I'm stunned, absolutely stunned (your sarcasm meter should start going off about now) by the double standard that exists with complaining about coaching decisions. All last week, I heard about how a decision is judged on what happens thereafter. Well, by that standard, I saw plenty of decisions that were bad enough to merit complaint, but not a single talking head is yelping about it. Okay, so those were not in prominent prime time games. Well, then Gary Kubiak, with one timeout in hand, in position for a deep field goal from the thirty yard line with a kicker who had already missed from the same distance and had missed a last second attempt to tie the week before, uses that timeout by instructing his quarterback to take the snap and fall to the center of the field behind the line of scrimmage. Kris Brown, even with that excellent centering job, missed the kick badly. I mean, if ever there was a bone-headed decision that also lead to a bad result, this was it, in front of the whole Monday night football watching universe.

Two days later, and I'm still waiting for the firestorm.

Gary Kubiak even said (not that he would say anything differently) that he would do the same thing again:

I wouldn’t do that any different. I mean, we had a goal: We had to get our football team in field goal position and with eight seconds left, having Kris (Brown) right there at a 48, 49-yard field goal, I’m not going to take a chance of a penalty, a sack, or a turnover that would take you out of having any chance to play any more football. So, I’d do that the same way.

Ahhh, so that's it. See, I was under the mistaken assumption that the goal was to win the game. I guess it's to get in field goal position. Mission accomplished, if that's your goal. If the goal was to give the team the best chance to win the game, though, not so much.
(Continued)

On Monday, I posited a way to predict future NFL team performance while ignoring things like points scored, points allowed and win-loss record. Instead, I argued that we should break each team into four parts: passing efficiency, rushing efficiency, defensive passing efficiency and defensive rushing efficiency.

Passing efficiency is defined as simply net passing yards per attempt ((passing yards minus sack yards lost), divided by (pass attempts plus sacks)). Rushing efficiency is just yards per carry; the defensive statistics follow the same method. After comparing each team to the league average in each of the four categories, we can see how many yards per attempt better than average each team is. We add up the four yards per attempt measures relative to league average to come up with a total score, multiply by five, and viola! Team ratings!

Does this sound kooky? Sure. But my research indicates that it may be more accurate than common perception. Let's see what the numbers say through ten weeks. For both offensive and defensive ratings, positive numbers are good and negative numbers are bad. In addition to the four categories (passing offense, rushing offensive, passing defense, rushing defense), I've included total offense and total defense grades, for you to sort as you desire.
(Continued)

Last week, a high level cat fight broke out over Malcolm Gladwell's book "What The Dog Saw" when Dr. Steven Pinker wrote a critique in the NY Times. That critique included a reference to one essay in the book, which originally ran last December in the New Yorker, entitled "Most Likely to Succeed: how do we hire when we don't know who's right for the job?" In that essay, Gladwell states, in reference to what he calls the quarterback problem, that "[t]here are certain jobs where almost nothing you can learn about candidates before they start predicts how they’ll do once they’re hired." Pinker responded that "[i]t is simply not true that a quarterback’s rank in the draft is uncorrelated with his success in the pros."

Gladwell fought back on his blog. His responses were primarily attacks upon the individuals later cited by Pinker to support the position that draft position does matter, contrary to what Gladwell claimed, with minor reference that the critiques failed to appreciate the difference between aggregate performance and per play performance. He closed with:

I have enormous respect for Professor Pinker, and his description of me as “minor genius” made even my mother blush. But maybe on the question of subjects like quarterbacks, we should agree that our differences owe less to what can be found in the scientific literature than they do to what can be found on Google.

This, of course, piqued my interest. I admit to having heard reference to Gladwell's essay that originally ran last December, but had not paid it much attention. When I see defenses that are primarily based on attacks of the person, and what I see as an initially questionable assumption (per play statistics are all important; aggregates do not matter), well, I feel compelled to dig further. I happen to believe that the merits of an argument rise and fall on the quality of the facts and analysis, and not on who made it. This is true whether the arguments are presented in a scientific journal or on a blog. Oh, and I wanted to add something that could be found with a Google search.
(Continued)

I don't advocate gambling on football games, and neither does the P-F-R blog. Point-spread data are very useful as historical guides to understanding the perception at any point in time and to measure how the public may improperly value certain teams. The past is never a perfect prediction of the future, and the results of this post are intended for educational purposes, only.

About a year ago I wrote a preliminary post on how to grade the best defenses in NFL history. I focused on four categories to rank defenses, as I didn't think there was one best stat to use. Today I'm going to use four "basic" categories to grade each team; rushing yards per carry, net yards per pass attempt, rushing yards per carry allowed, and net yards per pass attempt allowed.

