Passer
Rating
The
NFL's fiendishly complex passer rating was devised in 1971 by Don Smith,
and implemented in 1973. Prior to that, NFL had struggled with how
to crown a passing king. In the mid1930s, when the league began
keeping individual player stats, the passing leader was the quarterback
with the most passing yardage. From
1938 to 1940, the passer with the highest completion percentage was
number one. For 1941 they invented a system ranking the league's
quarterbacks in each of six separate categories  touchdown passes,
yards, interception percentage, etc.  and if you were firstplace in
touchdowns you'd get one point, and if you were 10th place in yardage
you'd get 10 points, and the guy with the lowest total for the six
categories was the top passer. Then
over the next thirty years the criteria waffled back and forth,
reverting occasionally to single categories, like
averagegainperpassattempt, that were interesting but really didn't
tell the whole story. By the time Woodstock brought the era of
free love to a close, the league had returned to a rotisseriestyle
point system where quarterbacks received ranking numbers relative to
their peers' performance in four different passing categories, and the
one with lowest total got the kitty. This
was deemed an inequitable system, because it depended on relative peer
performance and wasn't a meaningful measure of how a quarterback does
from one year to the
next. So
in 1971, Commissioner Pete Rozelle asked the NFL's statistical committee
to fix it. They turned to Don Smith, an executive at the Pro
Football Hall of Fame who was known as a statistical whiz, who developed
the passer rating. Smith's goal was to build a system where each
quarterbacking performance could get a fixed rating that wouldn't depend
on how other quarterbacks did. Smith
liked the numerical cocktail, mixing what were essentially the only the
passing stats tracked  completion percentage, passing yardage,
touchdowns and interceptions. He decided that these four basic
statistics could be used to rate passers  an "average"
performance in each of those four categories would score one point, and
a recordlevel performance would score two points. And of course,
playing very poorly will score zero. Using
data provided from the Elias Sports Bureau, Smith determined that the
average completion percentage in 1970 was about 50%. Equaling that
would be good for one point toward a passer's rating total. The
record at the time was just over 70%, so Smith wanted a 70% completion
percentage to generate two points. The first step of the math
below basically converts 50% to 1, 70% to 2, and provides a sliding
scale for performances in between. Smith
then got league averages for yardsperpassattempt (7), percentage of
passes scoring touchdowns (5%), and percentage of passes intercepted
(5.5%), and for each of those he devised a conversion formula to give a
player one point for working at that average rate, two points for a
record level, and as low as zero points for really eating it. Finally,
the score was adjusted to a passer rating where a really excellent
performance would be about 100. In a move that probably made sense
at the time but has has had everyone else confused for three decades, he
multiplied the raw total by 100 and divided by 6, turning a
statistically average performance  1s across the board  into
66.7. It also made the maximum rating a ridiculous 158.2. The
toprated years of all time are:
Steve Young 
1984 
112.8 
Joe Montana 
1989 
112.4 
Milt Plum 
1960 
110.4 
Sammy Baugh 
1945 
109.9 
And
no one with more than 1,500 pass attempts has maintained a rating above
100. History's leader, Young, retired at 96.8. Behind him are
Montana, Dan Marino, Brett Favre and Peyton Manning.
Notice
that ratings have improved since the early 1970s. In part that is
because NFL rules have opened up the pass game. The "illegal
chuck" rule forced defenders to back off receivers. Refs
lightened up on holding calls against offensive linemen. Then came
the "clearly in the grasp rule" to protect quarterbacks from
brutality by wouldbe sackers. And receivers started wearing
sticky gloves. And windfree indoor stadiums with fast fake turf
turned teams like the St. Louis Rams into passing factories. There's
much more pass offense today, and that explains why the alltime top
five looks like a list made by somebody born after John Belushi died.
By
1979 the league completion average hit 54.1 percent, and it has never
been below that since. And in the 1980s, Bill Walsh and the San
Francisco 49ers devised and pioneered the West Coast offense, which uses
highpercentage, shortyardage completions.
You
couldn't invent a better scheme to juice QB rating numbers. Because, it
turns out, the formula mathematically whacks guys who try to throw long.
Imagine two quarterbacks  Joe Montana and Broadway Joe Namath  who
both drive their teams 30 yards to a touchdown in three plays.
Montana does it with three 10yard passes. His completion
percentage is 100%, and for the drive his rating is 147.9.
Broadway Joe throws two incomplete passes, then on a clutch third and
long he finds a receiver in the end zone  touchdown! For the
exact same result, his rating is 111.1.
Notice
also that even complete passes that lose yardage (the drawback of the
West Coast scheme) can, in some weirdball situations, boost a
quarterback's rating.
Four
categories are used as a basis for compiling a rating:
•
Percentage of completions per attempt
• Average yards gained per attempt
• Percentage of touchdown passes per attempt
• Percentage of interceptions per attempt
Remember
that the statistic presented here measures passers, not quarterbacks 
it does not quantify leadership, play calling, tenacity, or any of the
other attributes of a great quarterback.
