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.

Coaches need to get out of their heads this binary thought process of "in field goal position" and "out of field goal range." Every yard matters when it comes to giving your team the chance to win. Yet week after week, year after year, we see coaches get inside that magical 35 yard line and freeze. Don't move! The goal posts can see you! Don't try anything that might get you outside the range of their siren's song!

And week after week, year after year, we see kickers shockingly miss a higher percentage of kicks from 50 yards out than they do from 35. Weird how that works.

As indicated by Kubiak's comments, he was thinking about this negatively (what can go wrong?). Why wouldn't he? Clearly, he made a ridiculously horrible decision and the uproar is minute; it's all on Brown. If he had called a play and his team leader had thrown an interception, though, we know what the reaction would have been. He clearly is a follower of the saying "when you pass, three things can happen, and two of them are bad." I'd like to introduce its counterpart. When you kick, three things can happen, and two of them are bad. I doubt that catches on, but the "bad" things that happen on a kick happen more frequently from 49 yards out than the "bad" things that happen on a pass. Or how about this one. When you drive a car, three things can happen, and two of them are bad. I'm beginning to wonder how Kubiak mustered the courage to drive to the game with that kind of fear of failure.

Let's try to break this down to see how costly Kubiak's coaching out of fear of failure was to the Texans on Monday night. If we are going to break it down simply but effectively, we want to consider what the chances that Brown made the kick using the Kubiak strategy, versus the chances of winning when considering the various things that could happen if he ran an actual play.

Brian Burke of Advanced NFL Stats posted a graph showing the likelihood of success for field goals depending on the line of scrimmage. I'm going to discount any "Brown's a choker" factor in this analysis, but if you are inclined to weigh that in, it won't help Kubiak's case. Anyway, I'm going to give Brown a 62% chance of making a 49 yard field goal based on the league-wide numbers, his career, and the venue. So, that's our expectation of Kubiak's actual decision, which is to take an almost one yard loss to move the ball over three yards, and kick a 49 yard attempt. Remember, that kick definitely only sends the game to overtime, so from there, we need to cut the chances in half. A 62% chance of going to overtime, and a 31% chance of ultimately winning the game.

Before I get to the alternatives, a quick intermission about the actual centering of the ball. I apologize for breaking out the trigonometry on you. Centering the ball matters the most when you are closer to the goal posts, and it matters more in college where the hash marks are farther than six yards apart. It might make sense in some small marginal way if you are going to kick the game winning kick inside the 10. But it simply cannot matter at the distance for this kick. If you want to think of it like a triangle, with one point being the hashmark, one being the center of the field at the same yard marker, and the final point being the point on the ground directly below the upright meeting the crossbar, then we can see this is so. The distance (three yards) from the hashmark to the center is the base of the triangle, and from the center point to the crossbar/upright is the length. As the length of the kick decreases, the angle increases. In this case, a 3 yard base and a 49 yard length results in a 3.5 degree angle change on the kick. I'm inclined to say no effect, but convince me otherwise.

Now, turning back to the alternatives to simply centering the ball. I'm going to view this from the perspective of a pass play, as that is the more optimal decision in that particular situation generally, and definitely for the Texans specifically. Kubiak was worried about the negatives that could happen: penalties, turnovers, sacks. Let's get those out first.

The Texans are averaging 6.3 penalties per game. That, however, is an overall number that also includes defensive and special teams penalties. I don't have the specific breakdown on offense, but even if we assume half of those are offensive, then the Texans are going to have less than a 5% chance of an offensive penalty there. I'll go all the way up to 5% to give Kubiak the benefit of the doubt. Not all penalties are equal. The clock is already stopped, so a false start or other pre-snap penalty will cost yardage, but not time or the timeout, the team is still in "field goal range" back another five yards, and you can still run a play to get the yardage back (and more). A post-snap penalty that results in time coming off the clock could be more costly, basically leaving the Texans out of field goal range and with no choice but to throw to the end zone from about their own 40. I won't bore you with further details (because they don't have a huge effect on the final numbers) but I am splitting out these things and including both possibilities in the final numbers.

