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NCAA and NFL passefficiency formulas
By Richard Linde, Updated 16 April 2004
The passefficiency rating is a measure of a quarterback’s passing ability, and
not a measure of his overall ability, which includes leadership, play calling,
clockmanagement and a variety of skills that determine a
quarterback’s performance.
In both cases (NFL and NCAA), the formulas involve computations for four
categories of performance; they are: (1) yards per pass attempt, (2) pass
completions per pass attempt, (3) touchdowns per pass attempt and (4)
interceptions per pass attempt.
The NCAA formula provides an openended computation for the four
categories, while the NFL formula caps the categories so they cannot be above or
below certain values.
In the NCAA formula, four constants (i.e., 8.4, 100, 330, and 200) are used to
"ensure" that an average passer will have a rating of 100. The two constants
involving yards per attempt (8.4) and completions per pass attempt (100)
were chosen so that the average passer would have a total of 100 points when the
two categories were added together. The constants involving touchdowns per pass
attempt and interceptions per pass attempt (330 and 200 respectively) were
chosen to cancel out each category (i.e., x  y = 0). The four constants were
chosen by examining passing statistics involving team play from 1965 (when
twoplatoon football was implemented) to 1979.
Since 1979, NCAA passers have improved on technique and receivers have become
more surehanded, while the liberal use of hands rules for offensive linemen have
given passers more time to look for an open receiver. An average passer who
sported a 100 rating from years' past would be considered a poor passer in college football today
[2].
In the NFL, the average standard is 1.000. The bottom is .000. To earn a 2.000
rating, a passer must perform at exceptional levels, i.e., 70 percent in
completions, 10 percent in touchdowns, 1.5 percent in interceptions, and 11
yards average gain per pass attempt [1]. The maximum a passer can receive in any
category is 2.375, while the lowest is zero. A perfect passer would have a
rating of 158.3, i.e., 4*2.375/6*100 (see formula below).
By limiting the numbers calculated for each category between 0 and 2.375,
passers performing below and above certain levels will have the results for each
category adjusted, either upward or downward. If a passer has a pass completion
percentage less than 30%, his computation for that category is set to zero,
rather than to a negative number. Passers completing more than 77.5% of their
passes will have the result set downward to 2.375. Similarly, the
yardsperattempt is limited between 3.0 and 12.5 yards (02.375). The touchdown
percentage can be no more than 11.875% and the interception computational result
must be set to zero if it turns out to be a negative number.
The NFL formula was adopted in 1973.
NCAA PassEfficiency Formula
To determine a passefficiency rating, multiply a passer's yards per
attempt by 8.4; add the number obtained by multiplying pass completions per
attempt by 100; add the number obtained by multiplying touchdowns per attempt by
330; and subtract the number obtained by multiplying interceptions per attempt
by 200.The formula is as follows:
ER = TY/PA*8.4+PC/PA*100+TD/PA*330I/PA*200,
where TY=total yards; PC=pass completions; PA=pass attempts; TD=touchdowns;
I=Interceptions; ER=Efficiency Rating.
Factoring out 1/PA leaves:
ER = (TY*8.4+PC*100+TD*330I*200)/PA
Example: Cody Pickett’s stats as of 20 October 2003.
256 attempts
148 completions
8 interceptions
1913 yards
10 TD
1913/256*8.4 + 148/256*100 + 10/256*330  8/256*200=127.21
Pickett’s Passing efficiency rating is 127.2
NFL PassEfficiency Formula
A rating of 158.3 is considered perfect in professional football. A 100 rating
is considered spectacular.
The NFL Computation is as follows:
T = [((100 * PC/PA)  30.0) * 0.05] + [((TY/PA)  3.0) * 0.25] + [20 * TD/PA] +
[2.375  (25 * I/PA)]
ER = T/6.0 * 100
The four categories above, delineated by brackets, are capped at 0.0 (min) to
2.375 (max).
Assuming Pickett had been in the NFL – which will occur in 2004 – his NFL
passingefficiency rating (ER) would have been:
T = [((100 * 148 / 256)  30.0) * 0.05] + [((1913 / 256)  3.0) * 0.25] + [20 *
10 / 256] + [2.375  (25 * 8 / 256)]
T = [1.391] + [1.118] + [0.781] + [1.594] = 4.884
ER = 4.884/6.0 * 100 = 81.40
Pickett’s rating is 81.4.
None of Pickett’s categories needed capping, i.e., was greater than 2.375 or
less than 0.0. For example, had the last bracketed value been less than zero, a
value of 0.0 would have been inserted in its place.
Meaning of constants in
NFL formula: First bracket [((100 * PC/PA)  30.0) * 0.05]
100, 30, 05 – Multiply the completions per attempt by 100 to obtain the
percentage. Subtract 30 to ensure the percentage is not less than 30%
completions. If the result is less than zero, set the result to zero.
Multiplying the result by .05 ensures the percentage won't be greater than 77.5%
(i.e., greater than 2.375, that is 47.5*.05=2.375)). In the greater case, set the
result to 2.375.
Second bracket: [((TY/PA)  3.0) * 0.25]
3.0, .25 – The yards per completion can’t be less than 3; if the result is less
than zero, set the result to zero. Multiplying the result by .25 ensures the
yards per completion won't be greater than 12.5 (greater than 2.375; that is,
9.5*.25=2.375). If the result is greater than 2.375 set the result to 2.375.
Third bracket: [20 * TD/PA]
20 – Multiplying touchdowns per attempt by 20 ensures the result won’t be
greater than 11.875% (that is, 20 * .11875 = 2.375). If the result is greater than 2.375,
set the result to 2.375.
Fourth bracket: [2.375  (25 * I/PA)]
25 – Ensures that the interception percentage is not greater than 9.5% (that is, 25
* .095 = 2.375). If the result is less than zero, set the result to zero.
ER calculation: T/6.0 * 100
100, 6  Multiplying by 100 spreads the
ratings out. Dividing by six ensures that no pass rating will be above 158.3
(that is, 100*4*2.375/6=158.3).
Comparing NCAA and NFL formulas
using
Pac10 teams Running the
calculations for team play, we find some shifts in the rankings, notably the UW
moves from seventh in the Pac10 to fifth when the NFL formula is
used. In the NFL ranking, differences in completion percentage (56% to 51%)
and interception percentage (2.9% to 4.7%) move the Dawgs ahead of the
Beavers. USC and Cal post some outstanding numbers, NFLwise.
Team 
NCAA 
NFL 
Change 
U$C 
159.08 
110.41 
11 
Berserkly 
147.26 
100.77 
22 
Yucks 
134.99 
88.42 
33 
Sickses 
124.93 
83.36 
44 
Peevers 
124.49 
74.22 
57 
Palosers 
122.34 
74.31 
66 
Dawgs 
117.51 
75.93 
75 
Blewwins 
106.34 
66.22 
88 
Wildbrats 
93.8 
51.91 
910 
Treefolkers 
92.08 
54.55 
109 
Reference the following links:
[1] (NFL Formula)
[2] (Compute a passer's rating)
Richard Linde (a.k.a., Malamute) can be reached at
malamute@4malamute.com 