NFL Passer Rating

For the teacher:

NFL Passer Ratings are discussed every Sunday during the Fall. The following formulas will help the student to understand how the ratings are computed.

The teacher should work through several examples before assigning the problems on the worksheet. In the first seven problems, the student computes the values of a, b, c, d, and the Passer Rating. In the last four problems, the student is given the Passer Rating and must work backwards to solve for the missing variable.

Background:
The NFL passer rating formula includes four variables: completion percentage, yards per attempt, touchdowns per attempt, and interceptions per attempt.

Each of those variables is scaled to a value between 0 and 2.375, with 1.0 being statistically average (based on league data between 1960–1970).

Passer rating in the NFL is on a scale from 0 to 158.3.

The four separate calculations can be expressed in the following equations:

where
ATT = Number of passing attempts
COMP = Number of completions
YDS = Passing yards
TD = Touchdown passes
INT = Interceptions

If the result of any calculation is greater than 2.375, it is set to 2.375. If the result is a negative number, it is set to zero.

Then, the above calculations are used to complete the passer rating:

Click here for a printer version of the Passer Rating

Examples:

I like to use "real data" in my problems. All the data in the worksheet is accurate.

Here is the data for Matt Ryan who played for the Atlanta Falcons in 2017:
Completions: 342
Attempts: 529
Yards: 4,095
Touchdowns: 20
Interceptions: 12

Show the calculations for the variables:
a = 1.732
b = 1.185
c = .7561
d = 1.807
Passer rating = 91.4

Students may be interested in how you get a 0.0 passer rating or a 158.3 passer rating.
Peyton Manning got both of these ratings in games in 2004 and 2015.
Here is his data for those games:

On November 15, 2015:
Completions: 5
Attempts: 20
Yards: 35
Touchdowns: 0
Interceptions: 4

Show the calculations for the variables:
a = 0
b = 0
c = 0
d = 0
Passer rating = 0.0

On January 4, 2004:
Completions: 22
Attempts: 26
Yards: 377
Touchdowns:5
Interceptions: 0

Show the calculations for the variables:
a = 2.375
b = 2.375
c = 2.375
d = 2.375
Passer rating = 158.3

You may wish to show one example where you are given the passer rating and you have to solve for the number of completions.

Here is the data for Sonny Jurgensen who played for the Washington Redskins in 1974:
Passer rating = 94.5
Attempts: 167
Yards: 1,185
Touchdowns: 11
Interceptions: 5

Show the calculations for the variables:
a = 1.703
b = 1.023
c = 1.317
d = 1.626
Completions: 107