What's the best stat for measuring QB performance, part I: Passer rating

"nice passer rating" "thanks, nice super bowl win" - Kevin C. Cox

There may not be a singular "best stat" for quarterbacks, but if you had to rank them in order, what would come first? Passer rating makes it's case... if only you could understand it.

So far on Field Gulls I've detailed a couple of advanced stats, like DYAR and DVOA, but what of the less advanced? What are we really to make of the stats that have been around for decades, the classics, the first things that pop up when checking out a box score? And most importantly, would it be possible to answer the question: What is the best stat for measuring quarterbacks?

There probably won't be a "best stat" for a QB, more likely a top three or top five, but why don't we go on a journey to try and figure it out. Hell, Frodo and Sam once went on a journey that made Peter Jackson a billion dollars or something, and then later forced millions of fans to stupidly sit in a theater for nine more hours of The Hobbit for a book that was 320 pages.

Speaking of needlessly stretching things out, I was originally just going to list all the QB stats into one post, but soon realized that this first stat alone had a long history and interesting formula that I had never considered before. Passer rating has always just "been there" and we never asked why. Sort of like that mole on my right nipple, though that's only been there for three weeks and growing rapidly.

A lot of people use passer rating as their number one stat for quarterbacks, but should they? And do they even know what it means? Let's take a closer look.

Passer rating

Passer rating is like the McDonald's secret special sauce* of stats: Nobody knows what it is but everybody knows what it is. But do you really know what it is?

*Did you know it was called special sauce and not secret sauce? They're not actually even trying to hide anything!

Everyone will tell you that special sauce is just Thousand Island dressing -- mayo, ketchup, relish -- but not only is it a slight variation on the classic (probably consisting of onion, sugar, French dressing instead of ketchup) there's also the case of not taking into account the ingredients that go into the ingredients. What makes up the mayo? What makes up the relish? There are a bunch of steps that go into making special sauce that you don't know about or care about, which likely also includes 29-letter chemicals that are meaningless by the time they're going into your mouth, down to your belly, and out your butt.

In a way, passer rating also comes out of your butt. And it includes a shit-load of steps and calculations that are rendered somewhat meaningless by the time it becomes 97.2 or 102.7.

Much like the special sauce, you think you know the basic ingredients to passer rating: Touchdowns, interceptions, completions, and yards. But it is so much more than that. So much more that by the time you're done finding out what passer rating actually is, you'll probably hate it. Even if you already did hate it, you'll hate it more.

Passer rating was developed and implemented in 1973 as the NFL's new measure of evaluating the top quarterback each season. Per ProFootballHoF.com, previous measurements for a given season included things like total passing yards (1932-37), completion percentage (1938-40), yards per attempt (1950-59) and a number of other formulas that used inverse ranking systems that included those and other stats.

The Elias Sports Bureau teamed with the NFL to create passer rating and since '73, it has been the "official" measurement for naming the league's top quarterback... Though I don't know how many people would acknowledge or go along with that theory, or even if the league hands out some award for it. Last season that would've actually meant that Nick Foles, not Peyton Manning, was the league's top QB.

His passer rating came out to 119.2 against Manning's 115.1. The third-best QB in the league would've been the Bears' Josh McCown, coming in hot at 109.0. Two years ago, Aaron Rodgers posted a 122.5, the best of all-time. And all of these two and three-digit numbers with decimal points mean... well, they mean... you know what they mean, right? Wait, what do they mean? It's just, it's just passer rating, man. It doesn't mean anything. What do the oceans "mean"? What do airplanes "mean"? Just enjoy it, bro.

The way that I calculate passer rating is simple:

I Google "passer rating calculator" (I might cheat a little bit even and wait until Google suggests it after a word and a half) and it takes me to this website, PrimeComputing.com. When you're taken to Prime Computing, you're also reminded of the wonderful fact that the NCAA uses a different formula for passer rating! You know, sort of like how the NCAA uses 4.5-feet yards instead of those stupid NFL 3-foot yards.

