NFL Passer Score: A New and Improved Statistic for Measuring QB Play

Adam Fromal@fromal09National NBA Featured ColumnistDecember 25, 2010

NFL Passer Score: A New and Improved Statistic for Measuring QB Play

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    14 Dec 1998: Steve Young #8 of the San Francisco 49ers signals a touchdown during the game against the Detroit Lions at 3Com Park in San Francisco, California. The 49ers defeated the Lions 35-13. Mandatory Credit: Jed Jacobsohn  /Allsport
    Jed Jacobsohn/Getty Images

    In my spare time, I was looking back through the perfect games that have been played by quarterbacks in the history of the NFL. While gazing through this list of 158.3 ratings, two consecutive games caught my eye. 

    Frank Ryan in 1964 completed 12 of his 13 passes for 202 yards and five touchdowns. He received, of course, a perfect 158.3 passer rating. 

    The very next perfect performance in history was the next year. 

    Sonny Jurgenson in 1965 completed 12 of his 14 passes for 195 yards and three touchdowns. He also received the perfect rating. 

    This boggled my mind. Ryan completed a higher percentage of his passes, threw for more yards and scored more touchdowns. How in the world could they have the same rating? There was no way to qualify the level of perfection using the current quarterback rating system. 

    So I set out to find out exactly what the flaws were with the current system and then developed my own system, which is based on the old method. 

    I've called my new system Passer Score, or PS. 

    Read on for the details. Any feedback is appreciated. 

How Passer Rating Is Calculated

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    NASHVILLE, TN - DECEMBER 09:  Peyton Manning #18 of the Indianapolis Colts gives instructions to his team during the NFL game against the Tennessee Titans  at LP Field on December 9, 2010 in Nashville, Tennessee.  (Photo by Andy Lyons/Getty Images)
    Andy Lyons/Getty Images

    The current system for rating quarterbacks is called passer rating and was developed in 1971 by Don Smith's special committee. Seymour Siwoff and Don Weiss are also credited with the creation of the now-outdated stat. 

    Passer rating is comprised of five separate calculations, four of which deal with different statistics and the fifth of which (the actual passer rating) combines the original four. The first four (A, B, C and D) are mutations of completion percentage, average yards per attempt, touchdowns per attempt and interceptions per attempt.

    A: Based on Completion Percentage

    First, a quarterback's number of completions are divided by the number of attempts, resulting in the traditional format for completion percentage. Then, 0.3 is subtracted from the result and that end product is multiplied by five.

    B: Based on Average Yards per Attempt

    First, the traditional yards per attempt number is found by dividing passing yards by attempts. Three is subtracted from the result and then that number is multiplied by 0.25.

    C: Based on Touchdowns per Attempt

    The traditional touchdowns per attempt stat is found by dividing passing touchdowns by number of attempts. That number is subsequently multiplied by 20.

    D: Based on Interceptions per Attempt

    Dividing the number of interceptions by the number of attempts gives the traditional statistic for interceptions per attempt. That result is then multiplied by 25 and subtracted from 2.375 afterwards.

    Passer Rating: The Combination of A, B, C and D to Achieve the Final Statistic

    For each A, B, C and D, the number generated is compared to 2.375 and the minimum is taken. If it's positive that number stays, but if it's negative, it's replaced by 0. Because of this, four new numbers are generated. 

    Those numbers are added together and the sum is divided by six then multiplied by 100. 

    After all that, you've calculated a quarterback's passer rating. 


The Problems With Passer Rating

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    EAST RUTHERFORD, NJ - DECEMBER 19:  Michael Vick #7 of the Philadelphia Eagles stands by the huddle against the New York Giants at New Meadowlands Stadium on December 19, 2010 in East Rutherford, New Jersey.  (Photo by Nick Laham/Getty Images)
    Nick Laham/Getty Images

    Now that I've explained to you how passer rating is calculated, we can go over the problems with it.

    Subjectiveness

    First, the numbers don't really make sense. What is a good passer rating? Can anybody give me a definitive number? 

