Stats 101: Lesson 1, Passer Rating

Possibly the most used and least understood stat in sports conversation these days is the quarterback passer rating.  It's a trendy stat to use in water-cooler football talk, but it seems few fans realize what they mean when they cite it. It's a good, and fairly robust, stat because it incorporates multiple aspects of a player's performance into a single number.  Still, as we'll see, it may soon need some measure of adjustment to better reflect a changing game - especially if it is to be used to compare quarterbacks from different eras.  Wikipedia has an excellent entry on the subject, which served as the starting point for my research.  The NFL's official explanation is frankly lacking in detal.


The Basics

The passer rating is always a number between zero and 158.3, and is calculated from four components that are each limited to values between 0 and 2.375.  The components measure a quarterback's completion percentage [C], yards per attempt [Y], touchdowns per attempt [T], and interceptions per attempt.  The formula expressed in these terms is [(C + Y + T + I)/6] x 100 = passer rating.  The beauty of this formua is that it tracks all of the major passing statistics without regard to how often a quarterback throws the ball.  With each component calculated per attempt, it removes the problem of comparing a QB whose team passes 66% of the time to one whose team runs 66% of the time, for example.

The easiest mistake to make is to fail to set the limits to each of the components.  I will be pointing this out multiple times as we go on, because if limits are not used the resulting number is meaningless.  It is important to note that the formula does not automatically contain these limits.  (The exceptions are that 'I' cannot exceed 2.375 and 'T' cannot be less than 0, so two of eight limits are inherent in the formula.) If you are doing it by hand you must change all results below zero to zero and all results above 2.375 to 2.375.  If you are using a spreadsheet, you must set each component's minimum and maximum values.  The best way to illustrate why this is bad is with the "perfect pass."  If a quarterback attempts one pass, which is a completion for a 100-yard touchdown, the resulting passer rating would be 669.07 without constraints.  Conversely, if one pass is attempted and picked off the resulting passer rating without constraints is -414.58.  Ouch.

The other easy-to-make mistake is to confuse the NFL's passer rating with the NCAA's version, called  passing efficiency.  The NCAA formula uses different coefficients for each component and does not have bounds.  I'm discussing passer rating because 1) it is more widely known and 2) it is frankly a lot more meaningful.


The Components

"So how the heck do you calculate the components?  Stop telling us how NOT to find a passer rating and tell us how TO find one."

I know, right?  Here we go.

Completion percentage is given as C = [(Comp/Att x 100)-30]/20.  Note that this could range from -1.5 to 3.5, so the limits must be set.

Yards per attempt is given as Y = (yards/ATT -3) x 1/4.  Note that this could range from -0.75 to 24.25, so again the limits must be set.

Touchdowns per attempt is given as T = (TD/ATT) x 20.  Note that this could range from 0 to 20, so the upper limit must be set.

Interceptions per attempt is given as I = 2.375 - [(INT/ATT) x 25]. Note that this could range from -22.625 to 2.375, so the lower limit must be set.

So there it is; all you need to calculate a passer rating.  If you're one of those who loves to tinker with things, you can do some algebra and express the formula in a number of different ways.  The most straightforward, of course, is to plug in the expressions for C,Y,T,I into the master formula and simplify.  I prefer to calculate each component separately, because it is easier to remember to impose limits, if necessary.  Remember that any time you algebraically rearrange this formula you must do some calculations to retain the limits.

Then again, you could always cheat. Several such sites exist.  But that's no fun.


History and Answers to Some Obvious Questions

The passer rating seems to have entered the vernacular only recently, but it has been around since 1973 and has been retroactively applied to all NFL seasons.  It was the brainchild of Don Smith, one-time Pro Football Hall of Fame veep.  66.6 was intended as the standard, and although that was an approximation of the average passer at the time the league average has recently risen to above 80.  If this trend continues, it may make sense to adjust the maximum value of each component to compensate for the increased efficiency of the passing game.  For now, this is not a major problem as the perfect passer rating is rarely obtained even for a single game.

Q: I get zero, but why 2.375?
A: This limiting value was decided upon to obtain the "average" of 66.6, based on passing stats available in 1973.

Q: Why set limits at all?
A: The formula was designed as a sliding scale calculation in accordance with the law of diminishing returns.  Simply put, the designers did not want exceptionally poor or outstanding performances to produce uselessly inflated numbers.  (See above)


Flaws

Like any stat measuring individual performance in a team sport, the passer rating has its flaws.  For example, it cannot take into account interceptions or dropped passes that are not a mistake of the quarterback.  It also is not weighted for strength of opposing defenses, nor does it account for teammates.  How good is the offensive line?  How many yards after the catch does the receiver post?  This cool site lets you play with the formula by assigning different weights to each component, and even modifying some of the components.  Some of the results can be really illuminating - but make sure you pay attention to what you are doing to the numbers to know what your changes mean.

Another problem is that nothing a quarterback does on the ground is taken into consideration...although this is not a flaw, per se, given the formula's intent, (to measure passing, not quarterbacks).  As the passer rating has gained wider use as a sign of general QB quality, this has become a flaw.

Finally, I must here reiterate the changing nature of the game.  The limits set in 1973 are becoming increasingly suspect as the average passer rating increases.  It is probably worthwhile to a) establish era or year coefficients when comparing quarterbacks across time or b) redesign the formula with new maximums.  However, even without adjustment the passer rating remains a useful tool for comparison of quarterbacks who are contemporaries.


Further Applications

Leave it to a nerd like me to be excited by the prospects of what the passer rating could be used for but isn't yet.  It is already a powerful tool, but it has the potential to be much more powerful.  A dedicated (amateur or professional) statistician could answer a lot of intriguing questions through creative use of the passer rating.  For example:

How much does a great WR help a quarterback?

One could calculate, for example, Peyton Manning's passer rating to Marvin Harrison versus other receivers.  Or, track a wide receiver's effect on the passer rating of his quarterback as he switches teams.  One could even isolate a passer rating when a given WR is on the field to determine the indirect effect he has by drawing coverage, blocking, etc.  It could be an indirect way of discovering who brings what that doesn't show up in the box score.

How much does a good running game effect passer rating?

Any number of correlations could be established here.  It's always been a fundamental principle of some coaching philosophies that a good ground game opens up the passing game, and that balance is important.  One way of confirming or denying this would be to view how passer rating changes with the effectiveness of a running back.

What defenses are actually effective versus the pass?

How about checking on passer rating versus the prevent defense?  I have no idea what the numbers say, but I'd be willing to bet they would make coaches and DCs think twice about using this set too often.  Or: How do certain defensive schemes alter a given passer's rating?  Useful tools indeed for game planning and playbooks.

How does passer rating change with the weather?

Maybe this one is silly, but I'm curious.  Does the cold really make it harder?  How about wind, rain, and snow?

What routes yield the highest passer rating?

Is a short hook more likely to give a good rating?  How about a deep ball, a slant, or a cross?  Another way to edit that playbook.

Design your own.  The possibilities are limitless.


So, I hope you have left here more informed about the passer rating.  Now you can snigger at your friends who draw outrageous conclusions and wow them with your ability to calculate them .