50 Best Seasons in the NFL - Interceptions Thrown

In my previous post, I was discussing the merits of who got voted into the 2009 Pro Bowl versus who should be in. In doing so, I discovered an important fact. Jeff Garcia, Jason Campbell and Chad Pennington are having exceptional seasons, in terms of infrequency of interceptions thrown. So I decided to look back in history.


[Note: As I write this post, Pennington has thrown an interception against the Chiefs, and Garcia has thrown two against the Chargers.]


The table below shows the 50 best seasons in the NFL, as far as interceptions thrown. I have also included the component calculation that goes into the NFL passer rating formula.


Steve DeBerg's 1990 season ranks as the all-time near perfect season. His season, as well as David Garrard's 2007 season ranks as the only two seasons in NFL history, where less than 1.0% of a quarterback's pass attempts were intercepted. I have previously shown that the average interception rate in the NFL has continually decreased (or, that the interceptions component in the current NFL passer rating formula has increased). To be fair then, this list below is biased towards the more recent players. To make a true apples-to-apples comparison, one really needs to relate each of these seasons relative to the average rate in that season, something I hope to do in a future posting.


According to this table, in absolute terms (in other words, not relating each season to that season's average), the seasons that Campbell, Garcia, and Pennington are having in 2008 all rank in the Top 30, with Campbell's season ranking 11th-best all-time. Notice that both Garcia and Pennington have had seasons previously that are also in the Top 30.


I also want to point out two of the phenomenal seasons of Hall-of-Fame member Bart Starr. His 1966 season ranks 6th all-time in absolute terms (perhaps moving him up in the top 5 in relative terms), and his 1964 season ranks 19th all-time in absolute terms (in relative terms, it is most likely a Top-15 season, perhaps even a Top-10).

Debating the 2009 Pro-Bowl Selections

Earlier this week, the NFL announced the rosters for the 2009 Pro Bowl.  Representing the AFC are QBs Peyton Manning, making his ninth appearance, Jay Cutler, making his first appearance, and Brett Favre, making his tenth appearance, but first time representing the AFC.  Representing the NFC are QBs Kurt Warner, making his fourth appearance, and Drew Brees and Eli Manning, who is making his first appearance.  This will be the first time that brothers playing quarterback have been selected to the Pro Bowl.

I am really not sure what criteria the voters (the players) use to select these quarterbacks.  Some probably use statistics, such as the quarterback rating, even though no one actually understands the QB rating or how it is derived.  Some probably look at the team's performance, even though the quarterback may have little to do with the team's actual performance, or won-loss record.  And then some may simply be basing it on some other factors, such as like-ability, or popularity.  Based on the selections, it appears that voters reward players for a good team record and # of touchdowns thrown (to the average fan, these two factors seem like reasonable criteria, I'm sure).  I of course disagree, but then again, that is the reason for this post.  

The Pro Bowl is meant to be a reward for performing exceptionally well on the field, and, since it is voted on by the players, a recognition from one's teammates as well as competitors.  So how do these selections stack up?

Before I get into the details, a quick refresher on the NFL passer rating calculation.  I'll keep the math simple.  The NFL passer rating is made up of four different components (see here for the details), each with a maximum possible value of 2.375, and a minimum possible value of 0.  The four components are given equal weight in the calculation of the rating.  The four components are:

Pass Completion percentage

Yards per Completion

TDs per Attempt (Touchdown percentage)

INTs per Attempt (Interception percentage)

In the table below, I show how each of the quarterbacks scored on each component, how that translated to their QB rating, and their respective ranks (amongst each of the four components as well as the final QB rating).  I also include CMI for each quarterback, and I have previously discussed my preference for CMI versus the current NFL passer rating formula.  The players shaded in green were the ones voted in.  The players shaded in blue are my obvious snubs, and the players shaded in orange one could argue deserve to go.

Ok, now on to the #s.