    Truthfully, I couldn't. I have no idea what an average quarterback is supposed to have. Something around 60 or 70? 

    I've heard 100 thrown out as an idea for a good quarterback's passer rating, but no one in history has a career passer rating in triple digits.

    Lack of Negatives

    Because of the maximums and minimums used in the final part of the calculation, passer rating doesn't allow quarterbacks to have negatives in any category. 

    In other words, throwing two interceptions in 10 passes is just as bad as throwing three. By not allowing for the negatives, the rating is essentially saying that once you've reached a certain level of badness, playing worse doesn't hurt your team any more. 

    That's simply not true.

    Lack of Distinction for the Elites

    To get a perfect passer rating, a quarterback must attain the following statistical benchmarks: 77.5 percent completion rate, 12.5 yards per attempt, a touchdown on 11.875 percent of their attempts and no interceptions. 

    However, once those benchmarks are reached, it doesn't matter by how much a quarterback surpasses them.

    That was the problem with Ryan and Jurgenson in the original example. 

    A quarterback that gains 13 yards per attempt clearly doesn't help his team as much as one that gains 25 yards per attempt, but they are statistically of equal value to their team according to passer rating. 

General Overview Of Passer Score

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    SEATTLE, WA - DECEMBER 19:  Quarterback Matt Ryan #2 of the Atlanta Falcons rushes against the Seattle Seahawks at Qwest Field on December 19, 2010 in Seattle, Washington. (Photo by Otto Greule Jr/Getty Images)
    Otto Greule Jr/Getty Images

    In general, my formula for Passer Score is based off the same four statistics as passer rating: completion percentage, yards per attempt, touchdowns per attempt and interceptions per attempt. 

    However, not only does it allow for negatives, it also is put together in a way that a 0 PS means that the quarterback is perfectly average. A positive PS means the quarterback is above average while a negative PS means the quarterback is below average. 

    Each of the four individual components, with the exception of interceptions per attempt, is put together in a way so that a quarterback equalling the all-time record in the statistic will receive a component score of 25. For interceptions, a quarterback that throws no interceptions will receive a component score of 25. 

    Basically, if a quarterback throws no interceptions while equalling the all-time completion percentage mark, yards per completion mark and touchdowns per completion mark, they will receive a 100 PS. 

    Moreover, because it is possible to break those records in a single-game setting, it is possible to have a single-game PS of over 100. 

    The next few slides will explain each component. Once they're all found, they're simply added together to create PS.

    A caveat: the calculations are a bit more difficult, but they do make more sense. 

Component 1: Completion Percentage

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    GREEN BAY, WI - NOVEMBER 07: Aaron Rodgers #12 of the Green Bay Packers looks for a receiver against the Dallas Cowboys at Lambeau Field on November 7, 2010 in Green Bay, Wisconsin. The Packers defeated the Cowboys 45-7. (Photo by Jonathan Daniel/Getty Im
    Jonathan Daniel/Getty Images

    From the beginning of the Super Bowl era, 1966, to the end of the 2009-2010 season, there were 584,458 passes thrown in professional football. Of those, 329,220 were completed, good for a historical completion percentage of 56.3 percent. 

    However, the average completion percentage is trending upwards. In the 1960's 50.1 percent of passes were completed, 52.2 percent in the 1970's, 55.5 percent in the 1980's, 57.3 percent in the 1990's and 59.8 percent in the 2000's. The NFL's average completion percent seems to be leveling out right around 60 percent in recent years. 

    For that reason, we're going to set the historical "average" completion percentage at 58 percent. 

    The best seasonal completion percentage of all time is shared by two men. Ken Anderson in 1982 completed 70.6 percent of his passes and his record was matched by Drew Brees in 2009. 

    If we call that 70.6 percent the maximum, that means that the largest realistic difference between an individuals completion percentage and the "average" completion percentage is 12.6 percent.

