Showing posts with label Roger Staubach. Show all posts
Showing posts with label Roger Staubach. Show all posts

Sunday, March 1, 2009

First Year Quarterback Performance - An Evaluation Method

This past weekend, the New England Patriots traded Matt Cassel to the Kansas City Chiefs.  In fact, they traded linebacker Mike Vrabel and Cassel for a 2nd round pick (pick #34) in the upcoming April draft (see here for the details).  Depending on what your news source is, this was labeled as either a good deal for Kansas City, or a bad deal for New England.  The experts discussing this issue don't seem to support their arguments by any objective measures - they just opine.  I am not going to jump into the debate here.  I will offer this however - we will probably not know who will end up on the better end of this deal until many years from now, and even then, we may not know.  

What about the objective evidence?

Matt Cassel is not the only quarterback in 2008 that had a good year as a first-year quarterback.  There was Aaron Rodgers of the Packers, Shaun Hill of the 49'ers, and Matt Ryan of the Falcons.  There were four other quarterbacks who threw enough passes this year to make the list of first-year quarterbacks - Ryan Fitzpatrick of the Bengals, Joe Flacco of the Ravens, JaMarcus Russell of the Raiders and Tyler Thigpen of the Chiefs.  

Notice here that I didn't use the term rookie quarterback, but instead used the term first year.  The way I look at a quarterback, is that I only consider a quarterback who has thrown "enough" passes to qualify in a given year.  The # of passes has varied by year (as opposed to the fixed standard used by NFL.com).  For the 69-year period from 1940-2008, my database contains 1,451 passing seasons, 336 of which were by a quarterback qualifying for the first time.

How did the aforementioned 8 quarterbacks do?  

I use a statistical measure I have previously developed and discussed, called CMI (Completions Minus Interceptions, calculated as Completions/Attempts - 3*Interceptions/Attempts) instead of the NFL Passer Rating system (using the NFL passer rating system gets you essentially the same answers), and then use the standard deviation from the mean as the measuring stick (for the pool of qualifying passers, I calculate the the mean and standard deviations for each year, and relate a particular performance in that year to the mean using that year's standard deviation).  Using the mean and standard deviation this way not only allows me to compare these 8 quarterbacks relative to each other, but also relative to all quarterbacks this year, or any other year.

In a post not too long ago, I showed how, over the past 69 years from 1940-2008, when the standard deviation is used as the measuring stick, the accumulated data form a near-perfect theoretical standard normal distribution.  And I also showed how, this is true regardless of whether one used the NFL passer rating system or CMI as the statistical base.

I can now show you how these first year quarterbacks did compare to the rest of the QBs in 2008, using this measure.  But this picture may not tell us much, if anything.  Here's the graphical illustration:

Perhaps the only thing that may be apparent from this is that first year quarterbacks don't do nearly as well as quarterbacks with more experience.  Even drawing that conclusion from this is a little iffy.  However, it is clear (at least by this measure) that Cassel had the best year of the 8 first year QBs.  Rodgers was a close second.  JaMarcus Russell and Tyler Thigpen had disastrous first years.  In an earlier post regarding Jeff Garcia, I had suggested that Kansas City might be a good place for Garcia.  Scott Pioli, the new Chiefs' GM apparently was thinking the same thing - upgrade at quarterback, and he did - with Cassel.

Going back to the standard normal curve, let's look at just the first year performances.  Recall that, when all 1,451 seasons are aggregated in a histogram, it looks very much like a standard normal curve.

This doesn't quite look "normal", does it?  The first year performances appear skewed to the left, or, compared to all quarterback performances, appear to under-perform.  Since the total database is normally distributed, then performances in years 2 and beyond must obviously be skewed to the right.  This prompts the question: does experience improve performance, and, in particular, how and when?

One way to look at this is to take the entire database, and look at the average standard deviation from the mean for each additional year a player qualified.  Here's what that graph looks like.


Wow!  I didn't realize that it takes about 5 qualifying years to turn into an average quarterback.  And that's just for those playing that long!  Even though this graph goes out to 18 years, there is hardly any data beyond the 15th year (there are only 8 quarterbacks who have had qualifying seasons 16 different years).  According to this illustration, basically, first year quarterbacks, as a group, struggle mightily.  They then gradually improve each year until about year nine.  Quarterbacks, on average, must still endure sub-par years in years 2-4, and for those that survive, their reward is about four more years of improving performance, assuming they stay healthy for that long.

Note: This analysis - the method of breaking down a quarterback's expected career in terms of passing performance as it relates to experience and how it is expected to change over time, is the first I've seen published publicly.  But I digress.