AFC

Peyton Manning - As I mentioned in a previous post, he is having another great year.  He has a passer rating of 90.3 (through 14 games).  In the AFC, he ranks 5th, 7th, 4th and 6th in each of the components, good enough for 4th in terms of passer rating.  He is 3rd in the AFC in terms of # of touchdowns passes.  He has led the Colts to a 10-4 record.  He is 2nd in the AFC in terms of CMI.  Very difficult to argue against the selection.

Brett Favre - For the four components, he is ranked 1st, 9th, 2nd and 16th, good enough for 7th overall in passer rating in the AFC.  He has taken the Jets to a 9-5 record, and he has thrown 21 TDs, fourth amongst AFC quarterbacks.  He has also thrown 17 INTs, worst in the NFL.  He ranks 7th in the AFC in CMI.  Based on statistics, should not have made it.  The only explanation is that he is probably perceived to have helped turn around the Jets, and he has thrown a lot of touchdowns.

Jay Cutler - Jay Cutler got off to a red-hot start, and has since cooled off.  He ranks 9th, 4th, 3rd and 11th on each of the four components, placing him 5th in the AFC in Passer Rating.  The Broncos are 8-6, and his 24 touchdowns are second only to Philip Rivers' 28.  His CMI places him 9th in the AFC.  Based on statistics, again hard to see why he got voted into the Pro Bowl.

NFC

Kurt Warner - He led the Cardinals to a 8-6 record and the NFC West Division title.  He ranks 1st, 4th, 4th and 7th in each of the components, good enough for 2nd in the NFC in passer rating.  He has thrown 26 touchdowns, 2nd best in the NFC.  He ranks 2nd in CMI in the NFC.  Based on the #s, good enough to go.

Drew Brees - Started out blazing, but has had a couple of mediocre games recently.  Has led the Saints to a 7-7 record, and has thrown a league-high 28 touchdowns.  He has also thrown an NFC-high 16 interceptions.  He ranks 3rd, 3rd, 2nd and 10th in each of the components, good enough for 4th in the NFC in terms of passer rating.  He ranks 4th in CMI.  An acceptable choice for the Pro Bowl.

Eli Manning - He has led the NY Giants to an 11-3 record, coming off that Giant upset in last year's Super Bowl against the previously undefeated Pats.  He has thrown 20 touchdown passes, only 6th-best in the NFC.  His ranks in the four components are 10th, 11th, 5th and 5th respectively - making his passer rating only 9th-best in the NFC.  His CMI rank is 10th.  Clearly a sentimental pick here.  I would not have voted him in.

In summary,

Peyton Manning - In

Brett Favre - Out

Jay Cutler - Out

Kurt Warner - In

Drew Brees - In

Eli Manning - Out

Obvious Snubs

There are two, in my mind - one each in the AFC and NFC, respectively.  

In the AFC, Chad Pennington is an obvious snub.  Clearly, he doesn't get attention amongst his peers, because he doesn't throw a lot of touchdowns.  I've never understood why throwing a touchdown is so important to determining how good a passer someone is.  CMI, which has a 97% correlation with the current NFL passer rating, doesn't include touchdowns.  Pennington has thrown for only 14 touchdowns.  He has led the Miami Dolphins to a 9-5 record (keep in mind that Miami only won 1 game last season).  Based on the four components, he ranks 3rd, 3rd, 10th (the component associated with TDs), and 1st, good enough for second-best in the AFC in passer rating.  He ranks 1st in CMI.

In the NFC, Jeff Garcia is an obvious snub.  Although he has led the Bucs to a 9-5 record, he suffers from the same 'disease' that Pennington has.  He doesn't get a lot of recognition around the league for how good he is because he doesn't throw a lot of touchdowns.  He has 'only' thrown 10 touchdowns.  That hurts him in terms of passer rating, as he ranks, 2nd, 7th, 12th and 1st in each of the components, good for 3rd in the NFC in terms of passer rating.  He ranks #1 in the NFC in CMI.

