The Wacky Algebra of NFL Passer Rating

Artifact

The following formula calculates NFL Passer rating. (wiki)

(note: each component has a predetermined MAX and MIN value that appeared to be pulled out of thin air.)

Personally, I would simply present this equation to students at the beginning of class and let them stare at it a while and try to figure some things out in their heads. Eventually, the teacher and students should probably come up with some guiding questions.

Guiding Questions

• Who came up with this thing?
• Which “component” is most important to QB rating? Why?
• Why aren’t rushing yards included? Could we include them? How?
• Why do you divide by 6?
• Why do you multiply by 100 at the end?
• Does this convoluted formula correlate at all with being a good QB?
• Does the formula change with era? Should it?
• Can we change this formula to make Quarterback X look better? (There’s either a fan question or an agent question. For this region of the country, it would be John Elway.)

Suggested activities

There are a lot of routes you could go with it – comparing passer rating in different eras, creating your own formula that is either less or more complex, regressing passer rating with team offensive production to measure the importance of the quarterback and/or the validity of the formula – but I’m going to go one particular route: comparing the top two current career leaders in passer rating, who, as luck would have it, are still playing today.

Currently, the QB with the highest passer rating in NFL history (minimum 1500 attempts) is Green Bay quarterback (and apparently a regular personality here) Aaron Rodgers at 98.4 (stats can be found here). Phillip Rivers is second with 97.2 (stats found here). How many incompletion in a row would Rodgers have to throw in order to fall behind Rivers? How many interceptions would he have to throw in a row? Conversely, how many, say, touchdowns would Rivers have to throw to surpass Rodgers? Can we graph this mess?

Solution

Here’s how Rogers’ career passer rating was calculated.

Here’s how Rivers’ passer rating is calculated.

Line 1: Rogers currently has a passer rating of 98.4.

Line 2: Rogers if he threw only incomplete passes from here on out. From this point forward, let x be the passes thrown henceforth.

Line 3: Rivers’ current passer rating of 97.2.

Line 4: Rivers’ passer rating if he only threw touchdowns (of, let’s say, 10 yards) from here on out. We’d have to add 1x for each completion and 10x for the number of yards thrown.

Here’s the graph of these plots, windows adjusted accordingly.

It’s kind of amazing that it could potentially take fewer than 8 passes to change the career passing rating leaders from Rodgers to Rivers.

Here’s a related question.

Could Rivers possibly surpass Rodgers with just one pass? Or how about one pass from Rivers (presumably a long touchdown pass) and/or one pass from Rodgers (presumably an interception)?

Here’s Rivers’ calculated passer rating again, now set equal to Rodgers’ current value of 98.4. Let’s solve for x to see what kind of throw it would take to equal that value.

x=  651.9

So Rivers would have to throw a 652 yard TD pass to surpass Rodgers in one throw. Pretty unlikely.

There are a lot of scenarios with which to manipulate this formula.

This past year saw Philadelphia Eagles QB Michael Vick finish 4th in passer rating, but by some accounts he was the best QB in the league due to his rushing abilities, not calculated in Passer Rating. What would happen if we did include another category for rushing? Basically, isn’t a rush pretty much the same as a completed pass? Could we just tack on the yards and consider it another completion. What would that look like? Are those accounts right?

• If NFL passer rating is a tad too complex for your particular students, you could do something similar with baseball’s ERA, or Slugging Percentage, or OPS metrics.
• Or assign different groups different metrics (give your GT students NFL Passer Rating) and ask them to come up with a brief presentation about it.
• You are an NFL agent. Your client is, say, Vince Young. Create your OWN formula to present to an NFL franchise suggesting he’s worth more money. I know MLB agents do this all the time. (I may develop this one further as a potential PBL unit, but I’d prefer if someone else did it for me. Because I am lazy.)

There are a myriad of other questions to be answered about the passer rating formula. Any other suggested ways we could use this?

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