Ok, so we've taken a look at these 8 QBs relative to all quarterbacks in 2008, and we've taken a look at first year quarterbacks in general.  So the next step is to take a look at the best first year seasons.  In my database, there are 336 first year seasons in all (in other words, in the 69-year period from 1940-2008, 336 different quarterbacks threw enough passes in a season to qualify at least once).  The table below shows the 75 best.


Cassel (#48) and Rodgers (#60) are the only 2 of the 8 in 2008 that crack the top 75 all-time.  On the other end of the scale, we get JaMarcus Russell (#264) and Tyler Thigpen (#290).

When Matt Ryan (#128) got off to a solid start, and the Falcons surprised many by getting into the playoffs, there were many debates as to whether his season was one of the best ever by a first year player.  Not according to this measure.  Often, during those discussions, Kurt Warner's first year was brought up.  In looking at the table above, well, he did have an outstanding first year in 1999.  It ranks #6 all-time in terms of first year seasons.  The best ever - Roger Staubach's 1971 season (Staubach was a rookie in 1966, and played in both 1969 and 1970.  However, he didn't attempt enough passes in either year to qualify).  

Notable quarterbacks high on this list: Joe Montana in 1980 (#4), Tom Brady in 2001 (#14) - (see my post earlier comparing Brady's season to Cassel's here), Brett Favre in 1992 (#15), Dan Marino in 1983 (#21), and Johnny Unitas in 1956 (#22).  

Notable absentees:  Steve Young in 1986 (#154), Peyton Manning in 1998 (#208), Joe Namath in 1970 (#202)*, and Troy Aikman in 1989 (#311).  The all-time worst first year performance - Terry Bradshaw in 1970 (#337)*.

* Keep in mind that 1970 was the first year of the NFL following the merger, and 15 quarterbacks showed up in the database as having that year as their first year, although Bradshaw's 1970 season was his actual rookie season.

Are we done?  Hardly.  So after I went through this list, and still trying to objectively value Matt Cassel, I was interested in answering the following question(s):  what does the first-year tell us about a quarterback's future potential?  Do quarterbacks who have good first years, have good careers?  What about quarterbacks who have sub-par first years?  In other words, is there a correlation between year 1 performance and subsequent years?  When in doubt, it's always a good idea to take a look at the data.


Whoa!  The correlation between year 1 performance, and career performance, as measured by CMI standard deviations relative to the mean, is 0.75.  What that really means is that 57% of the variation in a quarterback's career performance can be explained by his year 1 performance.  I find that incredible.  So I looked a little deeper.  It turns out that 112 of the 336 quarterbacks only have 1 qualifying year.  And, for that group, the correlation coefficient is, well, 100%!  If I only looked at those quarterbacks whose career included at least 2 different years in which they threw enough passes to qualify, then the correlation coefficient drops to 64%.  Still quite remarkable.  

The table below breaks down the 336 first year seasons in terms of CMI standard deviations to see if we can glean any additional insight into whether a good first year translates into a good career and vice versa.


Well, the evidence is pretty clear.  Taken as two groups, players that have better than average (remember, the mean and standard deviation is relative to all quarterbacks, not just first year quarterbacks) first years tend to have longer careers and more productive careers than those that have sub-par first years.  And, breaking it down even further (in other words, just looking at the group whose first year was better than average, or the group whose first year was worse than average), you can clearly see that even within those sub-groups, the better the first year, the longer the career (although this correlation isn't nearly as strong), and the more productive the career. 

I haven't spent too much time on my blog discussing individual careers, except in the posts discussing Brett Favre and Jeff Garcia.  If I do this en masse, it would be such a powerful post - I'll basically be giving you my list of greatest passers to ever play the game, that I need to put a lot more thought into it than I have to-date.  In any case, some of the obvious names will show up on that list.  However, you'll find some exceptions as well (and I'm sure many of you will take exceptions to the list).  The point I really want to make here is that, when combining the table above, and the discussion following the list of the top 75 first years, it is quite remarkable how Troy Aikman "escaped" the trend, and turned into a great quarterback (or, more accurately, a great passer) - he truly turned out to be an exception (as for Young and Manning, even though they didn't rank well on the first year list, their first years weren't "that bad" compared to other first year seasons - as a matter of fact, Young's was "above average" compared to a typical first year).  Notice how I don't mention Bradshaw and Namath - it is because, statistically, their careers were sub-par.  When I publish my list of all-time greatest (and worst) passers, we'll get into it in more detail.

