The Adjusted NFL Passer Rating Revisited

This posting is an update and an enhancement to a previous posting that discussed the concept of the Adjusted NFL Passer Rating.  Back in 1971, when Don Smith, an executive with the Pro Football Hall of Fame, and his team developed the current NFL Passer Rating formula, he suggested that the intent of the formula was such that an 'average' Passer Rating would be equal to 66.7.  In essence, he decided that an average performance for each of the four components that make up the passer rating system should be equal to 1.0, with an exceptional performance defined as a score greater than 2.0, and a poor performance getting a 0.  Since the formula adds the scores for each of the four components and divides by 6, an average performance would be equal to 66.7.

Since we have seen that the average NFL passer rating has increased over time (see my previous post on the topic here), I was curious as to what the average in 2009 looked like, and, more importantly, what would the actual NFL passer ratings have looked like if we adjusted each of the components such that the averages for 2009 were in fact 1.0.

Recall that in the formula , based on data from the 1960's, adjustments are made to each of the four components such that the average for each component worked out to be 1.0.  The adjustments, call them k1, k2, k3 and k4, are:

• k1 = 30
• k2 = 3
• k3 = 1
• k4 = 1

Again, these factors were arrived at by looking at data from the 1960's.  And, these same factors are applied to the formula regardless of when a quarterback actually played.  This has the benefit of course of creating a formula that is the same for all quarterbacks against a fixed standard.  The problem of course is when the overall standard changes over time, and this is what has happened over the past 80 years or so.

Well, we don't have to use data from the 1960's.  We will use each year as a stand-alone year.  So, for 2009, the factors that make each component equal to 1.0 for an average performance turn out to be:

• 2009k1 = 40.90
• 2009k2 = 2.98
• 2009k3 = 1.20
• 2009k4 = 1.78

Likewise, the factors for 2008 were:

• 2008k1 = 41.00
• 2008k2 = 2.94
• 2008k3 = 1.28
• 2008k4 = 1.95

And, for good measure, the actual factors for the NFL for 1969 were:

• 1969k1 = 32.64
• 1969k2 = 2.99
• 1969k3 = 0.99
• 1969k4 = 1.12

These 1969 factors are very close to the k1, k2, k3 and k4 values used in the formula.

The table below shows the 2009 Adjusted Passer Ratings for the 32 quarterbacks that threw enough passes this past season to qualify.  The table also shows their actual 2009 NFL Passer Ratings.  You can see that the Adjusted Passer Ratings are clearly lower (as a group) than the actual NFL Passer Ratings.  That's because the actual NFL average passer rating in 2009 was 83.0, and, obviously, the average Adjusted Passer Rating for the NFL for 2009 was 66.7 (because we forced it to be so by adjusting the formula such that the average value for each component is equal to 1).

Although the Adjusted Passer Ratings themselves are a lot lower as a group than the actual NFL Passer Ratings, you'll notice that the rankings for each are essentially the same.  Why is that?  Very simply, since both calculations use the same essential formula with the values changed, all this really does is 'normalize' the actual ratings around a value of 66.7 as opposed to 83.0.  And yes, since the relative value of each of the four components now change, there should be some movement in the rankings.  Interestingly, I also included my CMTI calculations (and their respective ranks), and it also highly correlates with both the Adjusted Passer Rating rankings and the NFL Passer Rating Rankings.

Just so that you can see for yourself, I've included the table (shown below) that shows the average NFL passer rating by year from 1932 to 2009 using the current NFL passer rating formula (where k1 = 30, k2 = 3 and k3=k4=1 for all years), as well as the adjusted k1-k4 factors for each year.  There is no need to show the Adjusted Passer Rating for the NFL in each year, since it is the same in every year - 66.7.  If you look at the bottom of the table, for years 1960-1969, you'll see where Don Smith derived his k values from.

Looking at this table you should be able to understand why using the current NFL passer rating system is of little to no use when you need to compare quarterbacks from one era to another.  It can truly only be used to compare one passer versus another in any given year, but not across years.  It stands to reason then, that the current NFL passer rating formula isn't much use when evaluating a quarterback's career, especially ones who've had a long career (you can see the career NFL passer rating leaders here).  In future posts, I will discuss this in more detail.

