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Cobbled this together from two ESPN articles, one today and the latter from 4/2014... some pretty interesting looking prognosticatory evidence. May be more than most care to read. TL
R: QBR over first 16 starts looks like a very good predictor.
For reference, 2014:
(Bridgewater and Bortles each played >70% of snaps in another game, not included as "starts" above)

Was Carr's 2014 season a true showcase of the player he is and will be, or is it too early to tell?
ESPN Insider Mike Sando explored the topic last April and found that quarterbacks generally don't show great improvement in Total QBR beyond their first 16 starts.
There have been 44 quarterbacks to make their first 16 NFL starts since 2006 (not including Carr), and the average difference in QBR from their first 16 starts and their career totals is just 5.1 points.
Quarterbacks who started with a QBR under 40 (as Carr did) have seen even smaller differences (3.9 points on average). The biggest increase was by Mark Sanchez, whose career QBR is 9.8 points better than his first 16 starts (28.9).
A QBR of 50.0 is considered average, so Carr would need an improvement of nearly 12 points over his career to reach that mark. Only Matthew Stafford, who has improved by 13.4 points from his first 16 starts, has reached those levels. Stafford also had the talent level to be drafted No. 1 overall in 2009, and dealt with injuries early in his career.
What if how a quarterback plays right away tells an organization what it needs to know? Evidence collected over the past eight seasons supports that thinking almost without exception, providing a clear lens for viewing the game's most important position.
"The QBs who do well ultimately, do well as rookies or in their first season of starting -- they show you," ESPN analyst and six-time NFL executive of the year Bill Polian said. "If they are not above a certain threshold after their first 16 games, the odds are pretty good that they will not be a franchise quarterback. The odds are even stronger that they will wash out completely."
We have found strong trends among the 41 quarterbacks making their first 16 starts over the past eight seasons. The QBs with the worst performance metrics over those initial 16 starts flamed out. The fast starters reached the playoffs in every case, playing in three of the past five Super Bowls. Their futures appear bright. The QBs in the middle look as though they'll remain there in the majority of cases.
Every situation is different, of course, and many factors dictate whether a quarterback ultimately succeeds, but there have not yet been many exceptions to this general rule...
The seven fastest starters are on their way
A four-year body of work allows for definitive evaluation in most cases, and Total QBR agrees. The metric, explained here and vetted most recently by Chase Stuart of Football Perspective, identifies the best quarterbacks over time. For example, a look at quarterbacks with at least 60 starts since 2006 showed Peyton Manning, Aaron Rodgers, Tom Brady, Drew Brees and Matt Ryan as the only ones with QBR scores above 65.0, which ESPN has identified as a general cutoff for Pro Bowl-caliber play. Sixty starts was the cutoff because that is roughly how many we might expect a quarterback to make over the four-year period Polian thought was sufficient for a full analysis.
Code:QBR Leaders: First 16 starts* Rank QB W-L QBR 1 M.Ryan 11-5 73.4 2 T.Romo 11-5 72.1 3 R.Griffin 9-7 71.8 4 R.Wilson 11-5 71.7 5 C.Kaepernick 11-5 70.8 6 A.Rodgers 6-10 66.4 7 A.Luck 11-5 65.2 * Since 2006
With guidelines for top-notch play established, I pulled together a list showing the 41 quarterbacks who made their first 16 starts over the past eight seasons. We chose 2006 as the starting point because that is how far back the Total QBR data reaches, and eight seasons seemed like a manageable time frame.
The first chart lists the seven players sitting atop that 41-player list. These are the quarterbacks with the highest QBR scores over their first 16 games. Every one of those players appears headed down a generally successful path, with a couple of concerns: RG III stands out because his performance fell off last season following a knee injury, and Colin Kaepernick has played less than the others.
Generally speaking, an especially strong first 16 games in the absence of an injury such as the one Griffin suffered seems to foreshadow continued production whether or not the player went to a strong team. Philip Rivers was the next player on the list with a 60.1 QBR score for his first 16 games. From there, the names become a blur of mediocrity, crossed fingers and worse.
Ominous outlook at the bottom
The second chart shows which of the 41 players had the 15 lowest QBR scores for their first 16 career starts. The bottom nine -- Brady Quinn through Gabbert, with five first-round choices in that range -- have pretty much run their course as viable starters. Some of them, such as Sanchez and Tarvaris Jackson, played for teams with outstanding defenses. That helps explain why those two had better won-lost records than the other players with especially poor performance metrics.