    I wanted for a quarterback with a difference between those two stats of 12.6 percent to receive 25 points in this component, so I had to multiply the difference by 198.413 to have that happen. 

    That left the formula for Component 1 as: 198.413 multiplied by the difference between an individual's completion percentage and 58 percent. Mathematically, it's written as Component 1 = 198.413 * (Individual's completion percentage - 58%).

Component 2: Yards Per Attempt

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    SAN DIEGO, CA - DECEMBER 16:  Quarterback Philip Rivers #17 of the San Diego Chargers drops back to pass against the San Francisco 49ers at Qualcomm Stadium on December 16, 2010 in San Diego, California.  (Photo by Harry How/Getty Images)
    Harry How/Getty Images

    Over the same time period, the 3,739,331 attempted passes have gone for 7,478,662 yards, an average of 6.29 yards per attempt. Yards per attempt though has also been steadily trending upwards for as long as the Super Bowl has been around. 

    It is however starting to tail off a bit, which is why I set the "average" yards per attempt number at 6.3. 

    Over the course of a full season, the best yards per attempt was set by Sid Luckman. Way back in 1942, Luckman averaged 10.9 yards per pass throughout the season. Others have come close, but no one has ever matched that. 

    If we call that 10.9 yards per attempt the maximum, that means that the largest realistic difference between an individuals yard per attempt and the "average" yards per attempt is 4.6. 

    I wanted for a quarterback with a difference between those two stats of 4.6 to receive 25 points in this component, so I had to multiply the difference by 5.434 to make that happen. 

    That left the formula for Component 2 as: 5.434 multiplied by the difference between an individual's yards per attempt and 6.3. Mathematically, it's written as Component 2 = 5.434 * (Individual's yards per attempt - 6.3).

Component 3: Touchdowns Per Attempt

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    MINNEAPOLIS - NOVEMBER 21:  Quarterback Brett Favre #4 of the Minnesota Vikings looks for an open receiver while playing the Green Bay Packers at the Hubert H. Humphrey Metrodome on November 21, 2010 in Minneapolis, Minnesota.  (Photo by Matthew Stockman/
    Matthew Stockman/Getty Images

    With 49,154 touchdown passes thrown between 1966 and the start of this season, the historical average for touchdown passes per attempt is 0.0413. Just about four percent of passes have resulted in scores, at least scores for the offense. 

    That average appears to be leveling out right about at 0.0413, after falling precipitously during the 1980's and 1990's. Therefore, I made 0.0413 the "average" touchdown passes per attempt.

    Back in 1943, Sid Luckman set the mark for the most touchdown passes per attempt at 0.139, however it is clearly an outlying number. Second place is Frankie Albert's 1948 mark of 0.11. That is an outlier as well. 

    A more realistic number to strive for is Albert's 1949 number of 0.104, the third best of all time. 

    If we call that 0.104 the maximum, that means that the largest realistic difference between an individual's touchdown passes per attempt and the "average" touchdown passes per attempt is 0.0627. 

    I wanted for a quarterback with a difference between those two stats of 0.0627 to receive 25 points in this component, so I had to multiply the difference by 398.72.

    That left the formula for Component 3 as: 398.72 multiplied by the difference between an individual's touchdown passes per attempt and 0.0413. Mathematically, it's written as Component 3 = 398.72 * (touchdown passes per attempt - 0.0413).

Component 4: Interceptions Per Attempt

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    PITTSBURGH - DECEMBER 23:  Ben Roethlisberger #7 of the Pittsburgh Steelers signals after scoring a touchdown against the Carolina Panthers during the game on December 23, 2010 at Heinz Field in Pittsburgh, Pennsylvania.  (Photo by Jared Wickerham/Getty I
    Jared Wickerham/Getty Images

    Since 1966 and prior to the 2010 season, there had been 46,864 interceptions in football. That makes the historical interceptions per attempt number stand at .0394.  Fortunately for offenses, that is slightly lower than the touchdown statistic. 

    The historical number has been hovering right at .0394 for a while, so I'm going to call that the "average" interceptions per attempt. 

