Being a quarterback in American football involves a lot of math. Quarterbacks are judged statistically on all levels of football by their passing accuracy (which is called completion percentage), the number of touchdowns they throw, the number of interceptions they throw, and the number of yards they gain by passing.
This last statistic — passing yards — can be deceiving. For example, if a quarterback throws the ball 8 yards beyond the line of scrimmage and the receiver runs for another 42 yards after catching the ball, the quarterback is awarded 50 yards for the completion. (You may hear television commentators use the term yards after the catch to describe the yards that the receiver gains after catching the ball.) Quarterbacks also receive positive passing yards when they complete a pass behind the line of scrimmage — for example, a screen pass to a running back who goes on to run 15 yards. Those 15 yards are considered passing yards.
For a better understanding of what the quarterback’s numbers mean, take a look at Green Bay Packers quarterback Aaron Rodgers’s statistics for the 2009 season. He played in all 16 regular-season games.
| Att | Comp | Pct Comp | Yds | Yds/Att | TD | Int | Rating |
|---|---|---|---|---|---|---|---|
| 541 | 350 | 64.7 | 4,434 | 8.2 | 30 | 7 | 103.2 |
Here’s a breakdown of Rodgers’s statistics:
Att: He attempted 541 passes.
Comp: He completed 350 of those passes.
Pct Comp: He had a completion percentage of 64.7.
Yds: In attempting those 541 passes, his receivers gained 4,434 yards.
Yds/Att: The yards achieved equal an average gain per attempt of 8.2 yards.
TD: Rodgers’s teammates scored 30 touchdowns via his passing.
Int: The defense intercepted 7 of his passing attempts.
When you see a newspaper article about a football game, the story may state that the quarterback was 22 of 36, passing for 310 yards. Translation: He completed 22 of 36 pass attempts and gained 310 yards on those 22 completions. Not a bad game.
Last but not least, you have the NFL quarterback rating formula, also called the passer rating formula. It makes for an unusual math problem. Grab your calculator and follow these steps to figure it out:
Divide completed passes by pass attempts, subtract 0.3, and then divide by 0.2.
Divide passing yards by pass attempts, subtract 3, and then divide by 4.
Divide touchdown passes by pass attempts and then divide by 0.05.
Divide interceptions by pass attempts, subtract that number from 0.095, and divide the remainder by 0.04.
The sum of each step can’t be greater than 2.375 or less than zero.
Add the sums of the four preceding steps, multiply that number by 100, and divide by 6.
The final number is the quarterback rating, which in Rodgers’s case is 103.2.
A rating of 100 or above is considered very good; an average rating is in the 80 to 100 range, and anything below 80 is considered a poor quarterback rating.