I'm ignoring things like touchdowns, fumbles and interceptions. Why? Interception rates are essentially random, and fumble recovery rates are too. Touchdowns are slightly more predictable, but they don't correlate with future success as well as yards do. Therefore, instead of assigning some arbitrary value to touchdowns scored, I chose to leave them out. I could probably improve the formula by assigning a small weight for touchdowns (and maybe an even smaller weight to turnovers), but I'm trying to use some "basic" stats. On the other hand, I'm leaving in sack and sack yardage data, based on the work done by Jason to show that such numbers are predictable.
(Continued)

Internet message boards, twitter feeds and sports media are blowing up over Bill Belichick's decision to go for it on 4th and 2 from his own 28-yard line, up by six points, with 2:08 remaining. First, a quick review of the play.

The Pats came out with three WRs to Brady's left, with Wes Welker the nearest receiver to Brady on that side of the field. On Brady's right was Randy Moss isolated out wide, with Kevin Faulk in the backfield. Indy came out looking like they were going to blitz six -- they had the four WRs in tight, man-coverage, and safety Melvin Bullitt about fifteen yards deep to Brady's right. Brady then sent #33, Kevin Faulk, to go line up as the inside WR on the right side, and #33 (Bullitt) for the Colts came in to line up against him. Indy was now going to rush six against NE's five, while NE knew all five of their WRs were in single coverage. Brady recognized that he was going to have to make a quick and accurate pass.

It turns out that Faulk was the primary read all along, as he took twp steps, did a quick fake left, and then curled right just a yard or so past the first-down marker. Since the drive started after a touchback, the Pats needed to get to exactly the 30-yard line for the first down. The ball hit Faulk's hands but he bobbled the ball; Bullitt pushed Faulk backwards, and by the time he landed with possession of the ball, he was on New England's side of the 30-yard line.
(Continued)

A few weeks ago, I threw out this crazy idea about how to isolate a team's peak performance by SRS:

"Obviously, we can't run the SRS on single-game samples, because it requires multiple opponents to 'work'. But what if we broke each team-season down into 15 to 19 'mini-teams' based on 2-game stretches of the season? Like, the Patriots' win over the Jets in Week 1 of the 2007 season would be part of the 'New England Games 1-2' team, and so would their win against the Chargers the next week. And that Chargers team would be part of the 'San Diego Games 2-3' team, who played 'Green Bay Games 3-4' the next week, who played 'Minnesota Games 4-5' the week after that... and so on and so forth. Now, every 'team' connects to every other team, just like in the regular SRS, but we've also isolated team performance down to the most specific time period possible using the SRS method."

As a follow-up, I calculated the best and worst 2-game stretches by teams this decade (2009 isn't included because not all teams have played the same # of games yet). Remember, the SRS is focused on measuring a team's point differential vs. the point differential you'd expect an average team to have based on the game's location and the strength of the opponent; this method takes it even further and is only concerned with the strength of the opponent at the time of the game, meaning wins against teams with mediocre records can still be positive for a team's SOS if they play them either before or after a strong performance. I think there's definitely some logic to this, because (as Chase pointed out in the post that inspired this series) every game features a different version of the same team; sometimes the differences are so small as to be imperceptible, but sometimes they're huge (think the '07 Giants early in the season vs. late), so it really does matter when you catch a particular opponent.

(Continued)

This is the third installment in a series of posts looking at similar historical teams through six games. The first installment looked at teams with at least 3 wins among those who did not have a bye in the first six weeks. The second post looked at the teams with losing record who played six games through the first six weeks. This one finishes up with the twelve teams who played their sixth game last weekend.

I don't know that this is rocket science, but when a team gets off to a 6-0 start and sets a record for most points scored in the first six games of a season, they are going to compare favorably to some other really good teams that continued to be good. The Saints have the highest expected win total of any of the 32 teams in this study. The Cowboys have a large number of teams that went on huge winning streaks over the second half of the season in their group.

Overall, my playoff odds calculation turned out to be pretty reasonable. The sum of the odds for AFC teams equaled exactly 6.00 teams making the playoffs. The sum of the odds in the NFC teams was slightly high (6.20), but this is explained by so many bad teams playing their seventh game last week, so the "through six games" record is slightly over .500. Also, I'm not taking into account that the NFC has several teams logjammed at 4-2 right now, so it's going to take slightly more wins than average to make the NFC Playoffs. So feel free to tick off a percent or two for the NFC teams and their playoff odds.

Teams are listed in descending order of playoff chances.
(Continued)

Bear with me while I throw two crazy SRS variations out there at you...

First: In the wake of Super Bowl XLII (while I was still weeping, if I recall correctly), Chase wrote this super-philosophical post about there not being a greatest team ever -- that the '07 Patriots might have been the GOAT early in the season when they were blowing the doors off of everybody, but by the time the Giants faced them in SBXLII, that team no longer resembled the team that was being billed as the most dominant ever a few months before. Likewise, the Giants were playing really well by the time January and February rolled around, and were far superior to the sorta mediocre version that trotted out on the field early in the season. So according to Chase's logic, it wasn't like you could really pinpoint "The 2007 Patriots" or "The 2007 Giants", because those two teams didn't actually exist.

