6 -170 Mark Bruener 13 -167 Stepehen Alexander 9 -156 Stephen Spach 5 -148 Kerry Cash 6 -142 Player Years DYAR Brandon Pettigrew 4* -138 Justin Peelle 10 -136 Patrick Hape 7 -130 Lonnie Johnson 6 -128 Jeff King 7* -125 Walter Rasby 9 -124 Ben Troupe 4 -117 Delanie Walker 7* -116 Casey Fitzsimmons 7 -111 Daniel Coats 4 -110 Alex Smith 8* -109 Rob Housler 2* -107 Worst Receiving DYAR, Weighted Career

(Debuted 1991 or Later) Player Years DYAR Marco Battaglia 7 -184 Robert Royal 8 -172 Terry Hardy 4 -167 Greg DeLong 6 -153 Freddie Jones 8 -152 Stephen Spach 5 -128 Bo Scaife 6 -127 Brandon Pettigrew 4* -114 Kerry Cash 6 -110 Rob Housler 2* -104 Player Years DYAR Ben Troupe 4 -101 Patrick Hape 7 -100 Henry Lusk 2 -96 Daniel Coats 4 -92 Paul Green 4 -89 Lonnie Johnson 6 -87 Shad Meier 5 -85 John Owens 5 -85 Joey Haynos 2 -82 Boo Williams 4 -81 Shawn Nelson 2 -77 Michael Roan 6 -76 Worst Receiving DYAR, Six-Year Average

(Debuted 1991 or Later) Player Years DYAR Greg DeLong 6 -33 Terry Hardy 4 -31 Bo Scaife 6 -28 Stephen Spach 5 -25 Kerry Cash 6 -24 Brandon Pettigrew 4* -23 Marco Battaglia 6 -23 Lonnie Johnson 6 -21 Ben Troupe 4 -20 Daniel Coats 4 -18 Player Years DYAR Rob Housler 2* -18 Boo Williams 4 -18 Shad Meier 5 -18 Paul Green 4 -18 John Owens 5 -17 Henry Lusk 2 -17 Aaron Shea 6 -16 Michael Roan 6 -16 Patrick Hape 6 -15 Shannon Mitchell 4 -14 Joey Haynos 2 -14 Alonzo Mayes 3 -14

Mostly, it's the blocking tight end All-Stars, folks. That's the only way players like Mark Bruener and Justin Peelle show up here despite career lengths in the double digits. Bruener registered one horrible year of receiving DYAR in 1999 (-100), but it came on only 35 targets. The other 12 years involved minor fluctuations between his second-worst DYAR (-41 in 1998) and his best DYAR (37 in 2000). The same goes for Peelle. If not for his one bad year with the 2005 Chargers (-71 receiving DYAR in 20 targets), he wouldn't be anywhere near this list. It's safe to say both Bruener and Peelle remained on NFL rosters as long as they did because teams coveted their blocking ability, so it's kind of awkward to discuss their value only in terms of receiving. Such is the life of a blocking tight end; such is the state of limitations in play-by-play analysis.

On the flip side, the fact that there are so few receiving tight ends on these lists makes the ones who do appear look really bad. Freddie Jones deserves every bit of his No. 1 ranking according to aggregate DYAR. Since 1991, 19 different tight ends have had a season worse than -100 receiving DYAR. Jones is the only one to have accomplished that "feat" twice: -158 DYAR in 1998 and -108 DYAR in 2002. And yet, because he played on a couple of awful teams (turn-of-the-millenium Chargers and Cardinals), he too owes his standing in the table to a case of Brandon Pettigrew syndrome (nee Chris Chambers syndrome). Jones' 702 targets is by far the highest of any tight end above; only Stephen Alexander (429) and the aforementioned Pettigrew (393) broke 300.