Next, the sacks. Matt Schaub has a sack rate of 5.6% in Houston over the last three years. This year is slightly better at 4.9%, but again, benefit of reasonable doubt to Kubiak. So we'll go with 5.6% chance of a sack. That needs to be multiplied by 0.95 (because we've already taken out 5% of the plays due to the penalties), which means there was a 5.3% that play ends in a sack. I'm assuming that Schaub is not going to stay on the bull and take an 8 second sack there, and the Texans can still call timeout. A sack then, usually, is not going to end the game because the Texans have that timeout. Without again getting into the numbers from there, I am considering that Schaub could fumble and lose the ball on a sack, and that some sacks will be deeper than others, so that a sack could either result in a throw to the end zone, or a longer field goal attempt.

Finally, for the negatives, the interceptions. Schaub has thrown an interception on 2.7% of his passes in Houston over the last three years. It's a little lower than that this season, and those include hail mary passes and situations where he is playing from behind. I think Schaub's chances were a little less than that, but again, giving the benefit of the doubt to Kubiak and his fear of bad things, I'll go with 2.7% as his interception rate there. Again, because we have to discount the penalty and sack plays (which aren't included in that rate), the actual rate is dropped to 2.4% (2.7% of the remaining 90% of plays).

Now let's turn to the positives. With the timeout, the whole field is open, time is not a factor in getting a play run, and getting the player down and calling timeout (unless someone decides to run back and forth across the field), and there is thirty yards of field position so the defense can't just play near the line of scrimmage. The Texans could outright win the game if the Titans blow a coverage and let someone run free down the sideline. This is not a likely scenario, but a possibility.

Matt Schaub has completed 66.5% of his passes on over 1,000 throws in his Texans' career. Again, he is slightly higher this year, but we'll go with that number. The average completion is 12.1. We'll come of that a little, and give Kubiak the benefit of the doubt, and I'll assign a 3% chance of the Texans scoring outright on a blown coverage (which I suspect is very conservative and in favor of Kubiak again), and assume that the remaining completions will gain an average of 10 yards. When we adjust for the penalties and sacks, this means we have 2.7% of plays resulting in a win, 59.7% completed to the 20 yard line on average, and 24.9% falling incomplete (leaving the Texans in the same position, and with a timeout still so that Kubiak can center it to his heart's content).

How much is that 10 yards to the 20 yard line worth for a field goal attempt? Looking at Burke's graph again, it looks like the difference between the 20 and 31 is about 19% improvement on making the field goal. I'm going to give Brown an 81% chance of making the shorter field goal.

Finally, I'm assuming a 5% chance of a successful touchdown throw from about the 40 in the event a sack or holding penalty. It's not a full out hail mary, and Schaub could definitely get the throw into the end zone with some general accuracy for who he's trying to throw it to. I'm also assuming a drop to a 50% chance of Kris Brown making it if the kick becomes a 53 yarder due to a short sack or a penalty without further gain of yardage.

Throw all those numbers into the mix, run a second iteration for the 5 yard penalties where they get to still run another play, and the final result is 36.7% (with several assumptions in Kubiak's favor) for the Texans to win if he tries a pass with the timeout in hand and enough time to run a play. The timeout is the key here. Without it, those numbers drop dramatically on running another play.

When we compare that to his actual decision, we see that the centering of the ball cost his team at least a 5% chance of winning the game. That may not sound like a lot, but it's a pretty costly decision. In order to justify that decision, the centering the ball would have to have improved Brown's chances of making that kick from about 62% to about 72%. It's implausible that a 3.5% change in the angle from 49 yards out could matter more than moving the ball five yards upfield.

A better way to show how bad this decision is might be to look at how inept the quarterback and offense would have to be in order to make this a break even decision.

If we assume that the Texans would commit a penalty on 10% of their offensive plays, that the quarterback's sack rate is 10%, that he throws 10% of his passes to the other team, and completes only 45% of them to his own team at a rate of less than 11.0 per completion (so 4.9 yards per attempt), then, just maybe, this decision might have been justified (30.4% to 31.0% chance of winning). In other words, if the quarterback was substantially worse than Gary Kubiak the player. Check that, substantially worse than every quarterback who has played the game. Ever. How's that for a vote of confidence, Matt Schaub?

