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# Passer rating

Passer rating (also known as quarterback rating, QB rating, or passing efficiency in college football) is a measure of the performance of passers, primarily quarterbacks, in American football and Canadian football.[1] There are two formulae currently in use: one used by both the National Football League (NFL) and Canadian Football League (CFL), and the other used in NCAA football. Passer rating is calculated using a player's passing attempts, completions, yards, touchdowns, and interceptions. Since 1973, passer rating has been the official formula used by the NFL to determine its passing leader.[2] Passer rating in the NFL is on a scale from 0 to 158.3. Passing efficiency in college football is on a scale from −731.6 to 1261.6.

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#### Transcription

One stat you'll hear referenced from time to time during a football game is called Passer Rating. Which is a single number that seeks to describe how effective the quarterback, or whoever has been passing the ball, has been with his passes. It must be kept in mind the passer rating only attempt to describe the passing rather than the overall performance of the quarterback, which would include how well he can keep a play alive, the rushing yards he might have, or even his play-calling ability. The most confusing aspect of the passer rating is probably that it's on a scale from 0 to 158.3. But maybe we can reduce some of that confusion by breaking it down a bit further and looking at the things that go into finding the number. Passer rating is calculated based on five common stats: passes attempted, passes completed, yards gained, touchdown passes, and interceptions. and more specifically, from those numbers we can calculate: completion percentage, average yards per attempt, percentage of touchdown passes, and percentage of interceptions. These percentages and averages are then plugged into a formula that compares them to a standard that has been established based on passing performances over the years. As mentioned earlier, the highest possible rating is 158.3, which is considered a perfect passer rating. Though it's difficult to achieve, a quarterback does not have to throw a touchdown with every pass or even have to have an 100% completion rate to get a perfect rating. For a perfect single-game rating a quarterback must attempt at least ten passes he can't throw any interceptions, and he must have a minimum 77.5% completion, 12% touchdown pass percentage, and gain at least 12.5 yards per attempted pass. It's not an easy task although some quarterbacks have achieved the feat multiple times there will probably be one game out of an entire NFL season in which someone achieves a perfect passer rating. Short of being perfect, any game and certainly any season in which a quarterback has a passer rating over 100 is an excellent performance. An average passer rating would be around 70. Now if you want to get technical, the passer rating formula was developed in the 1970s and it looks something like this: Don't worry, it's not scary is it looks, because as we said it is comprised of four parts. Completion percentage, average yards per attempt, percentage of touchdown passes, and percentage of interceptions. The score in each of those four categories can range anywhere from 0 to 2.375. And that makes one about average. The best way to really understand this is probably to run through example so let's take a random game from Aaron Rodgers that he had back in 2009; he has traditionally had one of the strongest passer ratings of any quarterback. On this particular afternoon Rodgers and the Packers played San Francisco. Rogers ended up completing 32 of 45 passes attempted, which was good for 344 yards. Two of the passes were touchdown passes and he threw no interceptions. Part one is completion percentage. To get our number, we take our completions and divide it by the number of attempts to give us 71.1% completion percentage, or in decimal form 0.711. Our formula next tells us to subtract 0.3 from this, and then multiply that number by 5. Which comes out to 2.055. Part two is yards per attempt, so we take our 344 yards divide it by the 45 attempts--and note that this is passes attempted, not just the passes completed--and this gives us 7.644. From this number we subtract 3, to get 4.64 for and then divide that number by 4 which gives us 1.161. Next is touchdowns per attempt, so 2 divided by 45 tells us that nearly 5% of the passes ended up in the end zone. We then multiply that number, which is technically 0.044, by 20 which gives us 0.88. Finally we take our interceptions, which Rodgers threw none of on this afternoon, and divide that by 45. So we get zero. And then we multiply that by 25 which once again gives us zero. But since zero interceptions is good, we take this sum and we subtract it from the maximum score of 2.375, which leaves us with that 2.375. It's worth repeating here that the maximum total any one at these numbers can be is 2.375. Even if a quarterback were to complete 100% percent of his passes, and that would mean our value in that category would come out to be 3.5, but when we run through the next part of our calculation we would only give him the maximum value 2.375 in that category. We would not give him 3.5. And this is so that we don't give any one category too much weight over the others. The same thing applies with the minimum, which is zero. Even if we get a negative figure we would give him a total of zero in that category. But let's get back to Rogers. Our next step is to ad these four numbers up. So 2.055 + 1.161 + 0.88 + 2.375, that gives us 6.471. We then divide this number by 6 to get 1.078. Finally we multiply that by 100 to get our passer rating 107.8! So it was not a perfect afternoon for Rogers, but the Packers were able to defeat the 49ers and a passer rating 108 is a pretty great day, but you can 'double check' the math if you want to.

