by Vincent Verhei

Jay Cutler and Philip Rivers were co-leaders in interceptions last season, but nobody threw more passes that should have been intercepted than Andrew Luck. Shaun Hill threw more interceptions than he probably should have, while no quarterback had better luck on bad throws than Drew Stanton.

Confused? Welcome to the murky world of interceptions, which are determined by lucky bounces and bad circumstances about as often as they are by player skill. That's why we developed adjusted interceptions. Here's the basic idea, which we first introduced four years ago:

We add in plays where the quarterback only escaped an interception because the defender couldn't hold onto the ball (dropped interceptions, which we've been tracking in game charting since 2007). Starting in 2012, we also included plays where the defender didn't straight-out drop the ball but instead had it knocked out of his hands by an offensive receiver (a "defensed interception"). These are listed as "Drop/Def INT" in the table at the end of this page.

We subtract plays where the interception (or a dropped interception) is tipped to the defender by a receiver who should have caught the pass. These are listed as "Tip INT" and "Tip AND Drop INT" in the table.

We subtract Hail Mary interceptions as well as interceptions thrown in desperation on fourth down in the final 2:00 of a game. These are listed as "HM/End Q4" in the table. We also bent the rules and included an interception thrown by Chicago's Jimmy Clausen against Detroit in Week 16 that came on fourth-and-10 with 2:02 to go in the game and the Bears trailing 20-14.

Obviously, there's going to be a little bit of subjectivity here, but our game charters do their best. If the defender has to dive for a ball only to have it bounce off his fingertips, that's not a dropped interception.

Of those three categories, it's dropped interceptions that explain most of the difference between actual interceptions and adjusted interceptions. Jay Cutler led the league with just three "Hail Mary" interceptions, and Matt Ryan and Philip Rivers were the only other players with more than one. It's similar for interceptions (and dropped picks) that bounced off a receiver's hands; Teddy Bridgewater led the league with three, and Shaun Hill and Derek Carr were the only other quarterbacks with more than one.

Interceptions are notoriously hard to forecast from year to year, because there's so much random chance and statistical noise involved. Historically, we've found that adjusted interceptions have a higher year-to-year correlation than standard interception totals and are a better predictor of future interceptions. For the entire period from 2007 through 2013, the correlation coefficient for adjusted interception rate (0.30) is twice as high as the correlation for actual interception rate (0.15). In each set of years except one (2011-2012), adjusted interception rate was a better predictor of interceptions the next year than actual interception rate.

As we mentioned in the intro, Jay Cutler and Philip Rivers were co-leaders in interceptions last season, with 18 apiece. It was Andrew Luck, though, who finished first in adjusted interceptions with 23. Cutler was second, but then you have to go through six other players (Andy Dalton, Blake Bortles, Eli Manning, Brian Hoyer, Drew Brees, and Peyton Manning) before you get to Rivers, whose overall numbers skewed high because opponents had an annoying habit of not dropping his passes.

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Both total and adjusted interceptions, obviously, are strongly correlated with total pass attempts, which is why rate stats can be more telling here. Or can they? Aaron Rodgers had the lowest interception rate in the NFL last year, and was virtually tied with Alex Smith (Smith was actually better by a tiny degree) for the adjusted interception rate lead as well. At the other end of the spectrum, Jake Locker had the highest interception rate and the highest adjusted interception rate in all of football. So for all our fancy math, the names at the extremes don't change much.

Contrasting the two rate stats, though, can be illuminating. Take the Rams' Shaun Hill. His raw interception rate of 3.1 percent was just 30th out of 42 qualifying quarterbacks, but his adjusted interception rate of 2.2 percent was fourth. Hill, Teddy Bridgewater, and Josh McCown were the only qualifying quarterbacks with fewer adjusted interceptions than raw interceptions. Bridgewater's ranking improved from 29th to 15th in the move from raw rate to adjusted rate; McCown's, from 40th to ... uh, 31st. Well, he's still Josh McCown, after all. Other big movers include Mark Sanchez (37th to 26th), EJ Manuel (18th to seventh), and Robert Griffin (26th to 17th).