Other than that, good call.

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.

Remember, these rankings are pretty basic. No adjustment was made for strength of schedule, which means this undervalues teams like the Dolphins, Titans and Jets, and overvalues teams like the Vikings, Saints and Packers. Teams who have suffered serious injuries will be overvalued; teams who are seeing new players emerge are undervalued. Special teams are totally ignored in this analysis. All that said, this basic system has had some very good historical success against the spread, especially when the difference between the projected and actual point spreads are large.

Here are the week 12 projected point spreads:

Green Bay Packers @ Detroit Lions (+19.2)
Oakland Raiders @ Dallas Cowboys (-28.1)
New York Giants @ Denver Broncos (+0.6)
Tampa Bay Buccaneers @ Atlanta Falcons (-14)
Miami Dolphins @ Buffalo Bills (-2.9)
Cleveland Browns @ Cincinnati Bengals (-26.5)
Indianapolis Colts @ Houston Texans (+8.8)
Carolina Panthers @ New York Jets (-9.3)
Washington Redskins @ Philadelphia Eagles (-10.8)
Seattle Seahawks @ St. Louis Rams (+0.7)
Kansas City Chiefs @ San Diego Chargers (-22.4)
Jacksonville Jaguars @ San Francisco 49ers (-3.2)
Arizona Cardinals @ Tennessee Titans (-1.6)
Chicago Bears @ Minnesota Vikings (-11.6)
Pittsburgh Steelers @ Baltimore Ravens (+5.3)
New England Patriots @ New Orleans Saints (-10.8)

And here are the week 12 actual point spreads:

Green Bay Packers @ Detroit Lions (+10.5)
Oakland Raiders @ Dallas Cowboys (-13.5)
New York Giants @ Denver Broncos (+6.5)
Tampa Bay Buccaneers @ Atlanta Falcons (-11.5)
Miami Dolphins @ Buffalo Bills (+3)
Cleveland Browns @ Cincinnati Bengals (-14)
Indianapolis Colts @ Houston Texans (+3.5)
Carolina Panthers @ New York Jets (-3)
Washington Redskins @ Philadelphia Eagles (-9)
Seattle Seahawks @ St. Louis Rams (+3)
Kansas City Chiefs @ San Diego Chargers (-13.5)
Jacksonville Jaguars @ San Francisco 49ers (-3)
Arizona Cardinals @ Tennessee Titans (OFF)
Chicago Bears @ Minnesota Vikings (-10.5)
Pittsburgh Steelers @ Baltimore Ravens (OFF)
New England Patriots @ New Orleans Saints (-3)

Conclusions

Going game by game, we see:

Green Bay is undervalued by nearly 9 points (Detroit is about 19 points worse than GB; the Packers are only being given 10 points)
Dallas is undervalued by nearly 15 points
Denver is undervalued by about 6 points
Atlanta is undervalued by 2.5 points
Buffalo should be favored by 3; instead, they're 3-point dogs.
Cincinnati is undervalued by 12.5 points
Indianapolis is undervalued by 5.3 points
The Jets are undervalued by 6.3 points
Philadelphia is undervalued by 1.8 points
The Rams are undervalued by about 2 points
San Diego is undervalued by about 9 points
SF/JAX game is properly valued
Arizona game is off due to Warner's injury; I suspect with a healthy Warner, the line would be close to the projected line
Minnesota is undervalued by about 1 point
Pittsburgh game is off due to Roethlisberger's injury; I suspect Baltimore would probably be getting fewer than 5 points if Ben was healthy.
The Saints are undervalued by about 8 points

So now what? What does this all mean? If I was a betting man -- which I am not -- here's what I would do:

Dallas -14 (vs. the Raiders)

• Has Dallas suffered any major injuries? No.
  Has Dallas played a really easy schedule? They've had the 28th hardest (or 5th easiest) SOS according to Sagarin.
  Has Oakland improve their team? I suppose benching Russell and playing Gradkowski could be considered a good thing.
  Has Oakland played a really difficult schedule? They've got the 5th toughest SOS according to Sagarin.
  Is Oakland particularly capable of playing in Dallas due to proximity or past history? No.

