Passer Rating

Passer rating (known as passing efficiency or pass efficiency in NCAA football) is a measure of the performance of quarterbacks or any other passers in American football and Canadian football. There are at least two formulae currently in use: one officially used by the National Football League and the Canadian Football League, and one used in college football. Passer rating is calculated using each quarterback's completion percentage, passing yardage, touchdowns and interceptions.

CFL and NFL
The NFL's current passer rating (also known as quarterback rating) system was conceived by Pro Football Hall of Fame's retired vice president Don Smith in 1973. The system is a sliding scale design, where outstanding performances meet diminishing returns faster than sub-par ones. The best passer rating that a quarterback can obtain is 158.3, while the worst is zero. The architects of the passer rating had 66²⁄3 in mind as the "average" score, but as styles of play have changed, so have average passer ratings. The cumulative league-wide average passer rating for the years 2000 through 2003, all inclusive, was 78.9 (the figure is typically rounded to the nearest 1/10 of a point); however in 2004 the league average was 82.8. In 2007, the average was 83.5. Passer rating has been applied all seasons.

Calculation
Passer rating is determined by four statistical components, each of which is computed as a number between zero and 2.375. The benchmarks for these statistics are based on historical averages. If any of the raw components are beyond the limits of zero or 2.375, the component is set to limiting value of zero or 2.375 as the case may be.
 * The component for completion percentage, C, is calculated as: $${{COMP \over ATT} \times 100 - 30 \over 20}$$


 * The component for yards per attempt, Y, is calculated as: $$\left( { YDS \over ATT } - 3 \right) \times { 1 \over 4 }$$


 * The component for touchdowns per attempt, T, is calculated as: $${ TD \over ATT }\times 20$$


 * The component for interceptions per attempt, I, is calculated as: $$2.375 - \left( { INT \over ATT } \times 25 \right)$$

The four components are then added, divided by 6, and multiplied by 100. Thus, the formula for passer rating can be given as: "${\max(\min(C,2.375),0) + \max(\min(Y,2.375),0) + \max(\min(T,2.375),0) + \max(\min(I,2.375),0) \over 3}\times 50$." The Canadian Football League uses the same formula as the NFL. 

Perfect and Zero NFL passer ratings
Since each component of passer rating can be at most 2.375, the maximum passer rating is   "${4 \times 2.375 \over 6}\times 100 = 158.3$."

A perfect passer rating therefore comprises:


 * a completion percentage of at least 77.5%: $$2.375 \times 20 + 30 = 77.5$$


 * at least 12.5 yards per attempt: $$2.375 \times 4 + 3 = 12.5$$


 * at least 0.11875 touchdowns per attempt, or at most 8.42 attempts per touchdown: $${2.375 \over 20} = 0.11875$$ and


 * zero interceptions: $${ATT \times (2.375 - 2.375) \over 25} = 0$$

A zero passer rating comprises


 * a completion percentage of at most 30%: $$0 \times 20 + 30 = 30$$


 * 3 yards per attempt or less: $$0 \times 4 + 3 = 3$$


 * zero touchdowns: $${0 \over 20} = 0$$


 * at least 9.5 percent interceptions: $${ATT \times (2.375 - 0) \over 25} = 0.095$$

A passer who does not throw an interception has a minimum rating of 39.6.

NCAA
Passer rating, known formerly in college football as passing efficiency or pass efficiency, is based on player performances. The NCAA passing efficiency formula is:


 * The component for completion percentage, C, is calculated as: $${COMP \over ATT}\times 100$$


 * The component for yards per attempt, Y, is calculated as: $${YDS \over ATT}\times 8.4$$


 * The component for touchdowns per attempt, T, is calculated as: $${TD \over ATT }\times 330$$


 * The component for interceptions per attempt, I, is calculated as: $${ INT \over ATT }\times -200$$

The four components are then added. Thus, the formula for passer rating can be given as: $${(C + Y + T + I)}$$ The NCAA passer rating has an upper limit of 1,261.6 and a lower limit of -731.6. The upper limit value results if every pass thrown is a 99-yard touchdown and the lower limit if every pass thrown for a 99-yard loss. A passer who throws only interceptions will have a -200 rating. 

CFL
In CFL football Dave Dickenson of the BC Lions has produced some of the highest professional passing efficiency numbers. Although limited by injuries in 2005, he set two regular season records with a 74 percent completion percentage and an efficiency rating of 118.8. His numbers for the year were: 253/342, 3338 yards, 74% completion rate, 21 TDs, 5 INTs. He opened the 2006 season by setting a CFL single-game passing efficiency rating record of 150.61. He capped 3 of the 4 criteria for passing efficiency and was 28/34, 362 yards, 5 TDs, 0 INTs.

NFL
Steve Young currently holds the NFL record for the highest career passer rating for any player with at least 1500 attempts with a mark of 96.8. The highest passer rating for a complete season is 121.1 set by Peyton Manning in 2004. Also in 2005, rookie Ben Roethlisberger posted a mark of 98.1, setting a new record for first-year passers. There have been 34 quarterbacks to complete a game with a perfect passer rating of 158.3 (and only 4 to have accomplished this more than once), the most recent being Ben Roethlisberger in 2007.

NCAA
In NCAA Football Bowl Subdivision (formerly division I-A), the career record for passing efficiency is held by Ryan Dinwiddie of Boise State, who had a career mark of 168.9 between 2000 and 2003. The single-season record belongs to Colt Brennan of Hawaii, who amassed a passer rating of 186.0 over the 2006 season, while the freshman record belongs to Michael Vick of Virginia Tech, whose rating during the 1999 season was 180.4. Current NCAA Football Bowl Subdivision passing efficiency ratings can be found here.

External links and references

 * NFL.com QB Rating Page
 * Online QB Rating Calculator. NFL formula.
 * Online passer rating calculator for NFL/CFL, NCAA and AFL formulas
 * All-Time Top NFL Passer Ratings List
 * QB Rating Calculator
 * New York Times - The N.F.L.'s Passer Rating, Arcane and Misunderstood - January 14, 2004