So, in trying to look at Matt Cassel's first year performance objectively, we've looked at how quarterbacks perform as their careers progress, how quarterbacks perform in their first year, who had great first years, where Cassel's season ranks on that list, and, how a first year translates into (or, is predictive of) a career.  Now perhaps, we can view Matt Cassel's 2008 year in an objective manner, and, if so inclined, you can at least evaluate the trade armed with some data.

Naturally, while I was putting this post together a question popped into my mind, and that is:  is a quarterback's second year a good indicator of their career?  What about looking at their first and second years?  Check back in a week or two to find out.

Friday, February 6, 2009

The Importance of Interceptions (or lack thereof)


I have spent quite a bit of time lately talking about interceptions.  In case you have any doubt that an interception can make a difference you got that answer on Super Bowl Sunday.  In probably one of the greatest plays in Super Bowl history (until the catch by Santonio Holmes with 35 seconds left that gave the Steelers a come-from behind victory), with Arizona on the Pittsburgh 1 yard line, first and goal, and 18 seconds left in the first half, the Steelers' James Harrison picked off Arizona's Kurt Warner and returned it all the way for a touchdown as time expired.  This was, in effect, a 13-point play, as Arizona's expected points at the Pittsburgh 1 was about 6 points.  Brian Burke, who I've highlighted before, has an excellent post on the subject on his site at advancednflstats.com.   

Take a look at the graph below.  The blue line (on the left scale) shows the league average QB passer rating (for those QBs who thew enough passes during the season to qualify) by year since 1940.  As you know, the NFL's QB passer rating formula has four components - completion percentage, yards per attempt, touchdown percentage, and interception percentage (see my previous posts on the subject here and here).  When it was designed in 1973, the formula used the 1972 season as a "base", and hence created adjustments to each component, such that the average would be a score of 1.00 for each component, resulting in a passer rating for 66.7 for a quarterback who had average statistics in each of the four categories.  The actual calculations for each of the four components in 1972 yielded the following four figures - 1.085, 0.954, 0.897, and 1.043, respectively, which in turn yielded the average quarterback passer rating of 66.3 (the figure for the qualified leaders turns out only slightly higher - 67.9).  Back then, each of the four components were essentially balanced.

Today, it's a different story.  If the system was balanced, then we would expect the interceptions component to make up about 25% of the quarterback passer rating score.  Looking at the graph again, and this time looking at the red line (on the right scale) shows how much the interceptions component influences the league's quarterback rating system.  It hasn't been below 30% since 1983, and the last time it was "around" 25% was actually 1971.  The point is that the NFL passer rating system is not what it used to be, and interceptions are the leading weight in today's NFL passer rating system.

Let's take a look at another example.  Tom Brady's record-breaking 2007 season.  That year, Brady completed 398 of 578 passes, for 4,806 yards, and threw for 50 touchdowns while only throwing 8 interceptions.  His passer rating that year - 117.2, is second only to Peyton Manning's all-time best 121.1 in 2004.  Most people will remember the 50 touchdowns that Brady threw.  Impressive as it was, it wasn't that impressive (I'll have a post later on this subject).  Most people will not remember that he only threw 8 interceptions in 578 attempts.  That ranks as 14th best all-time in terms of single-season interception percentage (see Exhibit 2), and, it accounted for 29% of his quarterback passer rating that year (his touchdowns accounted for 25%).


There are 7 exhibits on interceptions attached to this post.   Note that for all exhibits, I only considered those passers in any given year that threw enough passes to qualify - in other words, if a quarterback threw 20 passes during a season, that would not be enough to qualify him.  On the nfl.com site, the minimum qualification standard is 14 passes per game (so, for the 2008 season, the standard would be 14 * 16 = 224 passes).  The NFL uses this standard EVERY year.  

I think this universal standard is inappropriate.  Using this method for example, only three passers qualified in 1940.  The 14 passes comes from the fact that during the 50's, 60's and 70's, the average number of passes attempted by a team during a game was about 28.  Of course, we all know that this has changed over time.  The average number of passes attempted in a game by a team was 32.3 in 2008.  It has been below 30.0 once since 1979.  

The standards that I use varies by year, and reflects the average # of passes attempted during these years.  Here are the standards:
1940-1946 - 6.5
1947-1960 - 11.0
1961-1969 - 14.0
1970-1977 - 12.0
1978-1994 - 15.0
1995-2008 - 16.0

Using these standards, I get 1,451 quarterbacks in my database, with a low of 9 quarterbacks qualifying in each of 1941 and 1943, and a high of 32 quarterbacks qualifying in each of 1999 and 2005.  For 2008, I had 30 quarterbacks in my qualified database, whereas the NFL.com has 32.  So, not a big difference in recent years.  I just think that applying a universal standard across all these years is silly, especially when the game has changed so much.