Finally, below are the best career receiving DYARs according to a simple sum, a weighted sum, and an average of the back's six best seasons (asterisk means the tight end is still active):

Best Receiving DYAR, Career

(Debuted 1991 or Later) Player Years DYAR Tony Gonzalez 16* 3,096 Antonio Gates 10* 2,275 Jason Witten 10* 1,727 Rob Gronkowski 3* 981 Heath Miller 8* 889 Todd Heap 12 740 Marcus Pollard 12 717 Ben Coates 10 703 Owen Daniels 7* 678 Tony McGee 11 655 Player Years DYAR Jeremy Shockey 10 603 Ken Dilger 10 594 Dallas Clark 10* 589 Frank Wycheck 11 541 Troy Drayton 8 511 Jermichael Finley 5* 504 Mark Chmura 7 461 Alge Crumpler 10 442 Jimmy Graham 3* 441 Jay Riemersma 8 422 Pete Mitchell 8 419 Tony Scheffler 7* 376 Best Receiving DYAR, Weighted Career

(Debuted 1991 or Later) Player Years DYAR Tony Gonzalez 16* 2,313 Antonio Gates 10* 1,898 Jason Witten 10* 1,418 Rob Gronkowski 3* 943 Heath Miller 8* 778 Ben Coates 10 689 Marcus Pollard 12 650 Todd Heap 12 643 Owen Daniels 7* 607 Ken Dilger 10 579 Player Years DYAR Dallas Clark 10* 579 Tony McGee 11 577 Frank Wycheck 11 527 Jeremy Shockey 10 518 Jermichael Finley 5* 475 Troy Drayton 8 461 Mark Chmura 7 441 Jimmy Graham 3* 426 Alge Crumpler 10 418 Jay Riemersma 8 401 Rickey Dudley 9 397 Pete Mitchell 8 382 Best Receiving DYAR, Six-Year Average

(Debuted 1991 or Later) Player Years DYAR Antonio Gates 6* 295 Tony Gonzalez 6* 291 Jason Witten 6* 212 Rob Gronkowski 3* 163 Heath Miller 6* 135 Ben Coates 6 135 Ken Dilger 6 115 Dallas Clark 6* 113 Marcus Pollard 6 110 Owen Daniels 6* 109 Player Years DYAR Todd Heap 6 108 Frank Wycheck 6 106 Tony McGee 6 101 Jermichael Finley 5* 84 Jeremy Shockey 6 83 Rickey Dudley 6 82 Jay Riemersma 6 80 Mark Chmura 6 78 Troy Drayton 6 77 Alge Crumpler 6 75 Benjamin Watson 6* 74 Jimmy Graham 3* 73

As I'm sure everyone expected, Tony Gonzalez pretty much blows away the field here. Since we're talking a lot about methods today, I'll use Gonzalez as an example of how the peak versus longevity argument goes off the rails sometimes. As I said in "Best Running Backs," hardly anyone cites a player's peak if he had a long career. As you can see in the table, the more we slide over to the peak side of the continuum, the less dominant Gonzalez appears, to the point where he drops out of the top spot according to the average of his best six seasons. Here's the thing: His 16th season (i.e., 2012) was the third-best season of his career according to receiving DYAR. Research shows that tight ends decline after age 29. Since he turned 30 in 2006, Gonzalez has made six Pro Bowls and two All-Pro first teams. In that time, he's amassed 1,316 receiving DYAR. Stated differently, if Gonzalez' career began when the average tight end declines, he would still own the third-best career since 1991.

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Back in May, Chase Stuart asked, "Can Jason Witten catch Jerry Rice's career receptions record?" The answer was "probably not, but he's a lot closer than you think." Can he catch Gonzalez in aggregate receiving DYAR? I think our answer is the same. Witten just completed his age-30 season, in which he amassed 192 DYAR, and he currently stands 1,369 DYAR behind Gonzalez. Conveniently, I just told you that Gonzalez had 1,316 DYAR after age 29. A quick back-of-the-envelope calculation tells us that, in order to catch Gonzalez, Witten would basically have to be the second coming of Gonzalez. Given his injury history, I don't think that's likely. (And in case you're wondering, Shannon Sharpe checks in at 2,075 DYAR with only one season prior to 1991. We'll be introducing DVOA ratings for 1990 next week, but I can tell you that Sharpe had a mere 5 receiving DYAR as a rookie, so his career will rank no better than third in perpetuity.)