(Continued)

Three weeks ago, I asked the question "what quarterback rate stats stay most consistent when a quarterback changes teams?" Today I'm going to follow up with what happens when the opposite occurs, and a team changes quarterbacks (through ineffectiveness, injury, or because the team "needs a change" because the defense is giving up 30 points a game). I pulled all teams that had two quarterbacks each throw 200 or more passes, since the merger, and just like last time, used the advanced passing rating in each of five categories (completion percentage, yards per attempt, touchdown percentage, interception percentage, and sack percentage) to compare. There are 73 pairs of quarterbacks who qualify, ranging from notable names like DeBerg and Montana for the 1980 San Fransisco 49ers, to notorious names like the Craig Whelihan/Ryan Leaf pairing for the 1998 Chargers. One pair of quarterbacks, Jay Schroeder and Steve Beuerlein, appear on the list twice, for different franchises, six years apart.

Some teams' numbers stayed fairly consistent when they changed, like when the 1995 Saint Louis Rams used Rypien in place of Chris Miller, or when the 1998 Giants exchanged Kent Graham for Danny Kanell. Other switches resulted in wild swings in performance, like when a young Dave Krieg replaced Jim Zorn for the 1983 Seahawks, or an elderly Dave Krieg replaced a struggling Scott Mitchell for the 1994 Lions.

Running the correlation coefficients for this group was a little dicey. I'll go ahead and report the numbers, since I used it in the last post. But unlke before, where I'm comparing what the exact same quarterbacks did a year later, here, I had to decide which quarterbacks to include in group 1, and which in group 2. I settled on putting the first quarterback to play that season in the first slot. Here are the correlation coefficients between starter A (first QB to play) and starter B for this group of two quarterback teams.

Yards Per Attempt:  +0.26
Completion Percentage: +0.25
Touchdown Percentage: +0.07
Sack Percentage:  +0.00
Interception Percentage: -0.08

There were enough cases where the backup played significantly worse or better than the original starter that the correlations among the group are not high. YPA and completion percentage do remain most constant. Sack percentage and Interception percentage are the least consistent.

Next, the absolute value differences between the two quarterbacks' advanced passing score, sorted from smallest difference to largest.

Yards Per Attempt:  16.90
Completion Percentage: 17.00
Touchdown Percentage: 18.40
Interception Percentage: 19.90
Sack Percentage:  20.00

Same story here, yards per attempt and completion percentage have the smallest change; interceptions and sacks the largest. Next, just like last time, I computed the ordinal rankings for each team to see what category was the least and most consistent.

Completion Percentage: 2.89
Yards Per Attempt:  2.92
Touchdown Percentage: 2.94
Sack Percentage:  3.01
Interception Percentage: 3.25

Same story here. Finally, I looked at the total change in a quarterback's performance with a new team (as measured by the sum of the absolute value differences in each category), and divided the change in each category by the overall change to assign a percentage of change. This last summary lists the number of times that each category represented 20% or less of the total change in a team's performance after a quarterback change.

Yards Per Attempt:  48 of 73
Completion Percentage: 40 of 73
Touchdown Percentage: 40 of 73
Sack Percentage:  39 of 73
Interception Percentage: 37 of 73

Yards per attempt stands out here. Again, sack and interception percentage were the least consistent and accounted for the most change in performance.

Several commenters had excellent points in the previous post. So let me say that I'm not at this point measuring the exact contribution of the quarterback versus that of his offensive line or skill position players in terms of percentages. That's above and beyond the scope of what these numbers show. What they do show, though, is some general information about the relative effects of luck or other factors, such as game situation. Let's do some general summarizing of the information from this and the previous post.

Yards per attempt and Completion Percentage are both somewhat consistent when a team changes quarterbacks, and are also somewhat consistent when a quarterback changes teams. This tells me that with a large enough sample size of throws, luck plays a much smaller role in these two stats. The quarterback himself has something to do with both of these, and the teammates (and I'll lump things like offensive scheme and playcalling here as well) have something to do with these two. Is it 30/70? 40/60? I don't think we can answer that from just this information.

Touchdown percentage is somewhat inconsistent when a team changes quarterbacks, and also somewhat inconsistent when a quarterback changes teams. Interception percentage even moreso. It is the most inconsistent both when a team changes quarterbacks and a quarterback changes teams. This tells me that luck and game context play a large role in determining touchdown rates, and an even larger role in interception rates. What percentage of the remainder belongs to the quarterback versus his teammates? Again, that's beyond the scope of what I've looked at so far.

Which brings us to sack rate. It is one of the most consistent things when a quarterback changes teams. It is one of the least consistent things when a team changes quarterbacks. This tells me that the quarterback plays a larger role than people think in determining a team's sack rate. Again, I don't know what exact percentage is attributable to the quarterback versus the line, and I certainly don't think the line is irrelevant in determining a quarterback taking hits. I just think we measure line play by the wrong stat if we focus solely on sack rate. Sack rate does seem to have a lot to do with a quarterback's style, decision making, and willingness (or unwillingness) to gamble with a throw before ready. A quarterback with a tendency to take fewer sacks is going to get rid of the ball; it's his yards per attempt and completion percentage that are going to reflect whether the line did a good job. Was he throwing the ball when he wanted to, or before he wanted to?