Possibly Overlooked

In the AFC, both Matt Schaub and Philip Rivers have possibly been overlooked.  Matt Schaub has led the Texans to a 7-7 record, and has a passer rating of 92.7, 3rd-best in the AFC.  In terms of the four components, he ranks 2nd, 2nd, 6th and 13th, respectively.  He is 3rd in the AFC in CMI.  Philip Rivers, although having a good year (in terms of the traditional touchdowns thrown), suffers from the Chargers being 6-8.  He leads the NFL in passer rating at 101.4, and leads the NFL in touchdowns thrown with 28.  He ranks 6th, 1st, 1st and 7th in each of the components, and ranks 4th in the AFC in CMI.

In the NFC, Jason Campbell and Aaron Rodgers have both been overlooked in my opinion.  Campbell's Redskins are 7-7 on the season, and he has thrown 'only' 12 touchdowns.  He ranks 7th, 12th, 13th, and 2nd in each of the four components, good enough for only 10th in terms of passer rating.  He ranks 3rd in CMI.  What hurts Rodgers most is the fact that the Packers are 5-9.  He ranks 4th in the NFC in touchdowns thrown, with 23.  He ranks 4th, 6th, 3rd and 9th in the four components, good for 6th in the NFC in passer rating.  His CMI rank is also 6th.

In looking at all these quarterbacks, something struck me, and that is the exceptional seasons that Garcia, Campbell and Pennington are having in terms of the infrequency of interceptions thrown (see here for their stats).  I'll have a post on this later.

It appears to me that what gets attention (and votes) is winning and throwing touchdowns.  At some point I will do an extensive analysis showing the relationship between a quarterback and winning.  What doesn't get attention (but should) is interceptions thrown.  

The table below shows the stats for the NFL's quarterbacks through 14 games this season (only those who 'qualified' (i.e. those throwing at least 224 passes) are shown.

Is Peyton Manning Having a Good Year?

Peyton Manning had a great game last night against the Jaguars, leading the Colts to a 31-24 victory, and a spot in the playoffs.  That makes it three games in a row now that he hasn't thrown an interception.  During that span, he has completed over 80% of his passes.

However, it seems to me that he hasn't received his proper due this year.  Perhaps it is because he has been rather mediocre until this recent stretch.  He did have three terrible games (week 3 at home against these same Jaguars, where he threw 2 picks and the Colts lost 23-21, week 7 on the road against the the Packers, where he threw two picks, and the Colts lost 34-14, and week 13, on the road against the Browns, where he again threw 2 picks, yet the Colts won 10-6).  He has thrown 2 picks in two other games this season, making it a total of 5 games this year where he has thrown at least two picks.  To truly appreciate how good Manning has been, consider this: Since 2002, he has never had a season where he threw 2 or more picks in a game in more than 2 games.

The table below compares each of Manning's years in the NFL.  For sake of comparison, I have included the league average CMI for qualified passers only - i.e. those who attempted at least 256 passes in a season (224 for the 14 games completed so far in the 2008 season).  The chart illustrates that the league average CMI has been steadily increasing during these years, and Manning continues to perform better than the league (he has done this every year, except for his rookie season - 1998).

From this data, I would conclude that he is indeed having a good year, at least as compared to the league.  He is having a typical year for him.

In the table below, the column "Manning CMI rel to League Avg" is calculated as follows:

Manning CMI Rel = [Manning CMI - League Avg CMI] / Std Dev of League Avg CMI

For example, for 2008,

Manning CPI Rel = [0.599 - 0.542] / 0.052 = 1.08

Is Matt Cassel The New Tom Brady?

Matt Cassel of the New England Patriots is having a good year.  He is 13th in the NFL in Passer Rating, after 14 games.  And, in what may seem eerily similar to one Mr. Tom Brady, he replaced Brady in the first game of the season, when Brady was lost to the season as a result of a leg injury.  Flashback to  September 2001, and the aforementioned Brady, replaced Drew Bledsoe as the quarterback of the New England Patriots.  The rest, as they say, is history.