To close out this series, I'll offer an anecdote that hopefully helps tie all of these anniversary columns together. Like many of you, my earliest memories of working with football stats came in the context of finding an advantage in fantasy football. When I went off to college, and ultimately graduate school, the field of football analytics didn't exist, and so my area of study was Sport Psychology, something fascinating to this boyhood fan of Joe Montana. In 2004, I discovered a little site called Football Outsiders, and, as an aspiring academic, I eventually found the Journal of Quantitative Analysis in Sports. The very first issue of said journal had an article entitled "Football's Hilbert Problems" and authored by Aaron Schatz, the guy running that little site I discovered the year before. The moment I read it, I was hooked, and so began a personal journey away from Sports Psychology towards football analytics: "You can get this kind of stuff published in an academic journal? People take this stuff seriously?" Without Aaron blazing a trail 10 years ago, I wouldn't be here, and I don't think the field would be as popular as it is today. For that, I think we all owe him a debt of gratitude.

As far as the meat of "Football's Hilbert Problems" goes, it's behind a pay wall, but the basic premise was to list the 10 most-vexing problems confronting those who analyze football statistics:

Standardization of football statistics and more intricate play-by-play

Opportunities on defense

Blocking

Park/Weather effects

Player comparisons

Strategy

Roster composition

Free agency

Draft and player development

College and pro football

Looking back years later, it's amazing to see how far we've come. Certain official scorers in certain stadiums are still nuts, but play-by-play is standardized for the most part, and we now have things like snap counts that have been added. Game charting projects, here and elsewhere, have gone a long way towards having at least something in the way of non-standard defensive stats. We've found that a deep roster is better than one with stars and scrubs. Analytics departments around the league have developed sophisticated ways to valuate free agents, and it's practically conventional wisdom that free agency is a real-world example of the winner's curse. Park and weather effects have been accounted for. Draft pick values are a dead horse at this point. FO's various rookie projection models have helped translate college stats to the NFL.

The only Hilbert problems that haven't progressed that far are blocking, player comparisons, and strategy. It's possible to measure blocking (we do), but error abounds when you don't know the blocking assignments. Also, there's the point I've belabored today: Whether or not you can measure it in a reliable way, how much of a tight end's value is wrapped up in his blocking ability? Doug Drinen guessed 30 percent, but establishing a more concrete proportion has been something largely ignored in the football analytics community. Similarly, game charting projects and the NFL's release of All-22 video has illuminated data about in-game strategies and tactics, but it's been used primarily as a way to describe the past (i.e., Team X lined up in 11 personnel 48 percent of the time last year) rather than to predict the future or research how specific strategies relate to winning statistically; and without being privy to the minutes of coaches meetings, it will be difficult to take that leap.

Finally, there's the inability to compare players independent of their teammates, which was the problem I highlighted in "Best and Worst Wide Receivers." To wit, Aaron wrote the following eight years ago (DPAR is the ancestor of DYAR):

DPAR cannot be used to compare players across positions, however, because it gives full value for passing plays to both quarterback and receiver, and does not adjust based on the quality of surrounding players on each team. As discussed above, much of the data needed to fully correct for the imperfections of DPAR does not currently exist.

It still doesn't exist. As FO enters its second decade, major progress on nine of the 10 Hilbert problems that Aaron delineated at the beginning of its first decade is not shabby at all. As loyal readers, you've been here to watch the process unfold. We hope you stick around for the day when that most intractable of Hilbert problems gets solved. Does 2023 work for you?