To me, it makes sense that sack rate would most belong to the quarterback. It is the simplest statistic, and the one that the quarterback can exercise the most control over. It is simply "to release the ball, or not release the ball". What happens after the releasing of the ball brings in a lot of other factors--teammates, the opponent, luck.

With Chase on vacation, I thought I'd lend a helping hand by calculating this week's college SRS ratings (for a very thorough explanation of the method we're using, go here first). As you can see, we have a new #1 team in the rankings:

(Continued)

This is the second part of the similarity scores; the methodology and the teams that have won 3 or more games and played six games are in part I. Here, we look at the ten teams with a losing record through six games. Next week, I'll close with the teams who are playing their sixth game this weekend.

One of the losing teams stands out as the most likely to make a run and turn it around. All but one of the Seahawks' comparables won at least five of their final ten games. The rest, well, it's not particular pretty. The most amazing is the Titans' collapse. They don't really have any similar teams (their most similar team has a score of only 608). I guess that's a good thing, because the bad news is that on the Titans' list, both the 1989 Cowboys and 2000 Chargers appear, and those teams that went 1-15. The worse news is that those weren't even the worst teams on the list, as the 2008 Lions also appear.

SEATTLE SEAHAWKS
weighted wins (last 10): 5.91
playoff chances: 27%

==============================================================
911	GNB	2000		2-4		7-3
896	CLE	1983		2-4		7-3
857	RAI	1996		2-4		5-5
856	CRD	1993		2-4		5-5
848	ATL	1983		2-4		5-5
845	PHI	2007		2-4		6-4
840	DET	1983		2-4		7-3
834	CLE	1980		3-3		8-2
831	CRD	2004		2-4		4-6
826	CAR	2000		2-4		5-5
==============================================================

OAKLAND RAIDERS
weighted wins (last 10): 4.15
playoff chances: 7%

==============================================================
763	TAM	1996		1-5		5-5
755	SFO	2007		2-4		3-7
744	NOR	1981		1-5		3-7
712	NEW	1988		2-4 		7-3
683	CRD	1990		2-4		3-7
655	PHI	1986		2-4		3-6-1
650	NYG	1996		2-4		4-6
645	CRD	1994		2-4		6-4
641	SDG	1988		2-4		4-6
638	GNB	1980		2-3-1		3-7
==============================================================

WASHINGTON REDSKINS
weighted wins (last 10): 4.48
playoff chances: 5%

==============================================================
838	KAN	1988		1-4-1		3-7
838	WAS	2004		2-4		4-6
818	RAV	1998		2-4		4-6
812	CLE	2005		2-4		4-6
812	RAV	2005		2-4		4-6
807	PHI	1985		2-4		5-5
805	RAI	1992		2-4		5-5
789	CLE	1991		2-4		4-6
779	CHI	1980		2-4		5-5
779	CLE	1988		3-3		7-3
==============================================================

BUFFALO BILLS
weighted wins (last 10): 4.00
playoff chances: 2%

==============================================================
888	CAR	1997		2-4		5-5
847	TAM	2006		2-4		2-7
824	RAM	1992		2-4		4-6
819	BUF	2006		2-4		5-5
817	CRD	1999		2-4		4-6
815	KAN	1989		2-4		6-3-1
813	CLE	2000		2-4		1-9
806	PHI	1984		2-4		4-5-1
799	NYG	1995		2-4		3-7
798	CIN	2004		2-4		6-4
==============================================================

CLEVELAND BROWNS
weighted wins (last 10): 3.78
playoff chances: 1%

==============================================================
891	PHI	1998		1-5		2-8
806	TAM	1996		1-5		5-5
754	NOR	1981		1-5		3-7
745	TAM	1993		1-5		4-6
745	HTX	2002		1-5		3-7
743	ATL	1999		1-5		4-6
732	OTI	2006		1-5		7-3
725	PIT	1986		1-5		5-5
707	KAN	2008		1-5		1-9
702	CHI	2000		1-5		4-6
==============================================================

KANSAS CITY CHIEFS
weighted wins (last 10): 3.66
playoff chances: 1%

==============================================================
923	GNB	1984		1-5		7-3
849	NYJ	2007		1-5		3-7
830	CAR	1995		1-5		6-4
821	TAM	1986		1-5		1-9
811	NYJ	1980		1-5		3-7
804	ATL	1997		1-5		6-4
785	WAS	1993		1-5		3-7
779	DET	2003		1-5		4-6
777	CAR	2001		1-5		0-10
773	CIN	1992		2-4		3-7
==============================================================

