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November 26, 2010

Just How The (Bleep) is the Passer Rating Determined Anyway?


After hearing the announcers mention Tom Brady's perfect passer rating of 158.3 during his Thanksgiving victory over Detroit, we put our mathematical thinking caps on and tried to figure it out. Maybe it was too much turkey, or perhaps the 24-pack we drank during the game, but our thinking caps didn't fit properly. Instead we went to the NFL Record & Fact Book. Apparently, this is how the passer rating is determined. We're pretty sure the Canadians or Al-Qaeda are behind this. Here goes:
Four categories are used as a basis for compiling a rating:
1. Percentage of completions per attempt
2. Average yards gained per attempt
3. Percentage of touchdown passes per attempt
4. Percentage of interceptions per attempt

The average standard is 1.000. The bottom is .000. To earn a 2.000 rating, a passer must perform at exceptional levels, i.e., 70 percent in completions, 10 percent in touchdowns, 1.5 percent in interceptions, and 11 yards average gain per pass attempt. 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 percent of his passes. The NFL record is 70.55 by Ken Anderson (Cincinnati, 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, 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, 1957).

In order to make the rating more understandable, the point rating is then converted into a scale of 100, with 158.3 being the highest rating a passer can achieve. In cases where statistical performance has been superior, it is possible for a passer to surpass a 100 rating. For example, take Peyton Manning’s record-setting season in 2004 when he completed 336 of 497 passes for 4,557 yards, 49 touchdowns, and 10 interceptions. The four calculations would be:

—Percentage of Completions—336 of 497 is 67.60 percent. Subtract 30 from the completion percentage (37.60) and multiply the result by 0.05. The result is a point rating of 1.880. 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.

—Average Yards Gained Per Attempt—4,557 yards divided by 497 attempts is 9.17. Subtract three yards from yards-per- attempt (6.17) and multiply the result by 0.25. The result is 1.543. 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.

—Percentage of Touchdown Passes—49 touchdowns in 497 attempts is 9.86 percent. Multiply the touchdown percentage by 0.2. The result is 1.972. Note: If the result is greater than 2.375 (touchdown percentage greater than 11.875), award 2.375.

—Percentage of Interceptions—10 interceptions in 497 attempts is 2.01 percent. Multiply the interception percentage by 0.25 (0.503) and subtract the number from 2.375. The result is 1.872.
Note: If the result is less than zero (interception percentage greater than 9.5), award zero points.

The sum of the four steps is (1.880 + 1.543 + 1.972 + 1.872) 7.267. The sum is then divided by six (1.211) and multiplied by 100. In this case, the result is 121.1. This same formula can be used to determine a passer rating for any player who attempts at least one pass.

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