    Damon Huard has the lowest interceptions per attempt mark of all time, .004 in 2006.  Yet, while it’s impossible to throw a touchdown on every pass and still throw enough passes to be eligible, it is feasible to have no interceptions in a season. Realistic? Maybe not, but it is still feasible. 

    If we call zero the minimum, that means that the largest realistic difference between the "average" interceptions per attempt and an individual's is.0394. 

    I wanted for a quarterback with a difference between those two stats of 0.0394 to receive 25 points in this component, so I had to multiply the difference by 634.52.

    That left the formula for Component 4 as: 634.52 multiplied by the difference between .0394 and an individual's interceptions per attempt. Mathematically, it's written as Component 4 = 634.52 * (.0394 - individual's interceptions per attempt).

    Note that the numbers in parentheses are reversed because having a higher number of interceptions is a negative thing. 

Passer Score

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    NEW ORLEANS, LA - DECEMBER 12:  Drew Brees #9  of the New Orleans Saints looks to throw the ball during the game against the St. Louis Rams at the Louisiana Superdome on December 12, 2010 in New Orleans, Louisiana.  (Photo by Chris Graythen/Getty Images)
    Chris Graythen/Getty Images

    The final step for calculating Passer Score is much simpler than the one used for passer rating. 

    Instead of worrying about maximums and minimums, the components are simply added up to produce the final score. By eliminating maximums and minimums, a higher range of scores, including negatives, is opened up. 

    For a single game, it's feasible that a quarterback could perform better than the seasonal records and have a Passer Score of over 100. However, over the course of a season, it's unlikely that a quarterback will be able to break records for all four statistics involved, making 100 a maximum seasonal Passer Score. 

Does Passer Score Solve The Subjectiveness Problem?

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    EAST RUTHERFORD, NJ - DECEMBER 19:  Eli Manning #10 of the New York Giants is sacked by Moise Fokou #53 of the Philadelphia Eagles at New Meadowlands Stadium on December 19, 2010 in East Rutherford, New Jersey.  (Photo by Nick Laham/Getty Images)
    Nick Laham/Getty Images

    A perfectly average quarterback, one that completes 58 percent of his passes, averages 6.3 yards per attempt, 0.0413 touchdowns per attempt and 0.0394 interceptions per attempt will have a Passer Score of exactly 0.0.

    Any quarterback that is statistically better than average will have a positive Passer Score while a below-average quarterback will have a negative one. 

    Let's take for example three quarterbacks this year. Tom Brady is having an excellent season, Matt Hasselbeck an average one, and Jimmy Clausen has been simply terrible. 

    As of Christmas Day in the 2010 season, Brady had completed 299 of his 449 passes for 3,561 yards, 31 touchdowns and four interceptions. Hasselbeck had completed 263 of his 440 passes for 2,977 yards, 12 touchdowns and 17 interceptions. Clausen had completed 138 of his 266 passes for 1,376 yards, 2 touchdowns and eight interceptions. 

    Their passer ratings don't tell us that much. It appears as though Brady's 109.92 rating is very good, but how do we qualify Hasselbeck's 73.08 and Clausen's 56.84. There are no benchmarks to go by. 

    Their Passer Scores tell a much more clear story. 

    Brady's Passer Score is an astounding 56.32, Hasselbeck's an almost perfectly average 0.94 and Clausen's is a terrible -25.82. 

    To understand just how great Brady's season has been, you need to know that the best season by a quarterback every, statistically speaking, was Peyton Manning's  2004 season when he posted a 121.11 passer rating and a 69.73 Passer Score. Both of those are the highest of all time. 

    In fact, just four seasons by quarterbacks have resulted in Passer Scores of over 60. Manning's 2004, Brady's 2007, Steve Young's 1997 and Joe Montana's 1989. Looking at the historical data, a Passer Score of over 50 is a great indication of a very good season. 

    50 is a nice and easy number to remember and helps to solve the subjectiveness problem. 

