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:



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Click here for a list of quarterbacks witha Perfect Passer Rating


Use the formulas above to answer the following three questions.

(1) Sonny Jurgensen (Washington Redskins, 1974) completed 107 passes out of 167 attempts for 1,185 yards with 11 touchdowns and 5 interceptions.   Determine the values of a, b, c, d, and his Passer Rating.

(2) Matt Ryan (Atlanta Falcons, 2017) completed 342 passes out of 529 attempts for 4,095 yards with 20 touchdowns and 12 interceptions.   Determine the values of a, b, c, d, and his Passer Rating.

(3) Patrick Mahomes (Kansas City Chiefs, 2017) attempted 35 passes for 284 yards with 0 touchdowns and 1 interception and a passer rating of 76.4.   Determine the values of a, b, c, d, and the number of passes he completed.

Solution to the Problem:

(1) Sonny Jurgensen
a = 1.703, b = 1.023, c = 1.317, d = 1.626
Passer rating = 94.5

(2) Matt Ryan
a = 1.732, b = 1.185, c = .7561, d = 1.807
Passer Rating = 91.36

(3) Patrick Mahomes
a = 1.642, b = 1.278, c = 0, d = 1.66
Completed passes = 22


Correctly solved by:

1. Ivy Joseph Pune, Maharashtra, India
2. James Alarie Flint, Michigan
3. Caden Sweep Mountain View High School,
Mountain View, Wyoming
4. Tyler Petersen Mountain View High School,
Mountain View, Wyoming
5. Brijesh Dave Mumbai City, Maharashtra, India