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Passing efficiency is known as one of the most arcane statistics in all of sports, so here I've provided some clarification.

Passing efficiency (A.K.A. passer rating) is a number indicative of a quarterback (or another player's) overall performance throwing the ball. It takes into account standards established for completion percentage, yards per attempt, touchdowns per attempt and interceptions per attempt, and allocates points according to how the quarterback's own statistics in these areas measure up to them.

NFL.com makes the important note that passer rating obviously can't take into account things like leadership and other intangibles that make a quarterback effective, so the passing efficiency stat is not a holistic measurement of the effectiveness of a QB.

The mathematical formula for calculating passing efficiency is fundamentally the same for the NCAA and the NFL, as the same stats are used, but passer ratings for the two levels end up being very different because the NFL scales values differently and also places caps on the amount of points that can be rewarded per statistic.

NCAA Passing Efficiency

The NCAA developed its formula in 1979 and fixed the values so that the average passer would end up with a rating of 100.0, but since that time passing statistics have improved greatly so as to render a rating of 100.0 as one of a fairly poor quarterback; for instance, Donovan McNabb had a rating of 155.1 for his college career. The NCAA career record for passing efficiency is 163.6, held by Danny Wuerffel of the University of Florida.

The Formula

( { (8.4 * yards) + (330 * touchdowns) - (200 * interceptions) + (100 * completions) } / attempts )

NFL Passing Efficiency

In the NFL computation, players are awarded according to percentages based on the same four statistical entities. The current formula was adopted in 1973 as a revision of the earlier version in order to eliminate inequities that had arisen in the computation of values. In the NFL, a rating of 100 is outstanding; to again reference Donovan McNabb, his passing efficency during his still young four-year NFL career is 79.3, while the all-time career leader is Steve Young of the San Francisco 49ers, who finished his tenure in the NFL with a rating of 96.8.

The Formula

{{ ((yards/attempts - 3) * 0.25) + ((touchdowns/attempts) * 0.2) + (2.375 - ((interceptions/attempts) * 0.25)) + (((completions/attempts) - 30) * 0.5) / 6} * 100}

Each of these four basic numbers that are added and then divided by six and multiplied by 100 is capped at a value of 2.375, except for the interception value, which is 'reverse-capped' at zero. The standard for each value is 1.000, which would leave the average NFL quarterback with a rating of 66.7.

Note: The NFL formula probably can be represented as the NCAA one can, with attempts expressed once at the end, which would make it clearer that the two formulas are similar, but I can't think that hard right now. *_*

Some info from myself, most paraphrased from public domain information at:
http://football.stassen.com/pass-eff/
http://nfl.com/news/981202qbrate.html

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