## History

Before the development of the passer rating, the NFL struggled with how to crown a passing leader. In the mid-1930s, it was the quarterback with the most passing yardage. From 1938 to 1940, it was the quarterback with the highest completion percentage. In 1941, a system was created that ranked the league's quarterbacks relative to their peers' performance. Over the next thirty years the criteria used to crown a passing leader changed several times, but the ranking system made it impossible to determine a quarterback's rank until all the other quarterbacks were done playing that week, or to compare quarterback performances across multiple seasons. In 1971, NFL commissioner Pete Rozelle asked the league's statistical committee to develop a better system.[3] The committee was headed by Don Smith of the Pro Football Hall of Fame, Seymour Siwoff of the Elias Sports Bureau, and NFL executive Don Weiss. Smith and Siwoff established passing performance standards based on data from all qualified pro football passers between 1960 and 1970, and used those data to create the passer rating. The formula was adopted by the NFL in 1973.[2]

## NFL and CFL formula

The NFL passer rating formula includes four variables: completion percentage, yards per attempt, touchdowns per attempt, and interceptions per attempt. Each of those variables is scaled to a value between 0 and 2.375, with 1.0 being statistically average (based on league data between 1960–1970). When the formula was first created, a 66.7 rating indicated an average performance, and a 100+ rating indicated an excellent performance.[3] However, passing performance has improved steadily since then and in 2017 the league average rating was 88.6.[4]

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

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

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

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

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

where

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

If the result of any calculation is greater than 2.375, it is set to 2.375. If the result is a negative number, it is set to zero.

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

${\displaystyle {\text{Passer Rating}}=\left({(a+b+c+d) \over 6}\right)\times 100}$

A perfect passer rating (158.3) requires at least:[1] A minimum rating (0.0) requires at best:

77.5% completion percentage
12.5 yards per attempt
11.875% TD/ATT (1 TD/8.421ATT)
No interceptions

30.0% completion percentage
3.0 yards per attempt
No touchdowns
9.5% INT/ATT (1INT/10.526ATT)

## NCAA formula

The NCAA passing efficiency formula is similar to that of the NFL passer rating, but does not impose limits on the four components:[5]

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

where

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

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.

In 2011, Sports Illustrated 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

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.[11] Ben Roethlisberger 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 record for the highest passer rating in a Super Bowl, at 150.92 in Super Bowl XXI.

## References

1. ^ a b "NFL.com – NFL Quarterback Rating Formula". Archived from the original on August 14, 2011. Retrieved August 6, 2011.
2. ^ a b "NFL's Passer Rating". Pro Football Hall of Fame Official Site. NFL. January 1, 2005. Archived from the original on October 3, 2015. Retrieved December 27, 2016.
3. ^ a b "QB Rating story / GQ magazine / by Don Steinberg". bluedonut.com. Archived from the original on September 18, 2013. Retrieved April 29, 2018.
4. ^ SteelersFan, Tim (July 23, 2009). "Did NFL Passer Ratings Spike in 2004 Or Have They Risen Steadily?". bleacher report. Bleacher Report, Inc. Archived from the original on December 28, 2016. Retrieved December 27, 2016.
5. ^ "NCAA and NFL Passing Efficiency computation". Football.stassen.com. Archived from the original on November 10, 2011. Retrieved November 15, 2011.
6. ^ "Kerry J. Byrne: In defense of passer rating". si.com. Archived from the original on December 11, 2017. Retrieved April 29, 2018.
7. ^ Cold Hard Football Facts: 40 and Fabulous: in praise of passer rating Archived August 17, 2012, at the Wayback Machine
8. ^
9. ^ "Player Game Finder Query Results". Pro Football Reference. Retrieved November 27, 2018.
10. ^ "Player Game Finder Query Results". Pro Football Reference. Retrieved November 27, 2018.
11. ^ King, Peter (November 15, 2010). "Patriots? Jets? Giants? There are no super NFL teams this season". Sports Illustrated. Archived from the original on December 7, 2010. Retrieved January 6, 2011.
12. ^ "Kyler Murray College Stats - College Football at Sports-Reference.com". College Football at Sports-Reference.com. Retrieved January 14, 2019. |archive-url= is malformed: timestamp (help)
13. ^ "Tua Tagovailoa College Stats - College Football at Sports-Reference.com". College Football at Sports-Reference.com. Retrieved January 14, 2019. |archive-url= is malformed: timestamp (help)
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