That year, Tom Brady had a great year.  A dream year.  Replacing Bledsoe in the 2nd game of the season, he went on to lead the Patriots to an 11-5 regular season record, and on to win Super Bowl XXXVI, 20-17 over the St. Louis Rams.  Brady was selected to the Pro Bowl, and was named Super Bowl MVP.  He finished 6th in the NFL in passing, with a Passer Rating of 86.5, and he had a CMI of 0.552 (see the table below).  That year, the league average CMI was 0.497, and his CMI was 1.25 Standard Deviations above the average.  Only Rich Gannon (2.54), Kurt Warner (1.57), and Jeff Garcia (1.33) had a better year that year.  

The graph below the table shows that he started out a little slow (understandably so), and played fairly consistently throughout the year, with a few spectacular (and one not so spectacular) games thrown in.  He didn't throw an interception in his first five games, but then threw 4 in a 31-20 loss at Denver in game 6.  All in all, he didn't throw a pick in nine games, the Patriots going 7-2 in those games.

So, how is Matt Cassel doing trying to imitate Tom Brady?

As mentioned earlier, his current Passer Rating is 87.1, a shade higher than Tom Brady's 86.5.  His CMI is 0.568, also better than Brady's 0.552.  He has six games to-date where he has not thrown an interception, leading the Pats to a 5-1 record in those games.  So how does Cassel's CMI of 0.568 compare to Brady's 0.552?  This is where the comparison ends.  In 2008, the league average CMI is 0.542, so Cassel's performance is 0.49 Standard Deviations above the average.  Good, but not great.  Good for 9th out of 30 quarterbacks who have thrown enough passes to qualify.  The table below shows a game-by-game comparison of Cassel's performances compared to Brady's 2001 season.

CMI - 1940 to 2007

I thought I had posted this earlier.  It is a set of graphical illustrations of CMI from 1940 to 2007.  For comparison sake, I have included NFL average QB Rating in the 2nd graph.  CMI is defined as follows:

CMI = Completions/Attempts - 3 * Interceptions/Attempts

This ratio can never exceed 100.0% (although it can be negative).

In my mind, a running back has 2 duties once he receives the ball - run with it, and don't fumble it.  Similarly, a wide receiver has 2 duties once he receives (catches) the ball - run with it, and don't fumble it.  And, a quarterback, similarly has 2 duties - complete the pass, and don't turn it over.  I realize it's too simplistic a view.  Eventually, I will incorporate sacks and fumbles into the formula.  Since I am very interested in comparing quarterbacks over time, once sacks are included, I can only go back in time to 1969 (since sack data was included).

Best 25 Seasons in History - CMI

Here's a list of the 25 best seasons in history in terms of CMI.  This list is different than a similar list I published earlier, based on QB Rating.  As I mentioned earlier, when looking at career CMI (versus career QB Rating), this list favors those quarterbacks who didn't throw a lot of interceptions.  What is particularly interesting, is Tom Brady's 2007 season.  He is rewarded on the QB Rating list (#2) for what he did - he threw 50 touchdowns.  He is rewarded here for what he didn't do - he didn't throw a lot of interceptions.  Also, interesting is that, according to this ranking, Peyton Manning had a better 2003 season than he did in 2004 (although he gets a lot of attention for what he did in 2004).  Again, this list is biased towards the more recent years, which of course suggests Sammy Baugh's season in 1945 must have been out of this world.  I will later on, look at these figures, relative to the time periods in which each of these seasons took place. 

Highest Career CMI

The two tables below show the Top 100 quarterbacks in terms of their career CMI. Surprising? Well, it should be. It doesn't meet with your expectations. Chad Pennington the best quarterback in history, terms of CMI. Well yes. And no. Keep in mind that Chad Pennington is no slouch - he has the 8th best all-time career QB Rating. As a matter of fact, the quarterbacks who have top 10 highest QB Ratings in history, are in the Top 10 in terms of CMI.