Code:QBR laggers: First 16 starts* Rank QB W-L QBR 27 M.Stafford 6-10 40.3 28 T.Tebow 9-7 39.8 29 M.Moore 7-9 39.5 30 S.Bradford 7-9 38.2 31 Kevin Kolb 6-10 38.0 32 G.Smith 8-8 35.9 33 B.Quinn 4-12 35.9 34 T.Jackson 8-8 35.3 35 M.Sanchez 9-7 34.6 36 B.Gradkowski 5-11 34.6 37 J.Russell 5-11 32.2 38 K.Clemens 6-10 27.7 39 J.Skelton 8-8 27.1 40 B.Weeden 5-11 25.8 41 Blaine Gabbert 4-12 21.8 * Since 2006
The information in this second chart supports the idea that players who struggle to produce early do not succeed in the long run, either. The implications for Stafford, Bradford and Smith are of particular interest. Stafford and Bradford joined terrible teams as rookies. Stafford has played better more recently, and Bradford has shown some positive signs without sustaining success. But neither has established himself as a consistent performer.
Smith, meanwhile, has played just one season. Conventional wisdom says it's far too early to draw conclusions on a player who was rushed into the New York Jets' lineup without sufficient weaponry to support him. That could be true. But we also know that a 35.9 QBR score through 16 starts puts Smith in a potentially precarious position one slot above the nine flameouts. As Polian said, the good ones tend to produce at a higher level right away, even when they join teams that had losing records before their arrival.
A quick look at the middle
The next chart shows quarterbacks falling between the two extremes through their initial 16 starts. Nine of the 19 are projected starters heading into the 2014 season, but of those nine, only Rivers has established himself as a consistent upper-tier quarterback. As noted, he was quite productive through his first 16 starts.
Code:QBR middlers: First 16 starts* Rank QB W-L QBR 8 P.Rivers 14-2 60.1 9 D.Anderson 9-7 59.1 10 M.Cassel 10-6 57.9 11 N.Foles 9-7 57.8 12 V.Young 10-6 57.3 13 C.Henne 9-7 56.5 14 C.Newton 6-10 56.2 15 J.Cutler 7-9 53.4 16 J.Locker 7-9 52.7 17 R.Tannehill 7-9 50.4 18 S.Hill 10-6 50.4 19 A.Dalton 9-7 49.8 20 M.Leinart 7-9 49.1 21 J.Campbell 7-9 47.5 22 J.Freeman 8-8 44.8 23 C.Ponder 6-10 43.9 24 T.Edwards 10-6 43.7 25 J.Flacco 11-5 43.1 26 C.McCoy 5-11 42.0 * Since 2006
For reference, consider that QBR scores correlate closely with winning percentages, so that teams averaging a QBR score around 50 will win about half their games over time. Eight of 39 qualifying quarterbacks finished 2013 with scores of 65 or higher, while 10 were beneath 40. Some of the players we're most interested in analyzing fell between those extremes through their first 16 starts and have yet to take a big step forward, so precedent isn't particularly encouraging.
A head coach and team executive consulted for this piece liked the research without buying in completely. The coach thought running the ball successfully was the No. 1 variable for most quarterbacks in general. He thought a team's commitment to the ground game was largely responsible for separating the "successful" and "unsuccessful" players listed in the charts. The executive said there were too many variables for a single performance metric to tell the full story.
"One of the arguments against metrics is, this is a team game and highly complex and not easily measurable," Polian said. "On the other hand, I think you could hypothesize that because the quarterback position is so important, there needs to be an objective way of measuring how that guy is performing and growing. It is not perfect. There are no absolutes. But it does give you at least some pretty serious food for thought in terms of how you construct your team and what your quarterback might become. The hypothesis that they will show you something early is overwhelmingly true."
For reference, 2014:
Derek Carr, 16 starts, QBR = 38.4
Blake Bortles, 13 starts, QBR = 21.9
Teddy Bridgewater, 12 starts, QBR = 50.2
Blake Bortles, 13 starts, QBR = 21.9
Teddy Bridgewater, 12 starts, QBR = 50.2
(Bridgewater and Bortles each played >70% of snaps in another game, not included as "starts" above)