3-foot yards? What is this, Ancient Rome!?

Take Russell Wilson's rookie season and plop the numbers into the Prime Computing calculator (26 TD, 10 INT, 393 attempts, 252 completions, 3,118 yards) and you'll get a passer rating of exactly 100. What does a "100" actually mean? Well, passer rating is put on a scale of 100 to make it "more understandable" according to the NFL, but in reality, a "100" means exactly what you think it means.

I mean, what do you think it means? If you're a fan of the NFL that pays attention to the stats, then you just know that 100 is very good. That 90 isn't bad at all. That 80 is starting to push it. And that under 80 is usually delving into Mark Sanchez territory. If you went back 30 or 40 years, a Mark Sanchez passer rating would be considered good. It just sort of changes over time, because passers are changing but the formula isn't. Or hasn't, at least.

So, what is the formula?

You might think, like I did, that it's (yards + touchdowns - interceptions * completion percentage) / the number of years since Pete Rozelle passed away. But it's a little more complicated than that.

From Wikipedia:

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

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

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

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

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

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

In other words, mm(x) = x, with two exceptions:
1. If x 2. If x > 2.375, then mm(x) = 2.375

I have a saying for calculations like the one above: Fuck that.
Now you're starting to see why the truth behind passer rating is a lot like the truth behind special sauce and the pure amount of high fructose corn syrup you're mainlining into your body.

Passer rating doesn't use "completion percentage" or "completions and attempts" exactly. It uses: Completion percentage minus 30 and then multiplied by .05. Every completion percentage at 30 or lower is created equal, which is good news for Geno Smith, I guess. However, there's also no incentive for a completion percentage higher than 77.5 because everything else up to 100 is also created equal.

Passer rating doesn't use "yards" it uses: Yards per attempt (which is actually great forward thinking in 1973 and earlier, since yards is a pretty shitty stat to refer to when measuring quarterbacks) minus three (well, here we go again) and multiplied by 0.25. The lowest figure that matters is 3.0 yards per attempt, and the best that matters is 12.5 Y/A. Everything else lower or higher doesn't matter.

Passer rating doesn't use "touchdowns" it uses: Touchdown percentage (attempts/TD) multiplied by 0.2.

And finally, passer rating uses interception percentage multiplied by 0.25 and then subtracted from the number 2.375!

All of those figures are centered around the number 2.375 and how far away you are from 2.375 is what really matters. Once you have the four figures above, you add them all together. Once you've done that, you divide by six. And finally after you've done that, you multiply by 100. And then you have "passer rating."

Ready to move to Russia yet? ("Move to Russia" is the new way of saying "Jump off a building")

I know that the men who created this formula are smarter than I am, or at least a lot better at math. I took four years too long to get my needed math credits in both high school and college, so perhaps all of these numbers would make sense to even the layest layman. Perhaps 2.375 is like "that other Pi that never gets enough credit." As far as I know, 2375 is the year that the world ends. (Haha, we'll all be long gone, suckers in the future.)

As far as I can tell, passer rating is nothing more than a guide. A point of reference for stat-heads to say, "Oh look, Aaron Rodgers is having a fine season again with a passer rating of 113.2." We know for the most part what is good and what is bad. We don't need passer rating to tell us that Ryan Fitzpatrick is bad, but it helps anyway. Even the NFL's official stance on their official stat is that "it measures passers, not quarterbacks."

Passer rating does not take into account things like fumbles, rushing yards, carries, sacks, game situation, defense, or sexiness. If it at least measured that last stat, Wilson would be the all-time leader in passer rating. It does not care if you throw a touchdown in overtime or in the third quarter of a blowout with Calvin Johnson lining up against Kelly Jennings.

In fact, no stat can do that last thing yet, and that's a pretty important thing.

Perhaps passer rating is flawed, confusing, and downright frustrating to think about once you know where it came from, but I've used it many times before and I'll use it again. Sometimes you don't have to tell me how the sauce is made, just shove it in my mouth.

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