I have shown before, that CMI has been steadily increasing over time. So obviously, QBs in more recent years have had higher CMIs than earlier quarterbacks. But the list below does give us a different picture of the top quarterbacks in history compared to a similar list ranked by QB Rating.


CMI does not reward quarterbacks that throw a lot of touchdowns per se (see Dan Marino). It does reward quarterbacks that do not throw a lot of interceptions (see Troy Aikman). Think about the teams that these two quarterbacks played on. Dan Marino never had a quality running back for an extended period of time. Troy Aikman had, well, Emmitt Smith, he of the NFL-record 164 career rushing touchdowns. CMI doesn't penalize a quarterback for sharing the backfield with a good running back.


My goal is to eventually identify the best passers in history, using CMI. The way to do it (in order to account for the ever increasing average CMI), is to relate each quarterback to his peers. I am currently working on methodology that can do this "properly".

Crazy, Debatable and Lucky

Today, the Green Bay Packers lost at home to the Houston Texans, 24-21 on a last-second field goal.  This dropped the Packers to 5-8 for the season, and, for all practical purposes, knocked them out of the playoffs.  I'm sure the Packer faithful will start to think what might have been....

The Packers were coming off a 13-3 season, having won their division handily, and were one win away from the Super Bowl, a loss to the eventual winner, the New York Giants at home.  

Then the soap opera started.  First, Brett Favre, the Packers QB for the past 16 seasons, decided it was time to retire.  The Packers, who had drafted Aaron Rodgers in 2005, were prepared.  During the offseason, the Packers named Aaron Rodgers the starting QB for the 2008 season.  Second, Brett Favre decided he wanted to play in 2008.  Nothing wrong with that.  Only that he had "lost" his starting job to Aaron Rodgers.  No way a future hall of famer is going to be carrying a clipboard for an untested, essentially rookie QB.  Not after the season Favre just had had.  After much ballyhoo, the Packers traded Favre to the New York Jets.  In return, the Packers received a conditional draft pick.  For now, it's a fairly safe bet that it will be at least a second rounder.  The Jets, who finished a lousy 4-12 season, now having found their "saviour", then released Chad Pennington.  Of course, the woeful Miami Dolphins, having just completed a miserable 1-15 season, and desperately needing some talent, promptly picked him up.

So there we have it.  The Packers make a "crazy" move, going with untested Aaron Rodgers, over Hall of Famer Favre.  The Jets, in need of a new direction, trade for Favre and release Pennington in a debatable move.  And the Dolphins, well, got lucky.  Pennington is a dramatic improvement over any Dolphin QB.

Ok, so that's how we all thought about it back in the beginning of the season.  So, let's take a look at how the decisions panned out, in terms of their actual performances.

The table at the top of this article shows each player's stats for the 2008 season, the 2007 season, and their career #s.

First, let's start with Rodgers.

He is having a very good year, despite the team's troubles.  His QB Rating is a robust 92.1 (league average is 85.3), and his CMI is 0.560, about 0.4 standard deviations above the mean of 0.538.  Not bad for being a first-year starter.  Compare him to three other first-year starters here.

Now, let's take a look at Favre.

He had a career year in 2007.  His QB Rating of 95.7 was only exceeded in his MVP years of 1995 (99.5) and 1996 (95.8).  His third MVP year, 1997, his QB rating was 92.6.  Favre's career QB Rating (leading up to the 2007 season) was 85.0.  It has since improved to 85.9 through 13 games of the 2008 season.  In terms of his CMI, 2007 was by far and away, his best year (0.581), eclipsing his previous best of 0.561 in 1995.  Given that it had been a long time since he had put up that kind of #s, it would be reasonable to assume that it wouldn't necessarily continue into 2008.  Well, he's having a (surprisingly) outstanding year in 2008.  His QB Rating is a healthy 88.2, and his CMI is 0.577 (almost as good as last year).  Is he why the Jets have improved?  Hard to say.  Especially, when you take a look at what Pennington has done this year.

