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        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 mid-1930s, 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 first-place 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 average-gain-per-pass-attempt, 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 rotisserie-style 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 record-level 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 yards-per-pass-attempt (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 top-rated 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 would-be sackers.  And receivers started wearing sticky gloves.  And wind-free 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 all-time 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 high-percentage, short-yardage 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 10-yard 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 1-4, 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 record-setting 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 (70.28-30=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 yards-per-attempt (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 single-season 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.  

(0.642-0.3)*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.


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