  Add up all of those things, and maybe Dallas shouldn't really be a 28-point favorite. But I still don't think I can justify this line. I'd confidently take the Cowboys.

Cincinnati -14 (vs. the Browns)

• Have the Bengals suffered any major injuries? Benson's hurt, but is likely to play against Cleveland.
  How's their SOS? 20th
  What about Cleveland? Brady Quinn could be on the verge of breaking out. Or something like that.
  How's their SOS? 8th.
  Is Cleveland particularly capable of playing well in Cleveland? They play there once a year and they're in the same state. On the other hand, since 1978, the road team has won only 41% of games in this Ohio rivalry.

  The Bengals appear to be undervalued by nearly two touchdowns. Sure, SOS, Brady Quinn and Cedric Benson all matter... but not that much. Take Cincinnati.

San Diego -13.5 (vs. the Chiefs)

• Any injury issues for SD? Nothing new.
  SOS? 16th.
  KC? Dwayne Bowe is out of the lineup, although Chris Chambers was the hero last week.
  SOS? 17th
  HFA? KC plays in SD once a year, but otherwise this is not an easy trip to make.

  I don't see anything to make me feel uncomfortable about the Chargers giving 13.5 points to Kansas City.

Green Bay -10.5 (@ Detroit)

• Injuries: Not only is Green Bay relatively healthy, but Matthew Stafford is not. What's up with this line?
  SOS: Green Bay has played cupcakes so far, evidenced by their third weakest SOS. Of course, Detroit's just another cupcake, and they've had a pretty easy schedule (#24), too.
  HFA? Green Bay hasn't always fared well indoors at Detroit, even against some bad Lions teams. That's particularly true on Thanksgiving, where Mike McMahon nearly beat them in '01 and Joey Harrington actually did beat them in '03. But GB blew out the Lions in Detroit last season, and I think we'll see a repeat of that again this year.

Take both Thanksgiving Day favorites (more on that Thanksgiving Night game, later).

New Orleans -3

• Injuries: the Saints have been hit by the injury bug of late, and (last weekend notwithstanding) have struggled on the field because of that in close wins over Miami, Atlanta, Carolina and St. Louis. The Patriots are pretty healthy.
  SOS: New Orleans has faced a super easy schedule (#31) while the Patriots have faced a slightly tougher than average slate.
  HFA? This would be the spot where an unprofessional journalist would make some crack about how the Pats are intimiately aware of how to tape practices before games at the Superdome. I won't be doing that; instead I'll say that generally, long trips to distinctly different climates from a team's home climate in stadiums in which such teams are unfamiliar with are generally tough road games. The Patriots have not played in New Orleans since Super Bowl XXXVI.

  I don't like taking what looks like a slumping NO team against a streaking NE team. But I'm sure there have been many times where teams had injuries/slumped and played hot teams in my dataset, and that's why the line was lower than projected. So I'm not going to use that as a reason to back off what the data said on Monday, so I'll take the Saints.

Four other games are close -- the Jets, Broncos, Bills and Colts are all undervalued by 5 or 6 points. The remainder of the games are either properly valued, or "off." I'd avoid the Jets game because of the big injuries to Leon Washington and Kris Jenkins, and the fact that my analysis ignores turnovers (they're generally unpredictable, but I'm going to make an exception for Mark Sanchez).

Denver is a 6.5 point dog to the Giants, when they really are just about even with New York as long as they're at home. The Giants have faced an easier schedule than the Broncos so far and playing in Denver is never easy. No, I don't feel excited about it, but I'll back the numbers here and say to take Denver.

The Bills/Dolphins game worries me because Miami has faced the #1 SOS so far this year while the Bills have faced the 21st hardest one; even without Ronnie Brown, I don't feel confident taking the worse team in my rankings that is overvalued due to SOS and only getting three points.

The Colts are better by about a half a yard per play in each of the four categories; they've faced a slightly easier schedule than Houston, but I don't think the HFA is significant when the Colts play in a dome and Indy plays in Houston's dome once a year. The numbers say to be cautious -- the Colts are only undervalued by 5.3 points -- but that passes my threshold.