Pennington's #s:

Chad is easily having his best year since his first full year in the league, in 1992.  Back then, he produced a QB Rating of 104.2 and a CMI of 0.644.  Only Tom Brady in 2007 (0.647), and Hall of Famer Troy Aikman, back in 2003 (0.645), have had better seasons.  This year, Chad's #s are a QB Rating of 93.7, and a CMI of 0.618.  Compare these to his career #s of 89.7 and 0.578.  By the way, Pennington's career CMI of 0.578 is the all-time career NFL mark.  Next is Steve Young at 0.565.  Pennington's #s are also, needless to say, a dramatic improvement compared to those of the 2007 Dolphins (QB Rating of 67.4, and CMI of 0.484).

So, what does this all mean?  It means that the Packers weren't crazy when they decided to put their faith in Rodgers, the Jets decision is debatable in giving up a 2nd round pick in 2009, and exchanging a QB who, while having an outstanding year, is not doing as well as the QB they gave up on, and the Dolphins got awfully lucky to end up with Pennington.

A Slight (but necessary) Digression

Brian Burke, who does some excellent analytical work at advancednflstats.com has made this observation regarding three first-year quarterbacks - Joe Flacco of Baltimore, Matt Ryan of Atlanta, and Matt Cassel of New England.  He suggests that their performance has been improving as the 2008 season has moved on. and shows their performance, graphically illustrating it in the following manner.  He uses a measure, "Adjusted YPA" or, Adjusted Yards per Attempt, defined as [Yards -40*Interceptions + 10*Touchdowns]/Attempt, and then looks at their 4-week moving average to compare the three quarterbacks.

Well, I decided to look myself.  I have been "casually observing" that Flacco and Ryan have been having some "pretty decent" games recently (Ryan is on my Fantasy team).  So, I decided to put my newly developed CMI to the test.

Here's what it shows:

It appears to be very consistent with what Brian found.  Matt Ryan has improved the most.  CMI shows that Matt Cassel has in fact had the least improvement, if any.  However, to his credit, he has been performing at a very high level from the beginning.  Looking at the table below, you see that both Ryan and Flacco have remarkably similar attempts and completions through the first 12 weeks, with their only difference being the # of interceptions thrown.  Also, you can see that Cassel attempts more than 5 passes per game more than the other two (partially reflecting the fact that New England has no running game).

Brian has, in the past, ventured into the "creating a new passer rating" space, and, in fact, created one.  He uses a concept called "Air Yards", defined as, [Yards - Yards After Catch] to relate "passer rating" to a team's wins and losses.  See his post here.  I agree with his approach generally.  In other words, if you look at his formula, it's a lot like CMI.

QB Wins Added = [(Air Yards - Sack Yards) * 1.56 - INTs * 50.5]/Pass Attempts - 3

where, (Air Yards - Sack Yards) is substituted for Completions.  In other words, he also takes out Touchdowns thrown and Yards per Attempt.  Brian is the first person I know of that does not include touchdowns as a part of a passer rating calculation, and he is to be commended for that.  My only real issue with Brian's calculation is that YAC, or, Yards After Catch, is not a readily available statistic, and hence, "Air Yards" is not easily calculated.

I am still developing CMI, and the next (enhanced) version will incorporate sacks.  Given that one of my goals is also to look back in time and be able to compare QBs over time, I will only be able to that back to 1969.

As I mentioned at the top, Brian is a very smart guy, and has done some very good work on a whole host of topics relating to the NFL, with particular attention to statistical rigor.  I will be referring to his site quite a bit in future postings.