There
are four individual steps in making the calculation  here is the math
for each step:
Step
1: Start with completion percentage. Subtract 30 and
divide by 20.
Step
2: Yards per attempt. Subtract 3 and divide by 4.
Step
3: Touchdown passes divided by pass attempts and multiply by 20.
Alternatively, divide the touchdown
percentage by 5.
Step
4: Start with 2.375. Subtract from that the interception percentage
(interceptions divided by pass
attempts) divided by 4.
(Note:
Sum of each step cannot be greater than 2.375 or less than 0.)
Add
the sum of 14, multiply by 100 and divide by 6.
The
rating formula simplifies to:
[25
+ 10 * (Completion Percentage) + 40 * (Touchdown Percentage)

50 * (Interception Percentage) + 50
* (Yards/Attempt)] /12
Note
that the weights on interception percentage and yards per attempt are
greatest in magnitude, closely followed by touchdown percentage. The
weight on completion percentage is a distant fourth in magnitude.
To
earn a 1.000 rating in each category, a passer must perform at
"average" levels, i.e., 50% in completions, 7.00 yards average
gain per pass attempt, 5% in touchdowns, and 5.5% in interceptions.
(These numbers were the mean for the 1970 football year, when Smith
devised the formula).
To
earn a 2.000 rating, a passer must perform at exceptional levels, i.e.,
70% in completions, 10% in touchdowns, 1.5% in interceptions, and 11
yards average gain per pass attempt.
The
fact that each component is limited to a maximum of 2.375 means that the
highest possible passer rating is 158.3. But the kind of season
required to get that kind of a rating is virtually impossible.
The
maximum a passer can receive in any category is 2.375.
For
example, to gain a 2.375 in completion percentage, a passer would have
to complete 77.5% of his passes. The NFL record is 70.55% by Ken
Anderson, who played with the Cincinnati Bengals in 1982).
To earn a 2.375 in percentage of
touchdowns, a passer would have to achieve a percentage of 11.9%.
The record is 13.9% by Sid Luckman (Chicago Bears in 1943).
To gain 2.375 in percentage of
interceptions, a passer would have to go the entire season without an
interception.
The 2.375 figure in average yards is
12.50, compared with the NFL record of 11.17 by Tommy O'Connell
(Cleveland Browns, 1957).
To
help make the formula more understandable, take Steve Young's
recordsetting season in 1994 when he completed 324 of 461 passes for
3,969 yards, 35 touchdowns, and 10 interceptions.
The
four calculations would be:
• Step 1: Percentage of Completions — 324 of 461 is
70.28%. Subtract 30 from the completion percentage (70.2830=40.28) and
divide the result by 20. The result is a point rating of 2.014.
Note: If the result is less than zero (comp. pct. less than
30.0%), award zero points. If the results are greater than 2.375
(comp. pct. greater than 77.5%), award 2.375.
•
Step 2: Average Yards Gained Per Attempt — 3,969 yards divided
by 461 attempts is 8.61. Subtract three yards from
yardsperattempt (5.61) and divide the result by 4. The result is
1.403.
Note:
If the result is less than zero (yards per attempt less than 3.0), award
zero points. If the result is greater than 2.375 (yards per
attempt greater than 12.5), award 2.375 points.
•
Step 3: Percentage of Touchdown Passes — 35 touchdowns in 461
attempts is 7.59%. Divide the touchdown percentage by 5. The
result is 1.518.
Note:
If the result is greater than 2.375 (touchdown percentage greater than
11.875), award 2.375.
•
Step 4: Percentage of Interceptions — 10 interceptions in 461
attempts is 2.17%. Divide the interception percentage by 4 (0.542) and
subtract the number from 2.375. The result is 1.833.
Note:
If the result is less than zero (interception percentage greater than
9.5), award zero points.
The
sum of the four steps is (2.014 + 1.402 + 1.518 + 1.833) 6.767. The sum
is then divided by six (1.128) and multiplied by 100. In this case, the
result is 112.793.
This
same formula can be used to determine a passer rating for any player who
attempts at least one pass. As another example,
take Dan Marino's astonishing season of
1984, when he set singleseason records for yards and TD passes  best
single season ever.
Step
1: He had 362 complete passes
out of 564 attempts, for a 64.2% completion percentage.
(0.6420.3)*5
= 1.709.
Step
2: He had 5,084 yards on 564
attempts, or a YPA of 9.01.
(9.01
 3)/4 = 1.5035.
Step
3: He had 48 touchdown passes 
a record that may never be broken  on 564 attempts, or a TD% of 8.5%.
(0.085*20)
= 1.702.
Step
4: He had 17 picks on 564
attempts, or a Int% of 3.01%.
2.375(3.01/4)
= 2.375  0.7535 = 1.6214.
Step
5: Adding steps 1 through 4, we
get 6.536; multiply the result by 100 and divide by 6, and we have 108.9.