So to recap, my system (tweaked by my subjective thoughts based on things the system ignores) says to take Dallas, Cincinnati, San Diego, Green Bay, the Broncos and the Colts. Whatever the results, I'll keep them to the comments, and then run this again next Wednesday. Anyone else care to make some predictions?

Happy Thanksgiving!

(How did we do this? Matt and the other dedicated folks at the Knobbe.org message board have spent a lot of time over the years updating this classic Nintendo football game, including the introduction of a 32-team ROM a few seasons ago. Sounds complicated, but don't worry, it's easy for you to enjoy the fruits of their labor: just get yourself an NES emulator, download the 2009 version of Tecmo here, and play to your heart's content. And be sure to check back at Matt's site for roster updates and more Tecmo-related goodness all season long.)

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.

I have little interest in whatever motivations drive Pinker and Gladwell's exchange. I'm interested only in the football aspect. Does draft position matter in predicting success? To see where Gladwell is coming from, we need to turn to his source. That source was an article published in the Journal of Productivity Analysis, entitled "Catching a draft: on the process of selecting quarterbacks in the National Football League amateur draft" by David Berri and Rob Simmons. In that article, Berri/Simmons looked at quarterbacks drafted between the 1st and 250th pick of a draft since 1970, found all cases where a quarterback from that group started at least one game in an NFL season, and then calculated performance using Berri's QB Score measure, on both an aggregrate and per play basis. The authors concluded, when looking at nearly 40 years of data, that a relationship between a quarterback's draft position and his subsequent NFL performance on a per-play level could not be found. In other words, later selected quarterbacks played as well as quarterbacks selected at the very top of the draft, when the number of opportunities was ignored, and they were assessed on how they played per play.

When the spat broke out between Gladwell and Pinker, Berri also posted some thoughts on his Wages of Wins website.

My sense is that Pinker never read our article. What he did find on the Internet is evidence that a quarterback’s aggregate performance (i.e. passing yards, seasons played, Pro Bowl appearances) is indeed related to draft position. And as Rob and I detailed in our article, this is true. Aggregate performance and draft position are statistically related. But as Rob and I argue, this is because in the NFL (like we see in the NBA) draft position is linked to playing time. And this link is independent of performance. In fact, Rob and I find that draft position – again, independent of performance – impacts a quarterback’s pay many years into a quarterback’s career.

It is the bolded part of that quote that I want to focus on. This is a key underlying assumption for the position that Gladwell (through Berri/Simmons) ultimately takes (Although apparently it was a position that Gladwell had assumed long before that article was written). If quarterbacks get playing time because of their status, independent of how good they are, then Gladwell's position has some support.

The math in the Berri/Simmons article is fine. They use their own measure, QB Score, rather than others like Adjusted Net Yards per Attempt or QB Rating, but ultimately, all those per-play measures are including roughly the same things, and the differences are not going to change the conclusions. We can say with reasonable certainty that, as Berri/Simmons find, later round quarterbacks who actually play in the NFL perform about as well as early draft picks who actually play. This part is adequately portrayed in the article.

What I cannot find support for in the article, other than the reference to a quarterback's pay, is the underlying key assumption that playing time is linked to draft position, and this link is independent of performance. Clearly, earlier drafted quarterbacks get an opportunity at a younger age on average than later drafted quarterbacks who eventually become starters, so draft position (along with opportunity and team need) does dictate how soon a quarterback gets a chance. Berri, however, separates out per-play performance based on years of experience and reports that correlations are non-existent on a per-play basis even looking at quarterbacks with 5+ years of experience in the league. So, I don't think Berri is making the "playing time related to draft position independent of performance" based only on rookie starters at age 22 and 23, with a belief that everything being equal thereafter.

To test the interplay of performance versus draft status, I looked at all quarterbacks going back to 1960 who threw 200 or more passes in the NFL at age 24. From this list, I excluded all undrafted free agents and all supplementary draft picks (where I can't assign a specific draft number), so that we are only measuring players who were drafted in the regular draft. I also excluded players who had not turned 29 years of age as of the 2008 season. I chose age 24 for a couple of reasons. First, prior to age 23, there are very few seasons where quarterbacks threw 200 passes. Matt Stafford, for example, has joined Fran Tarkenton and Drew Bledsoe as the only three quarterbacks to throw that amount at age 21. The second reason I chose age 24 is because, for most quarterbacks, it is not a true rookie season, and we get a much larger variety for draft position, as a higher number of guys not selected in the first round start to get some playing time.