In any case, now that we got the some of the technical stuff out of the way, here are the 7 exhibits:

Exhibit 1 - Chronological list of NFL leader (lowest) in interception percentage
Exhibit 2 - Best seasons in terms of interception percentage
Exhibit 3 - Best seasons in terms of standard deviations from the mean
Exhibit 4 - Worst seasons in terms of standard deviations from the mean
Exhibit 5 - Best (lowest) career interception rate (minimum of 1,000 passes attempted)
Exhibit 6 - Best career interception rate relative to league average
Exhibit 7 - Worst (highest) career interception rate relative to league average

Exhibit 1 - Chronological list:
Nothing spectacular here, it's simply each year's best.  I observe a few things: 
Clearly, the average interception rate has been decreasing every decade.  
The best quarterbacks in a given year seem to be around 1.8 standard deviations better than the average.
Slinging Sammy Baugh led the league 4 out of 6 years during the period from 1942 to 1947 - the only quarterback to have led the league on 4 separate occasions.  
6 quarterbacks - Bart Starr, Bobby Thomason, Charlie Conerly, Ken Anderson, Ken O'Brien, and Roger Staubach have led the league on 3 different occasions.
5 quarterbacks led the league in consecutive seasons - Sammy Baugh, Bobby Thomason, Milt Plum, Ken Anderson and Ken O'Brien.
Only 2 quarterbacks in history, Steve DeBerg in 1990 (0.90%), and David Garrard in 2007 (0.92%) completed a season where less than 1 percentage of their attempted passes were intercepted (this is not entirely evident by looking at Exhibit 1, but can be confirmed by Exhibit 2).  What's most unusual about DeBerg's performance that year was the fact that of the four interceptions he threw during the season, three of them were in one game!  In other words, he threw 1 INT the rest of the season.  Let's take a look at Exhibit 2.


Exhibit 2 - Best seasons in terms of interception percentage:
So indeed, only 2 quarterbacks have had seasons with fewer than 1% interceptions.  The list below is the kind of list that would show up in a record book.  
You'll see, for example, that Jason Campbell's 2008 season ranks in the top 5 all-time, and 2 other quarterbacks in 2008, Chad Pennington and Jeff Garcia, also had noteworthy seasons, with both finishing in the Top 30 all-time.  
If you look carefully, you'll notice that the list is dominated by quarterbacks in the past 2 decades.  Of the Top 50, 45 have occurred since 1990.  21 last decade and 24 this decade.  The 5 seasons in the top 50 not to have occurred in the last 19 years are Steve Bartkowski's 1983 season (#3), Bart Starr's 1966 and 1964 seasons, respectively (#7 and #18), and Ken O'Brien's 1985 and 1988 season's respectively (#36 and #38).  
So, what are we saying?  Are we saying that quarterbacks prior to 1990 were not very good?  No, not at all.  The league has changed.  From Exhibit 1, you can see that the average interception rate has been decreasing every decade.  So, we simply can't just compare a quarterback from one decade to another.  That's where Exhibit 3 comes in.  Let's take a look at that.


Exhibit 3 - Best seasons - Interceptions percentage, ranked by how different the particular season was compared to the mean, using the standard deviation as the measuring stick:
Wow, what a difference.  You can quickly see that this is a much better representation of the past 7 decades.
1940's - 3
1950's - 2
1960's - 10
1970's - 9
1980's - 7
1990's - 6
2000's - 13

Look at Bart Starr!  Ranked twice in the Top 5, and 3 times in the Top 25.  
And, this measure doesn't discount Steve DeBerg's and David Garrard's great seasons - they're both still in the Top 5.  But it does give one a bit more perspective.  In other words, this suggests that Bart Starr's 1962 season (which ranks #430 in absolute terms), when compared to everyone else's performance during that season, was better than David Garrard's performance, when compared to how all the other quarterbacks did in 2007.


Now for a little math.  Why are we using standard deviation as a measure of separation?  And why does using it make comparing quarterbacks across years more meaningful?  

A non-technical definition of the standard deviation is that it is a measure of the dispersion of a set of data around the average.  By dispersion we mean spread.  Knowing the average of the data, and knowing how spread the data is, we can try to determine how likely a given observed value is.  We can use this data to compare different data sets, and relate them to one another.   So for example, in a data set where the average is 5, and the standard deviation is 2, an observation of 8, would mean 1.5 standard deviations ((8-5)/2 = 1.5) above the the mean.  In a data set where the average was 7, and the standard deviation was 4, a value of 13 would also be 1.5 standard deviations from the mean.   You can now see why the use of a standard deviation could be useful in comparing different sets of data.  