DETROIT LIONS
weighted wins (last 10): 2.99
playoff chances: 1%

==============================================================
889	CLT	1981		1-5		1-9
838	CRD	1983		1-5		7-2-1
807	ATL	2003		1-5		4-6
784	NYG	1980		1-5		3-7
753	CHI	2003		1-5		6-4
739	DET	2008		0-6		0-10
733	NWE	1990		1-5		0-10
732	SDG	2000		0-6		1-9
709	RAM	1996		1-5		5-5
694	NYJ	1995		1-5		2-8
==============================================================

SAINT LOUIS RAMS
weighted wins (last 10): 2.98
playoff chances: 0%

==============================================================
821	CLT	1986		0-6		3-7
766	CIN	2002		0-6		2-8
705	DAL	1989		0-6		1-9
688	NWE	1992		0-6		2-8
682	OTI	1984		0-6		3-7
678	CHI	1997		0-6		4-6
675	WAS	2001		1-5		7-3
660	CIN	2000		0-6		4-6
655	HTX	2005		0-6		2-8
647	CLE	1999		0-6		2-8
==============================================================

TENNESSEE TITANS
weighted wins (last 10): 2.72
playoff chances: 0%

==============================================================
608	CHI	1997		0-6		4-6
588	SFO	2005		1-5		3-7
580	HTX	2005		0-6		2-8
512	WAS	1998		0-6		6-4
511	DET	2008		0-6		0-10
509	CIN	1991		0-6		3-7
496	SDG	2000		0-6		1-9
477	DAL	1989		0-6		1-9
464	CIN	1999		1-5		3-7
464	ATL	1985		0-6		4-6
==============================================================

TAMPA BAY BUCCANEERS
weighted wins (last 10): 2.69
playoff chances: 0%

==============================================================
872	NOR	1980		0-6		1-9
825	CIN	1991		0-6		3-7
823	CIN	1997		1-5		6-4
812	CLT	1997		0-6		3-7
805	ATL	1996		0-6		3-7
801	DET	2001		0-6		2-8
798	NYJ	1996		0-6		1-9
796	NWE	1990		1-5		0-10
795	CIN	1979		0-6		4-6
777	NWE	1993		1-5		4-6
==============================================================

I'm going to do some team similarity scores like what Doug did a couple of years ago. I'm not going to use the same methodology (not that either is better than the other), because I'm not going to look at specific game results. Rather, I am going to look at a team's overall profile, in terms of wins/losses, points scored and allowed, and yardage for and against.

Like Doug, I'm not putting a tremendous amount of time into deciding how to weigh each factor. I just went with adjustments that generally felt about right, and then made sure the results passed the sniff test.
(Continued)

Two weeks ago, I compiled a list of the top peak regular-season quarterbacks of all-time by averaging together their best 6 seasons (or all of their seasons if they didn't have 6 seasons) in a metric that attempts to estimate Football Outsiders' YAR (yards above replacement) via linear regression. The results were somewhat surprising -- underrated Cincinnati signal-caller Ken Anderson was ranked #1! -- but the concept was a hit, and many readers made suggestions to make the rankings better, so I figured I'd revisit our Peak QB list today and make some changes to the method.

(Continued)

What happens when a quarterback changes teams? Which performance stats remain most consistent, suggesting they are more the responsibility of the quarterback himself, and which are least consistent, suggesting that outside forces (such as teammates, game situation, and random luck) play a larger role?

To examine this, I took all quarterbacks since the merger, between ages 25 and 35, who threw 14 or more attempts per team game in consecutive seasons, but did so for a different team in year two. The result was 48 different quarterback seasons (a handful of players appear on the list more than once). I examined the five basic performance rate stats: yards per attempt, completion percentage, touchdown percentage, interception percentage, and sack percentage. Other stats, such as passer rating or net adjusted yards per attempt, are derivative stats that rely on some combination of these underlying performance measures. Oh, and I used the advanced passing ranking in those five categories, rather than the raw rate stats, to avoid any era bias affecting the results, and to be able to compare between statistics (so we can compare a change of 5% in completion percentage to a 2% drop in sack rate).
(Continued)

About three years ago, Doug ranked wide receivers by the percentage of team passing yards they accounted for, and he averaged together each WR's 6 best seasons according to that metric to create a ranking. This was his reasoning:

I am a big fan of rating players by the average of their best N seasons. It's not scientific, but it generally feels right to me in terms of weighting short brilliant careers with long merely-good ones. If you rate based on totals, you're going to favor the latter over the former by crediting guys for compiling raw numbers at the end of their career even if those numbers weren't of much value. If you rate based on averages, you end up penalizing guys for hanging around past their primes. In short, I think an 600-yard season by a 37-year-old wide receiver shouldn't count for him (because 600-yard seasons grow on trees) nor against him (because 600-yard seasons are at least as good as zero-yard seasons).

In my system, a guy can hang around as long as he wants and it won't hurt him. But it won't help him either, unless he does something truly valuable. The only advantage of having a long career is that it gives you more opportunities to generate valuable seasons. Why six seasons instead of four or seven or 10? No particular reason. It just seemed right.