I ran a regression with the following input variables for that group of quarterbacks:

1) the quarterback's per play value above or below league average at age 24 ("PERFORM"), using the formula for value used by Chase in his most recent "Greatest Quarterback of All-Time" series; and

2) the quarterback's draft position ("DRAFT"), using a draft value number used by Chase originally here.

The three separate outputs used were games from ages 25-29, games started from ages 25-29, and performance above or below replacement value from ages 25-29. I used the age 25-29 period as the output so that a) we would have a larger data set and not have to exclude all currently active players, and b) so that injuries later in the career or decisions to retire at one age versus the other (which we would assume are not dependent on either draft position or performance at age 24) are not factored. Of course, injuries still can determine how many games a specific QB played, but this limits that somewhat. Oh, and for players who had a strike year or played before 1978, all the outputs were normalized to a 16-game schedule (so that 80 games is the max available).

Here are the results:

GAMES STARTED FROM AGES 25 TO 29= ~ 34.69 + 8.49*PERFORM + 0.39*DRAFT

GAMES PLAYED FROM AGES 25 TO 29= ~ 46.78 + 6.56*PERFORM + 0.23*DRAFT

VALUE OVER REPLACEMENT FROM AGES 25 TO 29= ~ 1930 + 866*PERFORM + 31*DRAFT

All the variables were strongly significant. As it turns out, how the player performs at age 24 and the draft status both matter. The fact that draft status matters, though, doesn't automatically mean that all of it is due to teams starting high draft picks for no reason other than to justify their selection (though there is some of that). Some of the "draft status matters" is that the scouting is proven correct, and the limitations of separating quarterback performance measures from the contributions of teammates is shown, because the higher drafted quarterbacks perform better than lower drafted quarterbacks who happened to play about as well at age 24. The Troy Aikmans of the world sometimes pan out, and do so more frequently, than the below average performers who were not highly drafted.

That said, the results also support that some highly drafted quarterbacks do get more opportunities than their performance dictates. This is something that I tried to look at last year in regard to Joey Harrington, and I do think that teams commit more false positive errors in regard to high picks (continuing to give them plays when the evidence suggests they are highly likely not to pan out) than false negatives (giving up on a high pick too soon, only to have him succeed elsewhere). If you compare the variables for Games Started versus Value over Replacement, you will see that the PERFORM variable is about 100 times larger for Replacement Value compared to Games Started. In contrast, the DRAFT variable is only about 80 times larger. Thus, performance at age 24 is relatively more important in determining value over replacement (for those that continue to play) than for games started. To put it into specific examples, occasionally, Joey Harrington and Rick Mirer get to bounce around and start far more games than they should, and this happens more frequently for previous high picks than low picks who played about like Harrington or Mirer at age 24.

What is clear to me, though, is that performance matters. A lot. I know this is a shocking finding in a performance driven business like the NFL. I'll also add that my choice of a 200 pass attempts cutoff (instead of say, a 100 pass attempts cutoff) probably increased the importance of the DRAFT variable by excluding guys who were already being weeded out, despite their draft status, by age 24. Poster boys for the early draft busts such as Akili Smith, Art Schlichter, Todd Blackledge, Heath Shuler and Andre Ware didn't even make the data set because they didn't throw enough passes at age 24. Cade McNown was out of the league. Ryan Leaf, who is THE #1 poster boy, is included, and he started 3 more games in his NFL career. Performance (or at least not acting like a jerk while not performing) matters.

Here is a look at the projected Games, Games Started, and Value over Replacement for ages 25-29, for the players who threw 200 passes at age 24 since 2004.