Does Passer Score Solve The Negative Problem?

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    INDIANAPOLIS, IN - DECEMBER 19: David Garrard #9 of the Jacksonville Jaguars hands off to Maurice Jones-Drew #32 against the Indianapolis Colts at Lucas Oil Stadium on December 19, 2010 in Indianapolis, Indiana.  (Photo by Scott Boehm/Getty Images)
    Scott Boehm/Getty Images

    The answer to this question is a definitive yes. 

    Take two hypothetical seasons by a quarterback. 

    Quarterback A completes 70 of his 100 passes and they go for 700 yards, 18 touchdowns and 12 interceptions.

    Quarterback B completes 70 of his 100 passes and they go for 700 yards, 18 touchdowns and 14 interceptions.

    Well, since Quarterback B has identical stats to Quarterback A except for the fact that he threw two more interceptions, Quarterback B should have a worse evaluation. 

    Passer rating gives Quarterback A a rating of 89.58. It also gives Quarterback B a rating of 89.58. 

    Why? Because once the interceptions per attempt number hits a certain mark, it doesn't matter how much it exceeds the limit produced by the calculation by. Even though Quarterback B was statistically worse, passer rating thinks that they are statistically identical. If one of those extra two interceptions caused an extra loss, I guarantee that general managers wouldn't have identical statistical evaluations of the two. 

    Now, let's take a look at what Passer Score says. 

    Quarterback A receives a Passer Score of 31.73 while Quarterback B gets a 19.08. Quarterback B took a big hit for throwing those two extra interceptions. If the dip was bigger than you expected, it's because of the small number of passes each quarterback hypothetically threw. 

Does Passer Score Solve the Lack of Distinction for the Elite Problem?

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    KANSAS CITY, MO - DECEMBER 05:  Quarterback Matt Cassel #7 of the Kansas City Chiefs in action during the game against the Denver Broncos on December 5, 2010 at Arrowhead Stadium in Kansas City, Missouri.  (Photo by Jamie Squire/Getty Images)
    Jamie Squire/Getty Images

    To answer this question, let's take a look back at what grabbed my attention in the first place. 

    Frank Ryan in 1964 completed 12 of his 13 passes for 202 yards and five touchdowns. He received a passer rating of 158.3, supposedly "perfect."

    The next 158.3 rating went to Sonny Jurgenson in 1965 after the quarterback completed 12 of his 14 passes for 195 yards and three touchdowns. 

    Ryan completed a higher percentage of his passes, threw for more yards, threw more touchdown passes and received the exact same passer rating. Huh?

    Well, Passer Score gives Ryan a 280.16 while Jurgenson receives only a 190.42. Both incredible games, but it distinguishes the level of greatness. In fact, Ryan's game produced the highest single-game Passer Score of all-time. 

    To prove the point further, let's throw in one more game where the quarterback received a 158.3 passer rating. 

    In 1994, Craig Erickson completed 19 of his 24 passes for 313 yards and three touchdowns. While his passer rating was still 158.3, his Passer Score was only 137. That's a pretty sizable dip from 280.16. Erickson's 137 PS is actually the lowest Passer Score of any game that the passer rating calls perfect. 

Conclusion

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    ATLANTA - NOVEMBER 11:  Quarterback Joe Flacco #5 of the Baltimore Ravens against the Atlanta Falcons at Georgia Dome on November 11, 2010 in Atlanta, Georgia.  (Photo by Kevin C. Cox/Getty Images)
    Kevin C. Cox/Getty Images

    While the calculation involves slightly more complicated numbers because of the decimals, Passer Score is a much more accurate assessment of quarterback performances than passer rating. 

    It allows for negatives, gives benchmarks that the general public will understand, and distinguishes between the elite games and seasons in a way that passer rating can't. 

    At this point it's only a pipe dream, but hopefully this new statistic will eventually catch on and be popularized. 

    I'd love your feedback, criticism and support. Feel free to tell people about it and even start using it in your own evaluations. 

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