For career rankings, Doug later moved on to the method of taking 100% of the player’s best season, plus 95% of his second-best season, plus 90% of his third-best season, etc., but I think the "best N seasons" system has its place as well. Choosing six seasons feels like it strikes a nice balance between those pesky compilers and one-year wonders, because whether you're Ken O'Brien or Vinny Testaverde, six great seasons in the NFL don't grow on trees. It's arbitrary, sure, but that's kinda the nature of the beast when trying to balance peak value and cumulative value.

Anyway, I decided to apply Doug's old "best N seasons" method to quarterback careers, so first I translated all players' stats to modern numbers ("modern" = 1994-2008). Then, for the metric to evaluate the QBs, I decided to try something different. Avid web-watchers know that Football Outsiders has a metric called YAR -- yards above replacement -- which ranks players based on their contribution above a theoretical "replacement level" player at the same position. Unfortunately, since it's based on play-by-play data, it can only rank players back to 1994, the first year Aaron & co. have in their db. However, since we have box score numbers dating back much further than that, we can see which raw box score stats tend to lead to good YAR scores, and estimate a player's YAR from his standard stats.

In other words, I ran a regression on all quarterback passing & rushing YAR numbers from 1994-2008, and found that the following equations most closely estimate YAR:

qb_pYAR = (-6.641972655 * Att) + (3.651542626 * Cmp) + (0.977634 * pYds) + (13.15861425 * pTD) + (-42.88479071 * INT)

qb_rYAR = (-2.944447621 * Runs) + (0.60229537 * rYds) + (8.506708898 * TD)

Okay, so now we have every QB in NFL history translated to a common era, in this case 1994-2008, and we have a method by which we can evaluate their performance each year. All that's left is to crunch the numbers and see who averaged the most YAR in their six best seasons...

(Continued)

This is a goofy idea for a post, but here goes...

A few years ago, in order to write this well-intentioned but flawed monstrosity, I replicated what Football Outsiders called "translated" stats, a process which takes a player's stat line from one league environment and tries to determine what it would have looked like in another one. How did it work? I'll quote my own explanation from back in the day:

"How to translate: Take the raw stats. Calculate the completions/game, pass attempts/game, passing yards/game, TD passes/game, interceptions/game, rushing attempts/game, rushing yards/game, and rushing TD/game for the season in question. For the 2006 NFL, they went like this:

GP	LgCmp/G	LgAtt/G	LgPYds/G LgPTD/G LgInt/G LgRush/G LgRYds/G LgRTD/G
---------------------------------------------------------------------------
16	19.14	32.01	219.29	 1.27	 1.02	 28.22	  117.31   0.83

Now, divide the player total in each category (completions, passing yds, etc.) by the appropriate league numbers, and multiply by the 2006 numbers. Then adjust for the length of schedule, extrapolating the raw totals to a 16-game season. Like magic, your new totals will be normalized, able to go up against any other season without fear of cross-era distortions.

Let's take a look at an example... In 1966, Len Dawson of the Kansas City Chiefs put up this stat line en route to an AFL title and a spot in the very first Super Bowl:

                 +---------------------------------------+-----------------+
                 |              Passing                  |     Rushing     |
+----------+-----+---------------------------------------+-----------------+
| Year  TM |   G |  Comp   Att   PCT    YD   Y/A  TD INT |  Att  Yards  TD |
+----------+-----+---------------------------------------+-----------------+
| 1966 kan |  14 |   159   284  56.0  2527   8.9  26  10 |    24   167   0 |
+----------+-----+---------------------------------------+-----------------+

The environment of the 1966 AFL looked like this:

GP	LgCmp/G	LgAtt/G	LgPYds/G LgPTD/G LgInt/G LgRush/G LgRYds/G LgRTD/G
-----------------------------------------------------------------------------
14	14.62	31.60	215.30	 1.58	 1.72	 28.95	  116.13   0.90

So, after applying our normalization technique to Dawson's raw stats, this is the equivalent performance in the 2006 NFL:

                 +---------------------------------------+-----------------+
                 |              Passing                  |     Rushing     |
+----------+-----+---------------------------------------+-----------------+
| Year  TM |   G |  Comp   Att   PCT    YD   Y/A  TD INT |  Att  Yards  TD |
+----------+-----+---------------------------------------+-----------------+
| 2006 kan |  16 |   238   329  72.3  2942   8.9  24   7 |    27   193   0 |
+----------+-----+---------------------------------------+-----------------+

Repeating this procedure for every player-season in the NFL since 1950, we now have a database of stats that can be compared with each other to determine the best modern players at each position."

Simple? Sure. Flawed? Absolutely. But it's still kind of fun, and the results generally make sense. Now, if you really wanted to spice it up, you could translate using standard deviations above/below the mean (similar to what we do with our advanced passing metrics), but for these purposes I think the simple route is the way to go. Anyway, the result is a stat line that effectively places the player in a new context, where his numbers are perhaps easier to understand than had they been left in their raw form.