Ben Roethlisberger is notably underprojected here, but how many Quarterbacks have won 26 regular season games and a Super Bowl before age 24? 2006 was a down year for Big Ben, and our formula doesn't know about Ben's unique career before then. I included a projection for Russell based on his per play stats. The fact that a player like Tyler Thigpen (who was below average and a 7th round pick and hardly a star last year) has a similar projection in terms of games started to Jamarcus Russell (who has been horrible at age 24 as a the first overall pick) sums it up in a nutshell.

If you believe that the only reason Carson Palmer has played a lot more than Gibran Hamdan is because Palmer was drafted alot higher, then you can accept Gladwell's position. Otherwise, you probably cannot, at least to the extent Gladwell portrays, because we haven't accounted for the myriad of late round picks where the initial scouting met the performance teams were seeing in practice, and they never got any extended opportunity to play outside of the practice squad and pre-season contests. When we look at the top 20% of late round picks (those who are judged good enough to play or forced into action because of injuries) and they are roughly similar to the top 80% of high draft picks, that does not mean that late round picks are equal to early picks, and the NFL has a quarterback problem where nothing that happens before can predict what will happen in the future. Per play stats matter, and it's important to look at quarterbacks from that perspective, otherwise we reward compilers who get opportunities without merit. More opportunities matter too, though, and a quarterback who plays well over a larger sample size is likely better than a quarterback who plays well over a small one, particularly when qb stats are more volatile due to outside factors such as teammates.

This is a distinction that, as far as I can tell, Gladwell fails to grasp.

Perhaps most damning is the fact that they only scored 1 red zone TD (in two trips) against the miserable Browns, the NFL's 4th-worst scoring defense and its 2nd-worst D by yards per play allowed. Through the New England game they had scored 12 red zone TDs in four games, but they've sputtered badly of late once they get in the shadow of the opponent's goal posts, as Flacco's QB rating (a healthy 89.1 across all situations) is just 66.5 in the red zone. Compare that with Kurt Warner (110.3 red zone rating), Drew Brees (106.4), Peyton Manning (96.4), Tom Brady (95.8), Eli Manning (94.8), or even David Garrard (85.0), and it's easy to see why the Ravens aren't putting the necessary points on the board when they get close to the opponent's end zone. With their hopes of a return trip to the playoffs slipping away (they're 2-5 since beating Cleveland on September 27), Baltimore will have to start finishing their drives or the season could quickly become a bust.

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.

So I'm measuring, roughly, each team's ability to run, pass, stop the run and defend the pass. I could have, but chose not, to combine runing and pass defense. I'm not measuring these things as well as I could -- most significantly, I did not adjust for strength of schedule -- but I wanted to keep the data simple. I merely looked at how well, relative to league average, each team was in the four categories through their first ten games of the season.

I'll use the '01 Rams as an example. St. Louis rushed 416 times for 2,027 yards, an average of 4.87 yards per carry. The NFL average through ten games that season was 4.06 YPC, which (rounding errors aside) means the Rams averaged 0.82 more YPC than the league average. The Rams had an astounding 4,663 net passing yards (passing yards minus sack yards lost) on 591 net attempts (passes plus sacks); that average of 7.89 NY/A was 2.02 net yards per "attempts plus sacks" better than average. These Rams were pretty good on defense, too: they allowed 1,374 rushing yards on 366 carries in their first ten games; that 3.75 YPC allowed average was 0.30 YPC better than average. Their pass defense was even better, as the Rams allowed only 5.28 NY/A, 0.59 NY/A better than average.

I then added up each team's performance in each category relative to average to get a "team grade" relative to league average. The Rams '01 rating of 3.72 yards per play better than average (based on being 0.82 YPC and 2.02 NY/A better than average on offense, and 0.30 YPC allowed and 0.59 NY/A allowed tougher than average) was the best through ten games of any team from 1988 to 2007. I picked those years because I don't yet have 2008 point spread data in my database yet and because I wanted 20 years worth of data. In fact, here are the top 20 teams in terms of yards per play better than average through 10 games:

Okay, so now what? The very best teams teams are about 15-20 points better than league average, so (and this is where it gets really mathematical) I multiplied each team's "yards per play relative to average" score by five. That's it.

