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NCAA and NFL pass-efficiency formulas
By Richard Linde, Updated 16 April 2004

The pass-efficiency rating is a measure of a quarterback’s passing ability, and not a measure of his overall ability, which includes leadership, play calling, clock-management 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 open-ended 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 two-platoon football was implemented) to 1979.

Since 1979, NCAA passers have improved on technique and receivers have become more sure-handed, 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 yards-per-attempt is limited between 3.0 and 12.5 yards (0-2.375). 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 Pass-Efficiency Formula

To determine a pass-efficiency 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*330-I/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*330-I*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 Pass-Efficiency 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 passing-efficiency 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 Pac-10 teams

Running the calculations for team play, we find some shifts in the rankings, notably the UW moves from seventh in the Pac-10 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, NFL-wise.
 
Team NCAA NFL Change
U$C 159.08 110.41 1-1
Berserkly 147.26 100.77 2-2
Yucks 134.99 88.42 3-3
Sickses 124.93 83.36 4-4
Peevers 124.49 74.22 5-7
Palosers 122.34 74.31 6-6
Dawgs 117.51 75.93 7-5
Blewwins 106.34 66.22 8-8
Wildbrats 93.8 51.91 9-10
Treefolkers 92.08 54.55 10-9


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

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