Passer Rating

On Sunday February 7, the 2020 NFL season concluded when the Tampa Bay Buccaneers defeated the defending Super Bowl LIV champion Kansas City Chiefs in Super Bowl LV, giving the former its second championship and Tom Brady’s seventh ring and fifth Super Bowl MVP award. Also, a player on the Bucs went to my high school and I am happy he now has a ring.

In American football, the quarterback is the most important position because he can be the difference between winning a Super Bowl or simply going to the playoffs. However, football is a team sport so we cannot rely on the quarterback alone to win Super Bowls. That is for another time. I will be focusing on a quarterback statistic called the passer rating. It is calculated based off of the completed passes (comp)against attempts (att), number of yards passed (yds), number of touchdown passes (td), and interceptions (int) by the opposing team.

To get the formula, we need to make a few substitutions to make the equation cleaner

let a = (comp/att - 0.3) * 5
let b = (yds/att - 3) * 0.25
let c = (td/att) * 20
let d = 2.375 - (int*25/att)

Now we can put together the equation

let rating = ((a + b + c + d)/6) * 100. 

In the NFL, if a quarterback gets a rating higher than 158.3, it will be returned as 158.3. A passer rating of 158.3 is considered to be perfect. The full calculation is

function passerRating(comp, att, yds, td, int){
let a = (comp/att - 0.3) * 5
let b = (yds/att - 3) * 0.25
let c = (td/att) * 20
let d = 2.375 - (int*25/att)
let rating = ((a + b + c + d)/6) * 100
if(rating > 158.3){
return 158.3
}
return rating
}

With this formula, we can calculate how well a quarterback did in a game, a season, or an entire career. However, this is just a statistic, and the problem is that statistics never tell the entire story. Let’s look at an example. Say a quarterback completed 20 passes against 30 attempts for 300 yards and 2 touchdowns and no interceptions. His rating will be 121.53. Any rating above 100 is excellent so I can say he had an excellent game. While it is true, it could be because he faced a defense that was terrible at stopping the pass. If the opposing defense allowed on average 300 yards and 2 touchdown passes a game, then it is not as impressive. However, if he passed against a defense that allowed only 20 completions against 30 attempts, 180 passing yards, and 1 touchdown with an interception, this will be more impressive.

Over the years, the NFL is more pass friendly than ever before. If you look at the all-time career passer rating leaders, only 2 quarterbacks who ended their careers before the 2000 NFL season are in the top 20. Their names are Joe Montana and Steve Young, both quarterbacks who played for the San Francisco 49ers. When they were playing, defenses were allowed to maul quarterbacks and receivers without worrying about a flag. Now if defensive players were to try that today, they will get a flag every time. There is evidence that shows that the implementation of pass friendly rules have allowed a higher rating, more yards and touchdown passes, and higher completion percentages. I guarantee you, if Montana and Young were to play with today’s rules, they will be lighting up the league.

In the end, we should not rely too much on statistics because they don’t really decide who ends up as a Super Bowl champion. I guess people created this so commentators and fans use it for debating, though it can be used to get a contract players want.