2009 NFL Season - Passer Ratings

We now have data for the entire 2009 season, and I can calculate the best and worst performers for the season, using my standard measure, CMI - or more appropriately, Standard Deviations from mean CMI.  CMI is easily calculated, as it is simply [pass completion percentage] - 3 * [interception percentage].  I can calculate that at any point during the season.  In order to calculate the standard deviations from the mean CMI, I like to wait until the season is over (actually, even this can be calculated at any point during the season, but it's a lot simpler for me to just do it at the end of the season - perhaps next year, I can do this after every week during the regular NFL season).   For those of you familiar with statistics, the measure of standard deviation from the mean is also called a z-score (or z-value).  And, furthermore, z-score can be very easily converted to a percentile rank (assuming that the population is normally distributed.  In a later post, I will show that z scores for CMTI or NFL passer rating over the years is distributed normally).  The beautiful thing about a percentile rank is that it is always a number between 0 and 100.  What's not to like about that!

A quick couple of notes here regarding CMI, and many of the calculations that I will be using from here on out. While I will go through the exercise of creating arduous, complex and sometimes arbitrary (and even unnecessary) calculations, I will strive for simplicity whenever possible when I present my ideas, as I believe they are more likely to be accepted.   The use of percentile ranks is an example of this.

Last year, when I first developed CMI, and especially as I looked back in time, I had to figure out how many players to use each year to determine the number of qualifiers.  I went through some elaborate mechanisms to calculate the number of passes attempted during the season (per team per game), and some qualifying standard.  As you are aware, the NFL uses 14 passes per game as the standard.  And yes, while it is simple to use, I am not a big fan of that standard since the average # of passes attempted per game has changed (increased) over time, as you can see from the table below.

The standard today should be closer to 16.

Last year, I arbitrarily assigned a factor close to 50% (with adjustments for the earlier years) to the total # of passes attempted by each team per game to determine the # of qualifiers.  I realized this year, that if I simply used the # of teams in the league as the cutoff for determining the # of qualifiers, I get fairly close to my original method.  And because it is simple, easy to explain, does a better job (in my opinion, anyway) than the current NFL standard, I will use that as the cutoff.  The table below shows the # of qualifiers by season using the NFL standard, my original standard, and my current standard.

As you can see, the # of qualifiers, regardless of which method you select is fairly close in each year, with the exceptions being the earliest years, where the NFL method simply excludes too many passers (in my opinion anyway).  Also note that the the AAFC is excluded by the NFL altogether, while the AFL and NFL have been combined in the years 1960-1969 by the NFL.  This doesn't make sense to me, since each league played a different # of games (and had a different # of teams).  Regardless, if you combine the AFL and NFL results from my method, you get close to the #s used by the NFL.  While I think that my method works, I also recognize that this standard may not be the most appropriate for future NFL seasons.

OK, back to the passer ratings.

Because I will discuss other passer rating systems/calculations that are related to CMI in later posts, I will take this moment to re-classify CMI as CMTI (acronym stands for Completions Minus Three times Interceptions).  The definition itself hasn't changed - just the acronym.

The table below shows each of the qualifying quarterbacks with their 2009 season's statistics, their NFL passer rating, the percentile rank of their 2009 NFL passer rating (in other words, the converted z-scores), their 2009 rank in terms of NFL passer rating, their 2008 NFL passer rating, the percentile rank of their 2008 NFL passer rating, their 2008 NFL passer rating rank, their 2009 CMTI, 2009 CMTI percentile rank, their 2008 CMTI and 2008 CMTI percentile rank, and their 2008 CMTI ranking, and finally, their average 2-year CMTI percentile rank (again a # between 0 and 100), together with that ranking.

I don't think there's any question as to who the elite quarterbacks are.  Also notice the struggles of first-year quarterbacks in each year.

Happy New Year!

Hi Everyone.

Happy New Year to you all.

