For football fans, looking at stats of a quarterback, you have different measurables you try to evaluate the individual play of a quarterback with. Sometimes you are influenced by how your fantasy league is set up, or you are trying to compare today’s quarterback to your favourite QB growing up 2, 3, 4, or 5 decades ago.
For football scouts, evaluating measurables of a QB become harder because not only you start looking at the raw numbers, you start looking at style of offence, quality of offensive players around them, quality of opponents played against, play outside vs. inside, good weather or bad weather, with a lead or trailing, and on and on the breakdown happens.
Back in the early 70s, the NFL wanted to identify a passing champion, but does a QB merit a passing champion on 4000 yards passing with 40 interceptions? So the passing efficiency formula was crafted based on completion percentage, yards per attempt, touchdown percentage, and interception percentage. The idea was to have an “average” performance of a 66.7 rating, while a 100 rating performance was outstanding. Today, primarily due to rule changes favouring the passing game, an average performance has inflated to 90.0. The formula produces a perfect rating at 158, while conversely, the bottom score is 0.0
Let’s pull our high school math out and investigate the formula.
Passer Rating Formula
In its simplest form, the Passer Rating Formula is: ((a+b+c+d)/6)*100
where;
- a= Completion Component = (# of completions/passing attempt -0.3)*5
- b=Yards per Attempt Component = (passing yards/passing attempt – 3)*0.25
- c=Touchdown Percentage Component = (Passing TD’s/passing attempt)*20
- d=Interception Percentage Component = 2.375 -(Interceptions/passing attempt)*25
If any component calculation is greater than 2.375, it is set to 2.375.
If any component is a negative number, it is set to 0
Completion Component
To simplify this component, re-write the component in a mathematical slope-intercept form (y=mx+b)
Let a = y,
Let (# of completions/passing attempt -0.3)*5 = (x-0.3)*5 or:
y=5x-1.5
but remember, we have limits of when y is 0 and 2.375.
When y=0, x=0.30
When y=2.375, x=.775
All this tells us is if you have a completion percentage lower than 30%, this component is 0, if your completion percentage is greater than 77.5%, this component is capped at 2.375 and if it is somewhere in between, you fall on that graph.
Yards per Attempt Component
As we did above:
Let b = y
Let (passing yards/passing attempt – 3)*0.25 = (x-3)*0.25 or;
y=0.25x-0.75
When y=0, x=3
When y=2.375, x=12.5
which means: when yards per attempt is 3 yds/att or lower, this component is 0, if your yards per attempt is 12.5 yds/att or greater, this component is capped at 2.375 and if it is somewhere in between, you fall on that graph.
Touchdown Percentage Component
As we did above:
Let c = y
Let (Passing TD’s/passing attempt)*20 = x*20 or;
y=20x
When y=0, x=0
When y=2.375, x=0.11875
which means: when TD% is 0%, this component is 0, if your TD% is 11.875% greater, this component is capped at 2.375 and if it is somewhere in between, you fall on that graph.
Interception Percentage Component
As we did above:
Let d = y
Let 2.375 -(Interceptions/passing attempt)*25 = 2.375 -x*25 or;
y=2.375-25x
Of the 4 components,this one has the only negative slope and the steepest slope
When y=0, x=0.095
When y=2.375, x=0
which means: when INT% is 0%, this component is 2.375, if your INT% is 9.5% greater, this component is capped at 0 and if it is somewhere in between, you fall on that graph.
Now, that was in the simplest form. Based on 2001 CFL documentation, and following rounding/truncation rules, this is how you calculate Passing Efficiency: Let’s use Cody Fajardo’s passing stats (282/385, 3408 yds, 14 TD’s, 7 Int’s) from 2025 as an example.
Step 1 – Completion Percentage
- Completions divide by attempts (282/385=0.7324675)
- multiply by a hundred (73.24675)
- round to one decimal (73.2)
- if 30 or less, assign a zero value
- if 77.5 or greater, assign a value of 2.375
- otherwise, subtract 50 from this number (73.2-50=23.2)
- multiply by 0.05 (23.2*0.05=1.16)
- add 1 (1.16+1=2.16)
- take this number to final step
Step 2 – Average Gain
- Total yards divide by Attempts (3408/385=8.851948)
- round to two decimals (8.85)
- if 3.00 or less, assign a zero value
- if 12.5 or greater, assign a value of 2.375
- otherwise, subtract 7 from this number (8.85-7=1.85)
- multiply by 0.25 (1.85*.25=0.4625)
- round to two decimals (0.46)
- add 1 (0.46+1=1.46)
- take this number to final step
Step 3 – Percentage of Touchdowns
- Touchdowns thrown divide by attempts (14/385=0.036363636)
- multiply by 100 (3.6363636)
- round to one decimal (3.6)
- if zero, assign a zero value
- if result is 11.9 or greater, assign a value of 2.375
- otherwise, subtract 5.0 from this number (3.6-5.0=-1.4)
- multiply by 0.2 (-1.4*0.2=-0.28)
- add 1 (-0.28+1=0.72)
- take this number to final step
Step 4 – Percentage of Interceptions
- Interceptions thrown divide by attempts (7/385=0.0181347)
- multiply by 100 (1.81347)
- round to one decimal (1.8)
- if zero, assign a value of 2.375
- if 9.5 or greater, assign a zero value
- otherwise, subtract this number from 9.5 (9.5-1.8=7.7)
- multiply result by 0.25 (7.7*0.25=1.925)
- round to two decimals (1.93)
- take this value to final step
Final Step – Passing Efficiency Calculation
- sum up value from steps 1 to 4 (2.16+1.46+0.72+1.93=6.27)
- divide by 6 (6.27/6=1.045)
- multiply by 100 (104.5)
- truncate to one digit of decimal (104.5)
The formulas are the same but the direction on rounding could play a difference in some calculators.
***Note: To all the math educators out there, use this as an example of rounding and truncation ***
The advantage of the passing efficiency calculation is that it allows us to measure QBs game over game, year over year, and decade over decade as a measure. You can parse the data by quarter or while winning or losing. An incomplete pass that is intentionally thrown away punishes the completion percentage component but only below 77.5% and rewards the percentage of interceptions component. It does have drawbacks, as QB running yards are not considered or the number of times sacked
This tells me Fajardo’s strength last season was in his pass completion followed by low Interception percentage,while he was lacking in percentage of touchdowns thrown. Overall, Fajardo’s rating being above 100 is a solid measure.
Is it math class June yet?