So now the Rams go from being 3.72 yards per play better than average to being 18.6 points per game better than average. I did this for all of the 601 team-seasons (through ten games) from '88 to '07. Now here's what you should be thinking: Chase picked four relatively arbitrary stats, combined them in a totally arbitrary way without explaining why, and then multiplied them by a number he picked from his you know what. How could these possibly be useful?

I then looked at the 11th, 12th, 13th and 14th games of the season played by those 601 teams. I set a point spread for each game, where the spread was equal to the difference between the two teams in my "points over average" score plus three points to the home team. So when the '01 Rams (+18.6) played in Atlanta (-9.1) in week twelve, I set the point spread at St. Louis -24.8 points. The actual point spread was St. Louis -8; that difference of 17 points was the largest difference between my projected point spread and the actual point spread in the study. There were 1202 games played in my data set (games 11-14 of the '88 to '07 seasons); 508 times (42%) the actual point spread was within three points of my projected point spread.

To see how my system did, however, you need to look at the most extreme games. In 462 games, my projected point spread differed from the actual point spread by 5.0 points or more. The team my system would say was underrated by the point spread covered in 297 of those games and failed to cover in 152 of them; thirteen games were a push. A 297-152-13 record translates to a .657 winning percentage against the spread.

If you focus only on games where the projected and actual point spreads differed by 8.0 points or more, the teams heavily underrated by the point spread were 136-63-7, for a .677 winning percentage. Bump the requirement to 10.0 points differential or more, and the undervalued teams went 74-29-4, an incredible 0.710 winning percentage.

What's this mean? Whatever inputs are used to figure out the point spread, two things are clear: some information is being overvalued (likely things such as record, turnovers, red zone efficiency, return touchdowns against teams besides the Steelers) and other things are undervalued (rushing and passing efficiency on both sides of the ball). My formula created to pick "winners" was not very advanced; in addition to some fuzzy math, I totally ignored important things like strength of schedule (made doubly bad since, no doubt, the points spread takes this into account), injuries, and all of the great advances Jason has made with respect to the intricacies of home field advance (many of them available here). So what do we do now?

Come up with predicted point spreads for games over the next four weeks, and see how this formula works. We won't have a large enough sample size to feel very confident even if it works -- there might be only 15 games where the numbers say a team is a really good bet -- but we might as well track them starting this season.

Thanks to Peter R. Wolfe, who makes the final score of all college football games publicly available, here are the NCAA SRS ratings through twelve weeks:

And the conference ratings:

• Worst teams in a Big 6 conference? Washington State (26.7 SRS, 1-10), Maryland (35.9, 2-9), Louisville (36.4, 4-7) and Indiana (36.8, 4-8).

• Best teams outside of the Big 6 conferences? TCU (65.6, 11-0), Boise State (60.0, 11-0), BYU (52.1, 9-2), Utah (49.9, 9-2) and Air Force (49.8, 7-5).

• Most dominant win this season? Oklahoma beating Texas A&M 65-10 in Norman (MOV of 38, SOS of 47.7, for an SRS score of 85.7). Runners up: Oregon 42-3 over Cal (30, 54.7, 84.7); Texas Tech over Oklahoma this weekend 41-13 (24.5, 59.9, 84.4) and Stanford over USC 55-21 (30.5, 53.6, 84.1).

• Most embarrassing loss by an FBS team? Toledo losing at home to Western Michigan (SRS of 32.0) 58-26 (MOV of -29.5, SOS of 32.0, SRS score of 2.5).

• Worst loss by a Big 6 conference team? Texas A&M falling 62-14 (and it wasn't even that close) to Kansas State. MOV of -34.5, SOS of just 44.8, for an SRS score of only 10.3.

That's because, out of all the players in NFL/AFL history to face the Broncos franchise, no quarterback has ever performed better against Denver than Rivers -- and it's not particularly close.

Minimum 200 attempts, here are the all-time leaders in passer rating vs. the Denver Broncos:

Rivers also boasts the best career yards per attempt against Denver, as well as the top completion percentage.

And if you pro-rated his lifetime statistics vs. Denver into a full 16-game season (using his career mark of 453 attempts per 16 games), Rivers has amassed the equivalent of a 4,378-yard, 29-to-9 TD-INT ratio campaign against the Broncos. Very impressive numbers indeed.

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