Inside Derek Carr's rapid improvement

— -- Derek Carr threw for 513 yards and four touchdowns Sunday, and now he's one of the hottest stories of the NFL season. Carr has helped lead the Oakland Raiders?to a 6-2 record -- tied for first in the AFC West through eight games. He's also garnering legitimate MVP hype?and has emerged as the far-and-away star of the 2014 quarterback draft class.

How has he done it? The numbers provide some insight into Carr's development, as well as the Raiders' strong work in creating a winning environment around him. Let's take a closer look, with help from ESPN Stats & Information senior statistics analyst Jacob Nitzberg.

Carr was a polarizing draft prospect three years ago, in part because of the spread system he ran at Fresno State and also because of an alarming dip in production when pressured. He was incredibly accurate when in a clean pocket during his college career, completing 72 percent of those passes. But when under duress, his completion percentage dropped to 29 percent.

If Carr reacted that poorly to pressure in college, some wondered how he could possibly succeed in the NFL. Check out the chart.

Derek Carr under pressure, since 2014

As you can see, Carr struggled under pressure -- defined as dropbacks in which a quarterback is sacked, hit or put under duress -- in his first two seasons. This season, however, he has improved his Total Quarterback Rating (QBR) in those situations to 51.3, sixth best in the NFL. For context, the league average when under pressure is 30.6.

Carr appears to have made an adjustment in those situations, mostly throwing shorter passes when facing a heavy rush. From 2014-15, 25 percent of his passes under pressure traveled at least 15 yards downfield, and 13.4 percent went 20 or more yards downfield. This season, those percentages have dropped to 18.9 and 5.7, respectively.

That increase in higher-efficiency throws has spurred a significant reduction in off-target throws while under pressure, as illustrated in the chart below.

Derek Carr percentage of off-target throws under pressure

While it's clear that Carr has engineered improvement in an area that vexed him both in college and in his first two NFL seasons, here's a dirty little secret: The Raiders have minimized the pressure he has faced far better than most NFL franchises.

Carr has been sacked only nine times this season, fewest in the NFL for quarterbacks who have played eight games. Overall, he has been pressured on only 20.3 percent of his dropbacks, the third-lowest rate in the league.

The following gives you a sense of the disparity in sack rates between Carr and the NFL average. The takeaway: There are quarterbacks who are being sacked at a rate more than three times that of Carr.

2016 NFL quarterback sack rate

You might be wondering whether Carr is getting great protection, or if he's using his compact release to throw before the pass rush gets to him. Well, it's more the former than the latter. His average time before throwing this season is 2.47 seconds, slower than 20 other quarterbacks.

Here's the truth: The Raiders have made a big commitment to building their offensive line. They made Rodney Hudson the NFL's highest-paid center in 2015, then made free agent Kelechi Osemele the league's highest-paid guard in the spring. And the Raiders re-signed Donald Penn to play left tackle, allowing Osemele to remain at his natural position.

The Raiders have committed more salary-cap space to their offensive line than any other team in the NFL, and nearly?65 percent more than the league average.

2016 salary-cap commitment to O-line

Add it all up, and Carr has become one of the league's most efficient and productive quarterbacks. In his final season at Fresno State, Carr threw 50 touchdown passes and only eight interceptions. But would you believe he actually has a better touchdown-to-interception ratio in the NFL this season?

That's right; Carr has thrown 17 touchdowns against three interceptions, and his ratio of 5.67 is second only to Sam Bradford (eight touchdowns and one interception) as the best among QBs with at least five starts. Neither Tom Brady (12:0) nor Brian Hoyer (6:0) have enough starts to qualify.

Best TD/INT rate, 2016 (min. five starts)

Carr has had plenty of help this season. In addition to a well-fortified offensive line, his wide receivers have added an NFL-high 244 yards after first contact. The Raiders also have an accomplished offensive coaching staff, starting with coordinator Bill Musgrave, offensive line coach Mike Tice and quarterbacks coach Todd Downing.

Still, there have been missed opportunities to produce at an even greater rate. As a team, the Raiders have the NFL's seventh-worst drop rate at 5.3 percent. But no matter how you look at it, or whatever qualifiers you find, Derek Carr is having a breakout season.