Playing around with this method is basically the point here, but I also thought it would interesting to see how the two most recent Dallas Cowboys superstar QBs (Troy Aikman and Tony Romo) stack up across eras, since A) Romo is somewhat surprisingly very high on the all-time passing rate lists, B) Aikman has stats notoriously out of step with his reputation as an all-time great, and C) Aikman (among other Cowboy legends) criticized Romo's play after last year's brutal 44-6 season-ending loss to the Philadelphia Eagles.

Aikman played in an era with less leaguewide passing success than Romo has enjoyed, he threw the ball less (especially in the red zone) because Dallas had Emmitt Smith to carry the rushing load, and he has a number of bad (non-prime) seasons that drag down his career rates, while Romo's career essentially consists of nothing but prime seasons (ages 26-29). So what if we took Aikman's stats from ages 26-29, translated them from the 1992-1995 environment to 2006-2009, and prorated everything to Romo's attempts per game? How would Aikman's numbers look compared to those of Romo? Would he be in a better position to criticize a guy who's 3rd on the all-time career passer rating list?

As it turns out, yes. According to the translated stats, if Aikman had been afforded Romo's opportunity to play from 2006-09, throw the ball as much as Romo, and limit his career to just prime seasons, through Week 2 of the 2009 season he would: rank first all-time in career passer rating, first all-time in completion %, be tied for 8th all-time (4 spots behind Romo) in yards per attempt, rank 5th all-time in lowest interception %, and be 3rd all-time in career adjusted yards per attempt. Remember, Romo's real-life career looks like this:

So, basically, erasing the contextual advantages Romo has over Aikman was enough to boost Aikman from a rather pedestrian career 81.6 rating to a 97.5  mark-- and this isn't even taking into account the postseason, where Aikman's career numbers blow Romo's away.

Am I saying that Romo isn't a good QB? No, of course not. But I am saying that he has had a number of advantages in his career that allow him post such impressive stats. When people look at his numbers and compare them to players from the past without regard to changing league passing conditions, they are ignoring the built-in advantages that passers like Romo have. Aikman is just one example of a player whose stats receive a big boost from "the Romo treatment" -- a player like Len Dawson would post even more ridiculous numbers when translated to the modern game.

So while this is a somewhat silly, naive method, it shows that Aikman is more than justified in demanding more from his successor as the Cowboys' superstar QB. After all, giving him Romo's situation is enough to tack 15.9 points of passer rating onto Aikman's career mark, which was roughly the difference between Philip Rivers and Matt Cassel last season.

Tim Truemper, frequent commenter here on the P-F-R blog, recently e-mailed us with a question that had been bugging him: how much variance is there among teams with respect to roster stability in the free agency era?

Essentially, Tim wants to know if certain teams do a great job at retaining their guys and if certain teams do a poor job. That's a question that AV can help us answer.

I looked at every team from 1993 (the inception of free agency) to 2007, a fifteen year period. I recorded the AV of each player on each team for those fifteen seasons. Then, I noted whether each player was playing for that same team in the following season, was playing for no team, or was playing for another team. Generally, when a player is not on a team the following season, it's because of injury, retirement or lack of talent (and, occasionally, incarceration); that's not something that's affected by free agency, though, so I'm only going to focus on players who switch teams in the off-season. For simplicity's purposes, I've ignored the 1995 Browns as opposed to seeing if those players were on the '96 Ravens; I've also split the Browns into the old Browns and new Browns. I did not do the same things for other franchises that moved cities, and I don't have a terribly persuasive justification for that.
(Continued)

In the 2007 and 2008 off-seasons I wrote articles adjusting QB statistics for strength of schedule. Today brings the summer '09 update. As always, I've done essentially the same analysis for our fantasy football fans over at Footballguys.com.

Let's start with a look at the 2008 leaders in adjusted yards per attempt, defined as (passing yards + PTD*20 - INT*45)/attempts. All QBs with a minimum of 100 attempts are listed; the league average was 6.45 AY/A.

