In yesterday’s post, I examined the methodology behind passer rating. Here were the passer ratings for the 30 quarterbacks who threw enough passes to qualify for the crown in 2016:

Now, as we learned yesterday, passer rating is the result of four variables: completion percentage, yards per attempt, touchdown rate, and interception rate. Those variables are all scaled so that the average score is 1.0 for each variable. Then, we take an average of the four variables and multiply it by 66.67, since that was intended to be the league average passer rating (or, said differently and how it is more commonly represented in formulas, we sum the four numbers, divide by six, and multiply by 100).

So let’s take a look at the scores in each of the four variables for these 30 quarterbacks to better understand their 2016 passer ratings. The far right column shows the average of those variables, which again, is equivalent to their passer rating divided by 66.67.

For these 30 passers, the average completion percentage is not 1.00, but 1.67; even crazier, the interception rate variable is at 1.84! Touchdown rate is actually worse than it used to be, and checks in here at 0.89, while yards per attempt has stayed the most consistent (1.06). With minimal tweaking, you could solve any era-related issues with touchdown rate and yards per attempt.

No, the real problems are the ever-escalating completion percentage and interception rate variables. Think about it like this: when the formula was created, 5.5% was suppose to represent an average interception rate. Yet in 2016, Ryan Fitzpatrick had the worst rate at 4.2%, and no one else was above 3.6%! How much has the sharp decline in interception rate contributed to the huge increase in passer ratings?

The average passer rating “is supposed to be” 66.67. This year, it was 91.0 for these qualifying passers, which is because the our variables sum to 5.46 (divide by 6, and multiply by 100, and you get 91.0) when they are “supposed to” sum to 4.00. What accounts for that 1.46 in excess value? Well, 58% of that (i.e., 0.84 of the 1.46) is due to the rising interception rate.

So how do we “fix” the interception rate issue prevalent in passer rating? That’s the million dollar question. Because there are many ways to do it. One way is to do what Bryan did. The formula, when designed in 1972, had an expected average INT rate of 5.5%. So the formula, intending to yield an average result of 1.00, became:

2.375 – INT rate (expected = 5.5%) * 25

The 2.375 was reverse engineered, of course, since 0.055 * 25 equals 1.375. You need to get 1.375, on average, in the right side of the formula, and multiplying a player’s interception rate by 25 was a good way to do that when the average interception rate was between five and six.

Now? It’s less than half that. The interception rate was 2.3% last year, so one option for 2016 would be to make the formula this:

2.375 – INT rate * 60

Now if a player has a 2.3% interception rate, this formula will yield a variable of 0.995, which of course is essentially 1.00.

Sounds simple, right? But there are some issues with this. This changes the lower bounds of interception rate: whereas before, the maximum number was 9.5% (the result of 2.375 divided by 25), now the maximum interception rate is 3.96%. That means a passer with an interception rate of 4% is treated the same as one at 7%. Maybe this isn’t a huge issue — on a season-long basis, it only helps Ryan Fitzpatrick — but it is definitely going to be rough around the edges.

Another thing this does — and I’ll leave it to you to decide if it’s a feature or a bug — is that it increases the importance of interceptions. Let’s use Philip Rivers and Carson Palmer as examples. In 2016, Rivers had a passer rating of 87.9, and Palmer had a rating of 87.1. Rivers had the thinnest of edges: his four variables averaged 1.32, while Palmer’s four averaged 1.31.

Rivers had the 2nd worst interception rate (3.6%) in the NFL last year, but as a sign of how out-of-whack the numbers are, Rivers’ 2nd best variable was his interception rate, at 1.47. Palmer had a 2.3% interception rate, which turns into a 1.79 in the passer rating formula. Rivers’ superior edge in yards per attempt and touchdown rate were enough to help him overcome that difference and finish with a better passer rating than Palmer.

ow, what if we use our modified interception rate formula? If we multiply interception rate by 60, not 25, and subtract that result from 2.375? Well, Rivers’ grade would drop from 1.47 to 0.20. That’s pretty stark, although perhaps appropriate given that he had the 2nd-worst rate in the NFL. Palmer? He was just a hair worse than league average, so his grade in this metric would drop from 1.79 to 0.97.

What does that mean for the formula? Keeping everything else constant, Rivers’ four variables would now average to 1.00, while Palmer’s would average to 1.10. So while Rivers had a slight lead in passer rating before, now Palmer would edge him out considerably, 73.5 to 66.7.

So, is that good? It puts more weight on interceptions, but given that interceptions were already valued at -100 in the old formula, I’m not so sure this intuitive era adjustment is the proper way to go about things.

To take another example, Matt Ryan led the NFL in passer rating at 117.1, and he had a 1.3% interception rate with 7 interceptions on 534 attempts. If he had 8 interceptions on 538 attempts, his interception rate would jump to 1.5%, but his passer rating would only drop to 116.3. ^[1]On 538 attempts, one more interception is worth about 0.002 to a player’s interception rate. In the formula, you multiply that by 25, so the variable would decrease by 0.05. That number would … Continue reading Now, if instead, we used this era-adjusted formula, Ryan’s 2016 passer rating would be 109.5. Give him 8 interceptions instead of 7, though, and his passer rating drops to 107.6. ^[2]That’s because the 0.002 gets multiplied by 60, and then divided by 6 and multiplied by 100….so a change of about 2 points. This era adjustment makes interceptions 2.4 times more significant than they were before.

What do you guys think?