I was wrong about Derek Carr.

Over the offseason, I questioned -- not  Christian Ponder and Josh Freeman. Not great, Bob!

The follow-up written on Carr simply dug into his horrible circumstances, to which I concluded the following:

The reason I brought up Carr's first-season NEP numbers and compared them to historical rookies is because there seems to be a trend in first-year performance -- in terms of Passing NEP -- predicting career-long success. This doesn't mean that this is a foolproof way of determining how well a quarterback's NFL career will go. Rather, this is a game of probability -- players who have played like Derek Carr in the past have typically not gone on to have sensational careers in the league.

To pinpoint examples would be the same as saying that teams should forgo drafting a quarterback in the early rounds of the NFL Draft because Tom Brady was found in the sixth round. Meanwhile, the majority of "hits" at the quarterback position are still coming early. You can't let exceptions overshadow the rule.

The fact is, Derek Carr had the 77th worst season from a quarterback with 200 or more drop backs since 2000 (there were 539 of these instances) in Passing NEP during a pass-friendly era. When looking only at rookie quarterbacks, his score ranked in the bottom-quarter percentile. Regardless of his weapons -- regardless of his running game -- this cannot be defined in any way, shape or form as good.

That's why I don't have a lot of optimism moving forward.

The idea of not letting exceptions overshadow the rule is important here. Because Carr has really been the exception, not the rule.

Major Improvements

The use of data in football is always a debated topic because, unlike a sport like baseball, there's more than a single one-on-one matchup happening in a given moment. It's not just pitcher versus batter -- it's 11 players versus 11 players, all with unique and individual matchups that change on each play.

Data doesn't capture absolutely everything. Context is always important, which is why I wrote the follow-up article on Carr in the first place. 

But data can tell us a whole lot, as it captures every play a player makes, something our brains can't cognitively do when watching film.

I bring this up because some statistics are better than others. Quarterback wins, for instance, don't tell us a whole lot -- if one quarterback plays identically to another, but that same quarterback loses more games, why is it the quarterback's fault?

Raw yardage, touchdown and interception totals don't tell us everything, either. Yards can be skewed heavily by garbage time, touchdowns by opportunity and play-calling, and interceptions by risk-aversion. 

This is all a huge reason Net Expected Points exists. Rather than assuming a 10-yard gain on 3rd-and-15 is the same as a 10-yard gain on 3rd-and-9, NEP captures the true impact each play makes based on how it changes a team's expected scoring.

For purposes of analyzing Carr's Year 1 to Year 2 change, we'll be looking at metrics that have correlated strongly to winning at the quarterback position: Passer Rating, Yards per Attempt (Y/A), Adjusted Yards per Attempt (AY/A), and Adjusted Net Yards per Attempt (ANY/A). If you need a refresher on any of these statistics, take a look at ProFootballReference.com's glossary.

According to Pro Football Reference's [amazing] data, 125 quarterbacks have attempted at least 200 passes during their rookie campaigns in NFL history. (For the record, that includes this season.) Among these quarterbacks, 89 attempted another 200 in their second season. 

This is the subset we're concerned with.

Now here's the fun stuff -- take a look at the top-five quarterbacks in Passer Rating improvement from Year 1 to Year 2:

Hey, look who's there -- it's Derek Carr! Among the 89 quarterbacks who threw 200 or more passes in both Year 1 and Year 2, Carr's jump in Passer Rating (granted, we're still not finished with his second season) is fifth best. Fifth best in NFL history.

Here's a look at quarterback improvements in Y/A, AY/A, and ANY/A from Year 1 to Year 2:

Derek Carr. Derek Carr. Derek Carr. Yup, he's one of the best improvement-wise in these categories, too.

In case you're wondering, the same holds true within our Passing Net Expected Points per drop back metric. Since the turn of the century, here are the most improved passers from Year 1 to Year 2:

You've probably noticed two names popping up pretty consistently here: Josh Freeman and Nick Foles. This isn't all that surprising, not only because of their bad rookie seasons, but because of their anomalous -- yes, anomalous -- second seasons in the league.

After only starting six games and playing in seven during his rookie year (he hit the 200 pass attempt threshold), Nick Foles, if you recall, had a 27-to-2 touchdown-to-interception ratio during his sophomore campaign. He's the only quarterback since the merger to throw 20 touchdowns -- let alone 27 -- while tossing 2 or fewer interceptions. Remember when I talked about touchdowns and interceptions not telling the whole story? Foles, who's now benched for Case Keenum on a completely different team just two years later, is a perfect example of that.

Freeman's jump was a little more believable, as he was able to take care of the football, throwing just six interceptions during his second year. But his interception rate was also kind of an outlier -- among every quarterback who dropped back to pass at least 200 times during their second NFL season (185 quarterbacks), Freeman's interception rate was only worse than the aforementioned Foles.

In other words, we have two quarterbacks in the modern era making Carr-like Year 1 to Year 2 jumps, and both had outlier seasons -- seasons that were nearly impossible to predict.

What Does This Mean for Carr?

To be clear, this isn't me telling you Derek Carr is going to suffer the same fate Nick Foles and Josh Freeman have. Instead, it's to point out that Carr's progression is something we just rarely, rarely see.

There are valid and honest reasons for his improvement, of course. The Raiders switched up their coaching staff, they added playmakers for him to throw to, Latavius Murray looks like he's here to stay, and the offensive line has meshed together to form one of the better units in football.

Those are the reasons to feel optimistic about Carr's future. Whereas players like Foles and Freeman saw a wild boost in production based on little, Carr's increase in value has come not only because he's gotten better as a passer, but quite literally every circumstance around him became better. Everything hit. It's been the perfect storm.

To me, Derek Carr is always going to be the quarterback who brought fire to my Twitter mentions and email inbox (you keep being you, Raider fans). But to math, Derek Carr is always going to be the quarterback who broke probability. 

And it's because Derek Carr is truly an outlier.