As you can see from Exhibit 1, the league average interception rate has been changing over time.  In addition, while I have not shown it explicitly, the standard deviation around the mean has also been changing.  As a matter of fact, in the early 1940's, the standard deviations were quite high because there were fewer players involved, the number of attempted passes were fewer, and arguably the talent pool was not as great (i.e. passing was a fairly new concept).  

By relating a given observation of an interception rate in 1943 to the mean interception rate that year, and the standard deviation of interception rate that year, one can then compare that particular observation to an observation of an interception rate in 2003, by its relationship to the mean and standard deviation of interception rates in 2003.  If one assumes, in particular,  that in any given year, that all observations about the mean are distributed normally (i.e. a "bell-shaped" curve), then the comparisons become that much more meaningful.  For example we know that in a standard bell-curve, that approximately 68% of the observations will fall into a band +/- 1 standard deviation from the mean, and approximately 95% of observations will fall into a band +/- 2 standard deviations from the mean.  Also, if, after relating the observations in each year to each year's mean and standard deviation, one aggregates the data across all years (since the data has been "normalized" to the same scale - a number in relation to a mean and standard deviation; in the example earlier, the observation of 8 in the first data set has the same value on a normalized basis as the observation of 13 in the second data set - 1.5), then the aggregated data should look like a standard normal curve, with a mean of 0, and a standard deviation of 1.  

Well, I went through the trouble of doing that, and guess what - that is exactly what the looks like.  All 1,451 qualified passers over the 69 years from 1940 to 2008 were analyzed in this manner, and the result is in the graphical illustration below.  The average for the entire data set is -0.06 (close to 0), and the standard deviation is 1.00!  Also, it turns out that 69% of the observations are within +/- 1 standard deviation, and 96% are within +/- 2 standard deviations.  Quite a remarkable achievement!  I've graphed a standard normal distribution as well, so that you can see for yourself how close the actual data is to the theoretical curve.


Exhibit 4 - Same as Exhibit 3, except ranks the worst seasons:
Terry Bradshaw's 1970 rookie season ranks as the all-time worst.  And Vinny Testaverde's 1998 campaign is not that far behind.  Although Testaverde's rookie season was 1987, he didn't "get exposed" until 1988.  Most recently, Gus Frerotte's 2008 campaign was an absolute disaster.  There's some names on the list that I would not have expected to see (let's face it, these are the 50 worst performances over the past 69 years - 1,451 quarterback seasons) - names like Favre and Aikman, along with the aforementioned Bradshaw.  What was even more surprising to me was that they each showed up not once, but twice!

So now you've seen the best and the worst seasons.  How about careers?  Let's take a look at Exhibit 5.


Exhibit 5 - Lowest career interception rate - absolute figures - with a minimum of 1,000 passes attempted:
For reasons I discussed above, I don't like this list that much, as it is biased towards the more recent years.  But, since people like looking at these types of lists, I have included it.  Exhibits 6 (best) and 7 (worst) reorder the data after a player's career has been compared to the average during their career.


Exhibits 6 (best/lowest) and 7 (worst/highest) - career interception rate relative to league average during the same time:
First question is: why, after the long dissertation about standard deviations, am I not using that as the measuring stick?  Simple answer - it's difficult!  It was a relatively simply exercise to calculate standard deviations for each year.  And it's not that difficult to do it for a given set of consecutive years.  Where it becomes increasingly difficult is to do it for every combination of multiple years, over a 69-year period.  At some point before the 2009 NFL season, I'll have it done.  That will be a better reflection of who had good or bad careers, but, in the meantime, this will have to suffice.  It's the next best thing.  It is most certainly better than the absolute comparison shown in Exhibit 5.

Ok, on to a few observations.

Exhibit 6 is a who's who of quarterbacks in football history.  Taking out the 13 players who are either currently playing, or who have retired in the past five years (i.e. not Hall of Fame eligible), 14 of the remaining 37 are in the Hall of Fame.  Let's look at it another way.  There are 27 quarterbacks who are in the Hall of Fame, who played football post 1940.  And two of them, Arnie Herber, and Clarence (Ace) Parker, played much of their careers before 1940.  Of the remaining 25, 14 show up in Exhibit 6.  

Who are the 14?
Steve Young (#14)

And 2 more, Y.A. Tittle (#53), and Troy Aikman (#55) just missed being in the Top 50.  Not a bad list.

What about Exhibit 7?  3 Hall of Famers, Joe Namath, George Blanda, and Terry Bradshaw are in the worst 50 all-time, in terms of their career interception percentage as it relates to the league average during the time that they played.