Simplifying the QB Rating System

This graph illustrates a comparison between the QB Rating and only the components for Completions and Interceptions.  The components for Yards per Attempt and Touchdowns are ignored.  The data shows a correlation of 0.970.  Interestingly, the Yards per Attempt and Touchdowns components, when added together, have a slight negative (-0.17) correlation with the QB Rating calculation.  In a previous post, I had shown that correlations of just the Completions component with the QB Rating was 0.956, and the Interceptions component was 0.965, respectively.  What this shows, at least to me anyway, is that we could simplify the QB Rating to only include 2 components - Completion Rate and Interception Rate.

The QB Rating formula is as follows:

Q = (J+K+L+M)*100/6

where,

Q = QB Rating

J = max(min(C, 2.375), 0)

K = max(min(Y, 2.375), 0)

L = max(min(T, 2.375), 0)

M = max(min(I, 2.375), 0)

and where,

C = ([Completions/Attempts]*100 - 30)/20

Y = ([Yards/Attempts] - 3)/4

T = [Touchdowns/Attempts]*20

I = (2.375 - [Interceptions/Attempts]*25)

Here's how we will go about simplifying the QB Rating calculation:

As discussed above, we can eliminate the K and L terms, since the J and M terms have an almost perfect positive correlation with the QB Rating.

We get, 

Q ≈ k*(J + M)*100/6

where,

k = non-zero scalar

Let's further simplify the equation by doing the following:

Let's remove the restrictions on a max and a min for each term (in my opinion, these restrictions are arbitrary, and when looking at annual league average data, the restrictions haven't come into play since 1943).

And, by removing the approximation and by substituting back for the J and M terms, we get

Q*100/6 = ([Completions/Attempts]*100 - 30)/20 + 2.375 - [Interceptions/Attempts]*25

Re-arranging terms, we get

(Q*100/6 - 2.375 + 1.5)/5 = [Completions/Attempts] - [Interceptions/Attempts]*5

or,

Q(new) = C/A - b*I/A

where,

Q(new) = New QB Rating

C/A = Completions/Attempts

I/A = Interceptions/Attempts

b = factor to be determined (in my preliminary research, it appears that b would be a number close to 3)

So, there we have it, a (much) simplified new QB Rating System.  It only looks at completion rate and interception rate, and no fancy mathematical gyrations.  It is easy to understand, easy to explain, not arbitrary, simple to calculate and it also has the amazing beauty of never exceeding 100.0%!  It still does have the issue of not being comparable over time (i.e. players in the 1940's versus players from the 1990's).  I will address this issue in an upcoming post.

For simplicity, I'd like to call this new rating system CMI, or, short for Completions Minus Interceptions (sort of like the OPS statistic in baseball - on-base plus slugging).

The QB Rating System and Its Four Components

The graphs above illustrate how each of the four components of the QB Rating System actually relate to the QB Rating.  

The first component (shown in the first graph, in blue), relating to Completions per Attempt (or, Completion Rate), has a correlation coefficient of 0.956 with the QB Rating system.  I've actually taken the calculation of the completion rate in the QB Rating System itself (remember, it's scaled to be a number between 0 and 2.375).  This doesn't change the correlation since it is a linear transformation of the Completion Rate.  If Don Smith (the creator of the QB Rating System) had simply decided that a quarterback was going to be rated by his pass completion rate, and not tried to adjust for league averages and include other components, we wouldn't be having this debate.  Besides, the Completion Rate has an elegance about it in that it can never be greater than 100% (nor less than 0%).

The second component (shown in the second graph, in green), relating to Yards per Attempt, has a correlation coefficient of 0.492 with the QB Rating system.  Besides, the calculation itself has historically hovered around the intended average of 1.000.  This in and of itself is interesting.  Since Yards per Attempt = Yard per Completion * Completions per Attempt, and we have seen from the first illustration that Completions per Attempt has been steadily increasing over time, then Yards per Completion must be proportionally decreasing over time.  This should come as no surprise, as NFL offenses have adopted the West Coast Offense to varying degrees since its introduction to the game in the late seventies/early eighties by Bill Walsh of the San Francisco 49ers.  The West Coast Offense is known for its highly precise, short passes.