Four quarterbacks dropped at least ten spots in the rankings when we move from raw interception rate to adjusted rate: Ryan Fitzpatrick (22nd to 33rd), Brian Hoyer (27th to 39th), Michael Vick (eighth to 34th), and Drew Stanton (12th to 41st). And now we must discuss the unbelievably lucky season Mr. Stanton enjoyed for Arizona. He threw only five actual interceptions last year, but 13 adjusted, an eight-pick difference that was the biggest in the league. Stanton and Vick were the only qualifiers last year who were more likely to see defenders drop their passes than actually intercept them. Eight of Stanton's passes resulted in dropped interceptions; only Brian Hoyer had more. Now remember this: Stanton only threw 241 passes (not including pass interference calls) last season, 31st in the NFL and less than half of Drew Brees' league-high 653. Think about how ridiculous it is that somebody with so few passing plays still finished so high in any counting stat, even in something obscure like dropped interceptions. Put it this way: in 241 passes, Stanton would have needed to average better than 20 yards per throw to finish second in passing yardage. To finish second in completions, he would have needed to connect on 172 percent of his throws, which would be impossible unless he started throwing two balls at once, and would even then still be very impressive. Coming into last season, Stanton had nine career interceptions in 187 passes, a rate of 4.8 percent that is much more indicative of his true passing abilities than his one-in-a-million 2014 campaign.

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Adjusted interceptions for defenses are a little weird, because you're basically rewarding teams for dropping interceptions. It's worth noting, though, that Jacksonville was last in the league with six interceptions, and they only dropped two others. That's eight interceptable passes in 16 games. 26 defenses had at least twice as many. Cleveland (13) and Cincinnati (10) were first and second in dropped interceptions. Perhaps it's the water in Ohio? Of course, they were also tied for second in total interceptions behind San Francisco, which had nine dropped picks itself. In other words, the key to dropping a lot of picks is being good enough to break up tons of passes in the first place. For individuals, Malcolm Jenkins (PHI), Perrish Cox (SF), Joe Haden (CLE), and Kendrick Lewis (HOU) were tied for the league with three dropped picks each. Atlanta's Desmond Trufant had four would-be INTs, but two of them were characterized by charters as "defensed" by the offensive player.

The following table lists adjusted interceptions for all quarterbacks with at least 200 pass attempts. Remember that most quarterbacks will have more adjusted interceptions than actual interceptions. The leaguewide interception rate is 2.60 percent, and the leaguewide adjusted interception rate is 3.30 percent. Therefore the blue "difference" column represents the difference between the two rates compared to that -0.70 percent average, so that positive always means "threw fewer picks than expected" and negative means "threw more picks than expected."

Player Team INT HM/

End Q4 Drop/

Def INT Tip INT Tip AND

Drop INT Adj INT Pass Att

(no DPI) INT Rate Adj Rate Dif

(vs. Avg) Andrew Luck IND 16 0 8 1 0 23 616 2.6% 3.7% 0.4% Jay Cutler CHI 18 3 7 0 0 22 562 3.2% 3.9% 0.0% Andy Dalton CIN 17 0 4 0 0 21 481 3.5% 4.4% 0.1% Eli Manning NYG 14 0 7 0 1 20 600 2.3% 3.3% 0.3% Blake Bortles JAC 17 1 5 0 1 20 474 3.6% 4.2% -0.1% Brian Hoyer CLE 13 1 9 1 0 20 440 3.0% 4.5% 0.9% Drew Brees NO 17 0 2 0 0 19 653 2.6% 2.9% -0.4% Peyton Manning DEN 15 0 5 1 0 19 595 2.5% 3.2% 0.0% Matt Ryan ATL 14 2 6 0 0 18 623 2.2% 2.9% -0.1% Philip Rivers SD 18 2 2 0 0 18 570 3.2% 3.2% -0.7% Player Team INT HM/

