How many victories QBs are really worth

A productive Carson Palmer should improve Arizona's win total immensely in 2013. AP Photo/Jeff Chiu

The NFC West has learned in spectacular fashion just how much life can improve when a dynamic quarterback steps into the lineup.

The Arizona Cardinals saw it several years ago when they suddenly reached the Super Bowl with a rejuvenated Kurt Warner. The St. Louis Rams improved six games in the standings during their first season with Sam Bradford. Colin Kaepernick took the San Francisco 49ers within 5 yards of winning the Lombardi Trophy last season. The Seattle Seahawks' Russell Wilson wasn't far behind him as a rookie starter.

"One guy can change your whole outlook," new Cardinals coach Bruce Arians said earlier this offseason, before one guy changed his team's whole outlook.

The Cardinals' move to acquire Carson Palmer was the most significant player acquisition any NFC West team made this offseason -- not because Palmer is a great player at this stage, but because quarterbacks make all the difference and Palmer is so much better than the ones Arizona played with extensively last season.

Going from terrible to average (or above average) at quarterback means more than making similar improvements at positions of less importance. How much more does it mean? That is a question we addressed recently with regard to the effect Palmer could have in Arizona. It's one we'll consider in greater detail here regarding all the NFC West quarterbacks.

2008-12 Team W-L by Total QBR Range

In recent seasons, we have used Total QBR to measure quarterbacks' contributions to winning. The chart lays out won-loss records since 2008 in relation to scores on the 100-point QBR scale. These scores correlate closely with winning percentage. A team with a QBR score of 50 in a game has close to a 50-50 chance of winning, and so on.

From this, we can project how many added victories a quarterback provides his team in relation to predecessors, opponents, average quarterbacks and replacement-level ones.

The very best quarterbacks are easily identified. Teams can justify paying the best QBs whatever can be afforded from cash and salary-cap standpoints. But as we seek to separate hype from real value, it's helpful to know what the metrics say about specific players' contributions.

If evidence gathered over time suggests with some reliability that a quarterback adds two victories over average during a 16-game season, why pay him as though he adds four or five victories over average? These are issues teams should consider when deciding how much to pay their quarterbacks. NFC West teams specifically must decide over the next few years how much to pay Kaepernick, Wilson and Bradford.

With that, we take a look at what the evidence suggests for NFC West starters.

Carson Palmer, Cardinals

The level at which Palmer played for the Oakland Raiders last season should add about 2.8 victories relative to how the Cardinals' quarterbacks played last season. ESPN Stats & Information revised that figure down from 3.8 based on more accurate QBR scores for Kevin Kolb, John Skelton, Ryan Lindley and Brian Hoyer.

The methodology is pretty simple. We first average the 2012 single-game QBR scores for Palmer (44.2) and for the Cardinals' team as a whole (26.9). We then convert the difference between those figures (17.3) into percentage points and multiply by the number of games in an NFL regular season (16). The resulting figure approximates the number of added victories Arizona might realize if Palmer were to play at a similar level in 2013. For Palmer, it is 17.3 percent of 16 games, or about 2.8 games.

So, while QBR said Palmer was below average last season, it said the Cardinals were much worse than that. That is why Palmer can make such a big difference for Arizona even if he is once again slightly below average. And if Palmer were to pump up his play to a Pro Bowl level -- say, the 65.0 range on average -- the Cardinals could expect 6.1 additional victories over last season from the quarterback position alone.

Russell Wilson, Seahawks

Wilson's value to the Seahawks became increasingly pronounced as the 2012 season progressed. The difference between his average QBR score for the regular season (63.9) and the Seahawks' average score for 2011 (38.3) gave him credit for an additional 4.1 victories over 16 games.

Seattle improved from 7-9 in 2011 to 11-5 last season. Factors beyond quarterback play differentiated the Seahawks from one year to the next, of course. But none of them came close to the impact Wilson made.

That impact grows considerably if we focus more on how Wilson was playing later in the season, counting playoffs. His QBR averaged 75.2 over his final 11 games; projected over the course of a 16-game season, that works out to 5.9 added victories for Seattle relative to 2011.

Colin Kaepernick, 49ers

The 49ers were already a very good team when Kaepernick took over as the starting quarterback last season after former starter Alex Smith suffered a concussion (Kaepernick kept the job when Smith was healthy enough to play). Smith was playing at a high level, so the 49ers had less room for improvement.

Still, the numbers say Kaepernick (73.3 average QBR) provided an upgrade amounting to an additional 1.6 victories over a full regular season relative to what the team could have expected with Smith (63.0 average). The figure would grow to 2.9 additional victories with Kaepernick (versus 1.2 with the improved 2012 version of Smith) relative to the quarterback play San Francisco received in 2011.

Those numbers take into account how Kaepernick played during the regular season, when he started the final seven games. Factoring his performance in the playoffs would change the figures upward very slightly.

Sam Bradford, Rams

Bradford enters his fourth season with much at stake. He has yet to deliver on expectations, but there have been quite a few mitigating factors. Bradford has been injured at times. His supporting cast has been weak. What has he meant to the team?

There is no question Bradford improved last season. His average QBR score (50.1) was just that -- average. But it was substantially better than the Rams' 25.4 average from 2011, when Bradford was injured and sometimes unavailable. QBR says the improvement was worth an additional 4.0 victories for a team that improved from 2-14 to 7-8-1.

We can also see that Bradford's rookie average (42.1) was a substantial upgrade from where the Rams stood without him in 2009 (23.2). The difference then was 3.0 victories, providing some perspective for the role Bradford played in the Rams' improvement from 1-15 in 2009 to 7-9 in 2010. He was important, but he wasn't everything.

The Rams could expect to add another 2.4 victories from 2012 to 2013 if Bradford were to improve his 50.1 average QBR score from last season to 65.0, which ESPN considers near a Pro Bowl level.