# Quarterback rating

### Quarterback 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.

A perfect passer rating in the NFL is 158.3. A perfect passing efficiency in college football is 1261.6.

## History

The NFL's complex passer rating was devised in 1971 by a special committee headed by Don Smith, an executive at the Pro Football Hall of Fame.[1][2] Don Weiss created the passer rating.[2] Prior to that, the NFL had struggled with how to crown a passing ranking using multiple statistics.[1]

## NFL, AFL & CFL

The calculation of the NFL (and CFL) passer rating involves more steps than the NCAA formula. In order to establish a maximum value for an NFL player's passer rating, a separate calculation needs to be completed involving each of the following four categories: Completion Percentage, Average Yards Per Attempt, Percentage of Touchdown Passes, and Percentage of Interceptions. If the result in any category is less than 0, the given result should be 0. If the result in any category is greater than 2.375, the given result should be 2.375. This makes the maximum possible quarterback rating for the NFL 158.3. A perfect rating requires at least a 77.5% completion rate, at least 12.5 yards per attempt, a touchdown on at least 11.875% of attempts, and no interceptions.[3]

The four separate calculations can be expressed in the following equations:

$a = \left \left(\left\{\text\left\{COMP\right\} \over \text\left\{ATT\right\}\right\} - .3 \right \right) \times 5$

$b = \left \left(\left\{\text\left\{YARDS\right\} \over \text\left\{ATT\right\}\right\} - 3 \right \right) \times .25$

$c = \left \left(\left\{\text\left\{TD\right\} \over \text\left\{ATT\right\}\right\} \right \right) \times 20$

$d = 2.375 - \left \left(\left\{\text\left\{INT\right\} \over \text\left\{ATT\right\}\right\} \times 25 \right \right)$

where

ATT = Number of passing attempts
COMP = Number of completions
YARDS = Passing yards
TD = Touchdown passes
INT = Interceptions

Then, the above calculations are used to complete the passer rating:

$\text\left\{Passer Rating\right\}_\left\{\text\left\{NFL\right\}\right\} = \left \left(\left\{mm\left(a\right) + mm\left(b\right) + mm\left(c\right) + mm\left(d\right) \over 6\right\} \right \right) \times 100$
where $mm\left(x\right) = \text\left\{max\right\}\left(0, \text\left\{min\right\}\left(x, 2.375\right)\right)$

## NCAA

Passer rating, known formally in college football as passing efficiency or pass efficiency, is based on player performances. The NCAA passing efficiency formula is far simpler[4] than the NFL formula, as it lacks limits on the four components:

$\text\left\{Passer Rating\right\}_\left\{\text\left\{NCAA\right\}\right\} = \left\{\left(8.4 \times \text\left\{YDS\right\}\right) + \left(330 \times \text\left\{TD\right\}\right) + \left(100 \times \text\left\{COMP\right\}\right) - \left(200 \times \text\left\{INT\right\}\right) \over \text\left\{ATT\right\}\right\}$

The NCAA passer rating has an upper limit of 1,261.6 (every attempt is a 99-yard completion for touchdown), and a lower limit of -731.6 (every attempt is completed, but results in a 99-yard loss). A passer who throws only interceptions will have a -200 rating, as would a passer who only throws completed passes losing an average of 35.714 yards.

## Value and Limitations

As mentioned, both the NFL and NCAA passer rating formulae are only based on completion percentage, passing yardage, touchdowns, and interceptions. As the NFL notes, "It is important to remember that the system is used to rate passers, not quarterbacks. Statistics do not reflect leadership, play-calling, and other intangible factors that go into making a successful professional quarterback."[3] For example, it does not factor in rushing yards gained by such quarterbacks as Randall Cunningham, Steve Young, Michael Vick, and John Elway who were also known for their running ability. Nor does it measure a quarterback's win-loss record, how many times he has fumbled or been sacked, or evaluate his leadership and performance during crucial situations such as third-down efficiency or fourth-quarter scoring drives. Passer rating also provides no information about how good the quarterback's teammates are, including how well he is protected by his offensive line when trying to pass or how good his receivers are.

In 2011, the American sports network ESPN developed an alternative statistic called the total quarterback rating which purports to more accurately measure quarterbacks' contribution to their teams' winning.[5] However, the QBR rating system has met with significant backlash amongst fans and commentators alike.

After ESPN's unveiling of total quarterback rating, CNNSI.com published an article by Kerry Byrne of Cold Hard Football Facts highlighting the importance of passer rating in determining a team's success.[6] "Put most simply," the article states, "you cannot be a smart football analyst and dismiss passer rating. In fact, it's impossible to look at the incredible correlation of victory to passer rating and then dismiss it. You might as well dismiss the score of a game when determining a winner. [...] Few, if any, are more indicative of wins and losses than passer rating. Teams that posted a higher passer rating went 203-53 (.793) in 2010 and an incredible 151-29 (.839) after Week 5." Byrne made an expanded defense of the passer rating and its importance for the Pro Football Researchers Association in 2012.[7] The study noted that of the eight teams since 1940 to lead the league in both offensive passer rating and defensive passer rating, all won championships.[8]

## Records

### NFL

Aaron Rodgers holds the NFL record for the highest career passer rating for any player with at least 1,500 attempts, with a current mark of 104.9.[9] In 2011 Rodgers also set the record for highest passer rating in a single season with a 122.5 rating.[10] In 2012, rookie quarterback Robert Griffin III posted a perfect passer rating of 158.3, only the second rookie to do so, along with Drew Bledsoe.[11] Wide receiver Antwaan Randle El, with a passer rating of 157.5 from 21 completed passes of a possible 26, has the highest career rating of any non-QB with more than twenty attempts.[12] Peyton Manning holds the record for the most games with a perfect passer rating (4). As of 2012, 61 NFL quarterbacks have completed a game with a perfect passer rating of 158.3, and seven have done so multiple times. Phil Simms holds the Super Bowl record for the highest passer rating at 150.92 in Super Bowl XXI. Ben Roethlisberger holds the Super Bowl record for the lowest passer rating to win game, at 22.6 in Super Bowl XL.

### NCAA

In Division I FBS (formerly Division I-A), the career record for passing efficiency is held by Sam Bradford of Oklahoma, who had a career mark of 175.6 between 2007 and 2009.[13] The single-season record belongs to Russell Wilson of the Wisconsin Badgers, who achieved a passer rating of 191.8 over the 2011 season, while the freshman record belongs to Michael Vick of Virginia Tech, whose rating during the 1999 season was 180.4.