Passer rating

Passer rating is the name of the method for evaluating the performance of quarterbacks and any other passers officially used by the National Football League.

Calculation

The passer rating is determined by four statistics, each of which are computed as a number between zero and 2.375. The benchmarks for these statistics are based on historical averages. If any of the components are less than zero, they are reckoned as zero; if any are over 2.375, they are reckoned as 2.375.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• The completion percentage rating is calculated as $\{\{COMP\; over\; ATT\}\; imes\; 100\; -\; 30\; over\; 20\}$
• The rating for average yards per attempt is calculated as $left(\; \{\; YDS\; over\; ATT\; \}\; -\; 3\; ight)\; imes\; \{\; 1\; over\; 4\; \}$
• The rating for touchdowns per attempt is calculated as $\{\; TD\; over\; ATT\; \}\; imes\; 20$
• The rating for interceptions per attempt is calculated as $2.375\; -\; \{\; INT\; over\; ATT\; \}\; imes\; 25$

The result is then summed, divided by 6, and multipled by 100. Since each of these numbers is at most 2.375, the maximum passer rating is

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

{4 imes 2.375 over 6} imes 100 = 158.3.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~