name			att	pyd	ptd	int	ay/a
Philip Rivers		478	4009	34	11	8.77
Drew Brees		635	5069	34	17	7.85
Chad Pennington		476	3653	19	 7	7.81
Tarvaris Jackson	149	1056	 9	 2	7.69
Matt Schaub		380	3043	15	10	7.61
Kurt Warner		599	4582	30	14	7.60
Matt Ryan		434	3440	16	11	7.52
Aaron Rodgers		536	4038	28	13	7.49
Tony Romo		450	3448	26	14	7.42
Jake Delhomme		414	3288	15	12	7.36
Peyton Manning		555	4002	27	12	7.21
Jeff Garcia		376	2712	12	 6	7.13
Matt Cassel		516	3693	21	11	7.01
Jay Cutler		616	4526	25	18	6.84
Donovan McNabb		571	3916	23	11	6.80
Shaun Hill		288	2046	13	 8	6.76
Eli Manning		479	3238	21	10	6.70
Seneca Wallace		242	1532	11	 3	6.68
Trent Edwards		374	2699	11	10	6.60
Jason Campbell		506	3245	13	 6	6.39
Ben Roethlisberger	468	3308	17	15	6.35
Joe Flacco		428	2971	14	12	6.33
Sage Rosenfels		174	1431	 6	10	6.33
JaMarcus Russell	368	2423	13	 8	6.31
Kerry Collins		415	2676	12	 7	6.27
David Garrard		535	3620	15	13	6.23
J.T. O'Sullivan		220	1678	 8	11	6.10
Kyle Orton		465	2972	18	12	6.00
Tyler Thigpen		420	2608	18	12	5.78
Gus Frerotte		301	2157	12	15	5.72
Brett Favre		522	3472	22	22	5.60
Dan Orlovsky		255	1616	 8	 8	5.55
Marc Bulger		440	2720	11	13	5.35
Jon Kitna		120	 758	 5	 5	5.28
Daunte Culpepper	115	 786	 4	 6	5.18
Derek Anderson		283	1615	 9	 8	5.07
Carson Palmer		129	 731	 3	 4	4.74
Brian Griese		184	1073	 5	 7	4.66
Ryan Fitzpatrick	372	1905	 8	 9	4.46
Matt Hasselbeck		209	1216	 5	10	4.14
J.P. Losman		104	 584	 2	 5	3.84

(Continued)

If you hang around team message boards or websites or listen to talk radio this time of year, you will hear lots of discussion and debate about who teams should take. Inevitably (at least it seems to me), somebody will make some comment about how good teams build along the lines, or build from the inside out, or how teams that know what they are doing draft the big uglies. The quarterbacks, wide receivers, flashy defensive backs, these guys are risky! Take the offensive lineman, he's a safe pick, someone will call in and say, that's what a good franchise would do.

The problem is, I can't find any substantial evidence to support such a view. Plenty of anecdotal cases come to mind to counter those who point out that the Lions were idiots for spending first round picks on wide receivers. Namely, that same organization also is the last one (and only one I can find since 1978) to draft three offensive tackles in the first round in three straight years, from 1999-2001, and Aaron Gibson, Stockar McDougal and Jeff Backus didn't exactly set the Lions up for success. People also think of the Steelers as doing it the right way. In the last 15 years, they've actually taken more pass catchers than the Lions in the first round, with four wide receivers and two tight ends.

But those are just isolated examples that come to mind. I thought I would sit down and do a study to see how good and bad teams did draft in the first round, and determine if there were any differences in where they focused. I'll start by saying this is far from a perfect study (as with most) as it entails arbitrarily, though I hope logically, defining good and bad teams in a way that can be used to create useful categories with large sample sizes. We also know that while first round picks are important, they do not solely decide who is good and bad over a period of time. As Doug wrote about here, there are generally somewhere between 4 to 5 originally drafted first round picks starting for a team at a given time--which leaves most of the starters coming outside round one. Also, sometimes good teams draft bad players, and bad teams draft good players.

Still, acknowledging all that, I plowed forward.

(Continued)

Ignoring cost, which player should be better for the next seven or so years? Obviously this is an impossible question to answer, as projecting the future is usually pointless. The very first post in PFR blog history asked whether Shaun Alexander or Reggie Bush would be the better player going forward; unfortunately, neither of the above wasn't an option.

So while we don't *really* know who is going to be better, and there are tons of intangibles surrounding both Boldin and Crabtree, I thought I'd take my best stab at trying to project the future for both players. To begin, I looked at all WRs who were "similar" to Anquan Boldin. What does that mean? Two things; one, in any year between 1970 and 2001, the WR was either 27, 28 or 29 years old. Two, they had to have between 500 and 900 yards of "Adjusted Value" in that specific season, using the formula from the Greatest WR Ever Series. Boldin last year had 661 adjusted yards of value.

I chose 1970 since that's the year the two leagues merged; 2001 is a good end date because that gives all WRs in the study seven years following the specific year in question. There were 92 WRs that fit the "age 27-29" and "value of 500-900 yards" description, ranging from players like Alfred Jenkins (who was a first team All Pro at age 29 in 1981 but caught just two TDs the rest of his career) to Cris Carter (who earned his first Pro Bowl berth at age 28 in 1993 and would go back to Hawaii for each of the next seven seasons). Who knows how Boldin will turn out, but these 92 data points give us a good starting point. I used the cutoff of 500 and 900 yards to provide a large enough sample for Boldin; many more players had between 500 and 661 yards of value than between 661 and say, 822, so we have to use a higher top point that bottom point.

The important thing is that of those 92 WRs, the average player was 28 years old and had a value of +655 in year N. That sounds a lot like Boldin in 2008. So how did the average WR do going forward?

(Continued)