End Q4 Drop/

Def INT Tip INT Tip AND

Drop INT Adj INT Pass Att

(no DPI) INT Rate Adj Rate Dif

(vs. Avg) Derek Carr OAK 12 1 7 1 1 16 593 2.0% 2.7% 0.0% Ryan Tannehill MIA 12 1 6 1 0 16 590 2.0% 2.7% 0.0% Joe Flacco BAL 12 0 4 0 0 16 549 2.2% 2.9% 0.0% Matt Stafford DET 12 0 4 1 0 15 600 2.0% 2.5% -0.2% Geno Smith NYJ 13 0 2 0 0 15 366 3.6% 4.1% -0.2% Ben Roethlisberger PIT 9 0 5 0 0 14 600 1.5% 2.3% 0.1% Cam Newton CAR 12 1 4 1 0 14 446 2.7% 3.1% -0.2% Josh McCown TB 14 1 1 1 0 13 323 4.3% 4.0% -1.0% Ryan Fitzpatrick HOU 8 0 5 0 0 13 311 2.6% 4.2% 0.9% Drew Stanton ARI 5 0 8 0 0 13 241 2.1% 5.4% 2.6% Colin Kaepernick SF 10 0 2 0 0 12 479 2.1% 2.5% -0.3% Player Team INT HM/

End Q4 Drop/

Def INT Tip INT Tip AND

Drop INT Adj INT Pass Att

(no DPI) INT Rate Adj Rate Dif

(vs. Avg) Russell Wilson SEA 7 0 6 1 0 12 452 1.5% 2.7% 0.4% Kyle Orton BUF 10 0 2 0 0 12 445 2.2% 2.7% -0.2% Tony Romo DAL 9 0 3 0 0 12 433 2.1% 2.8% 0.0% Nick Foles PHI 10 1 3 0 0 12 313 3.2% 3.8% -0.1% Austin Davis STL 9 0 4 1 0 12 282 3.2% 4.3% 0.4% Tom Brady NE 9 0 2 0 0 11 581 1.5% 1.9% -0.4% Teddy Bridgewater MIN 12 1 3 3 0 11 397 3.0% 2.8% -0.9% Mark Sanchez PHI 11 0 1 1 0 11 309 3.6% 3.6% -0.7% Kirk Cousins WAS 9 0 0 0 0 9 204 4.4% 4.4% -0.7% Zach Mettenberger TEN 7 0 2 0 0 9 179 3.9% 5.0% 0.4% Player Team INT HM/

End Q4 Drop/

Def INT Tip INT Tip AND

Drop INT Adj INT Pass Att

(no DPI) INT Rate Adj Rate Dif

(vs. Avg) Jake Locker TEN 7 0 2 0 0 9 147 4.8% 6.1% 0.7% Mike Glennon TB 6 0 2 0 0 8 202 3.0% 4.0% 0.3% Aaron Rodgers GB 5 0 3 1 0 7 520 1.0% 1.3% -0.3% Alex Smith KC 6 0 0 0 0 6 466 1.3% 1.3% -0.7% Robert Griffin WAS 6 0 1 1 0 6 214 2.8% 2.8% -0.7% Shaun Hill STL 7 1 1 2 0 5 229 3.1% 2.2% -1.6% Carson Palmer ARI 3 0 2 0 0 5 225 1.3% 2.2% 0.2% Michael Vick NYJ 2 0 3 0 0 5 119 1.7% 4.2% 1.8% Charlie Whitehurst TEN 2 0 2 0 0 4 182 1.1% 2.2% 0.4% Colt McCoy WAS 3 0 1 0 0 4 128 2.3% 3.1% 0.1% EJ Manuel BUF 3 0 0 0 0 3 130 2.3% 2.3% -0.7%

Click here for a look at the adjusted interception numbers from 2013.