It's been awhile since I've posted.  The reasons are many, so I shall not go into them.  Regardless, I am back posting.

I have been able to do some additional research in the meantime.  I have added data from the 1932 - 1939 NFL seasons to my database.  I have also added the 1946-1949 AAFC seasons to the database as well as the 1960-1969 AFL seasons.  And of course, updated for the just concluded 2009 NFL season.

I think that adding the data from the AAFC in the late 1940's as well as the AFL during the 1960's makes for a much richer database.  There are those however, who do not believe that including that data makes sense.  I disagree.

Having spent some time thinking about my pursuit here (creating a new passer rating system for the NFL), I've created new statistical measures in addition to those I created last year that I will discuss in upcoming posts.  I've also improved upon my original concept of CMI.

Anyhow, I'm glad to be back posting and look forward to a terrific 2010.

Cheers,
Kiran

Was Steve McNair A Good Passer?

Earlier this month, Steve McNair was shot and killed. It was a story that caught everyone by surprise, and there was much said about his contributions to the game, and how he played the game. I thought it might be worthwhile to digress briefly from my current topic - the economics of the NFL Draft to take a look back at McNair's career.

Steve McNair was drafted in 1995 out of little-known Alcorn State. The 3rd overall pick in the draft, he was the 1st quarterback taken that year. The then Houston Oilers (now Tennessee Titans) drafted him ahead of current Titans quarterback Kerry Collins.

He started out his career backing up Chris Chandler in both 1995 and 1996 while the team was still the Houston Oilers. The first year in Tennessee, he took over the starting job. He had a sub-par first year (as most quarterbacks tend to do), and then went on to have a fine career. He is of course, most notably remembered for coming one yard short of leading the Titans to a victory against the St Louis Rams in Superbowl XXXIV. The table and chart below illustrate his career in terms of the standard deviations from the mean CMI.

As you can see, from 1998 until his retirement after the 2007 season, he finished each year at above the mean CMI, with the exceptions of the 2004 and 2007 seasons which were cut short due to injury. His best year was 2003, where he finished 1.40 standard deviations above the mean CMI. His statistics that year: 62.5% completion rate, and a 1.75% interception rate. For his performance on the field that year, he was named Co-NFL MVP along with Peyton Manning. He was traded to the Baltimore Ravens following the 2005 season.

All told, Steve McNair had 9 qualifying years in his 13-year career. Of the 51 quarterbacks since 1940 to throw enough passes to qualify in 9 or more seasons, he ranks 17th. His career average standard deviation from the mean CMI during his 9 years was 0.46, putting him in the company of quarterbacks such as Norm Van Brocklin, John Brodie and Sid Luckman. The chart below illustrates the 51 quarterbacks, and Steve McNair's standing among them.

NFl Draft Economics - Part 1 - Introduction

Here I will begin a series of posts discussing the economics of the NFL Draft.  The NFL Draft puzzles me.  Every year.  There are many economists (those who are both smarter and more qualified than I am) who've tried to explain it, and I'll cover their analyses in the posts to come. 

Naturally, this is a rather difficult topic to address in one simple post, so I'll do it over a few.  It's a very broad topic - it covers the evolution of the game, identifying and measuring talent, economics, labor issues, psychology, and human behavior, among others.  I won't go into all these topics, but will address some of them either directly or indirectly.  

Through all of this, the fundamental question I'll be trying to answer is why did the Detroit Lions take Matthew Stafford as the 1st pick in 2009 Draft, and pay him $78 million (actually, he has the potential to earn as much as $78 million over six years, and about $42 million is "guaranteed" - the reason the "guarantee" is in quotes is that while that is the quoted number in the press, his actual true guaranteed money is about $17 million).

And why did they do this after they took Joey Harrington with the 3rd pick overall in 2002?  And why did they do that after they took Andre Ware with the 7th overall pick in 1990?  And why did they do that after they took Chuck Long with the 12th overall pick in 1986?  That is the set of questions I'll attempt to answer.  There must be a reason why.  All the evidence suggests that they shouldn't have done this.  So why did they do this?