The third component (shown in the third graph, in dark blue), relating to Touchdown Rate, or, touchdowns per attempt, has a negative correlation with the QB Rating system over time.  The correlation is significant, at -0.521.  I found this to be remarkably surprising.  The calculation itself has remained tightly averaged around 0.800 since the merger of the AFL and the NFL in 1970.  

The last component (shown in the fourth graph, in purple), relating to Interception Rate, or interceptions per attempt, has an astounding 0.965 correlation coefficient with the QB Rating calculation (technically, the interception rate itself is negatively correlated with the QB Rating system, whereas the transformed calculation, with a minimum of 0 and a maximum of 2.375 has a positive calculation).  I certainly expected the first component, completions per attempt, to be highly positively correlated with the QB Rating system.  Although I expected this component to be also positively correlated, I did not expect that it would be more positively correlated with the QB Rating system.  I suppose we could all have saved ourselves a lot of headaches over the years if we simply designed the QB Rating System as 1 - Interceptions/Attempts.

NFL QB Ratings 1940 - 2007

The graphical illustration above shows the league average QB Ratings by year, for every year from 1940 to 2007.  As you can see, there has been a steady increase over time, and the average continues to increase.  There are many reasons for this, of course, including the gradual importance and development of the passing game, the changing of the rules to favor the passing game, the introduction of the West Coast Offense, etc.  In the next graph, I'll show each of the components that contribute to this increase in the QB Rating.

The 25 Best Seasons by a Quarterback (using current QB Formula)

Here are the 25 best seasons that a quarterback has had in the NFL (since 1940) using the current QB Rating system.  I have previously mentioned my dislike for the system.  However, for now, this is the list.

Note:  This list is slightly different than that shown at The Pro Football Hall of Fame.  The HOF has Bart Starr's 1968 season at #19 with a Rating of 104.3.  I did not include him here as he didn't "qualify", having only attempted 171 passes.  For 1968, I used 14 attempts per game (or, 196 for the season) as the qualifier.

Best Quarterbacks in History (in terms of current QB Rating Formula)

Here are the Top 50 quarterbacks all-time, based on QB Rating.  I only considered those with at least 1,500 pass attempts (and there were 142 in all over the course of history that had at least 1,500 attempts).  Data is only through the full 2007 season.  I will update this list following the end of the 2008 season.  One can clearly see the bias favoring the modern quarterback.

Here's the next 50.  One needs to look at this list if you wanted to see QB's from yesteryear.

So, it begs the question, does the QB Rating system need to be changed so that fair comparisons can be made over time?  After all, the methodology behind it indexes the statistics to the 1972 season.  

The Current QB Passer Rating System

The current QB Rating System for the NFL was invented in 1973 by Don Smith.  It is supposed to measure a quarterback's passing prowess.  It's a metric that uses 4 statistics to come up with a number that is supposed to represent the quality of a quarterback in terms of his passing ability.  The following are the four statistics used:  

1) A component, [C] for Completion Percentage, as defined by ({Completed Passes/Passes Attempted} * 100 - 30)/20

2) A component, [Y] for Yards per Attempt, as defined by ({Yards Thrown/Passes Attempted} - 3)/4

3) A component, [T] for Touchdown Percentage, as defined by ({Touchdown's Thrown/Passes Attempted} * 20)

4) A component, [I] for Interception Percentage, as defined by (2.375 - {Passes Intercepted/Passes Attempted} * 25)

Here's how the four statistics are used in the calculation of the metric:

QB Rating  = [max{min(C,2.375),0} + max{min(Y,2.375),0} + max{min(T,2.375),0) + max{min(I, 2.375),0}] * 100 / 6

This guarantees a QB Rating between 0 and 158.33.  

According to the Pro Football Hall of Fame, the NFL has historically changed the "Passer Rating" system a total of nine times.  However, the current Rating System has remained in place for the past 35 years.

All of which begs the question, why?