There are no fewer than four problems with passer rating.

1. It does not adjust for era.

2. It only includes four variables — completion percentage, yards per attempt, touchdown rate, and interception rate — which means valuable information like sacks, first downs, and rushing are excluded.

3. The variables it does include are improperly weighted: a completion is worth 20 yards (too much), a touchdown is worth 80 yards (also too much), and an interception is worth -100 ways (again, too much).

4. Like nearly all non-proprietary formulas, it does not provide any situational context: an interception on 1st-and-goal from the 1 is the same as an interception on a Hail Mary, a 10-yard catch on 4th-and-9 is the same as a 10-yard catch on 3rd-and-30, etc.

These are just some of the reasons why passer rating is stupid. For reasons I can’t quite articulate, I only want to focus on solving the issue presented by problem number one. Yes, it may be silly to artificially tie one hand behind my back, but my goal here is not to come up with a new formula, but just to fix one specific issue with passer rating that everyone can acknowledge.

The past two days, I have been writing about passer rating. If you ignore the upper and lower limits in the formula, passer rating’s four variables can be re-written like this:

A = (Cmp% – .30) * 5
B = (Y/A – 3.0) * .25
C = TD% * 20
D = 2.375 – Int% * 25

Now, take a look at the multipliers: it’s 5 for completions per attempt (i.e., completion percentage), .25 for yards per attempt, 20 for touchdowns per attempt, and -25 for interceptions per attempt.  Those coefficients tell you the relative weight put on each variable: since each yard (per attempt) is divided by 4, and each completion (per attempt) is multiplied by 5, that means a completion is worth 20 yards. A passer who is 4/7 for 76 yards is given the same 94.9 rating as a passer who is 5/7 for 56 yards. That’s because a completion is given 20 times as much weight as a yard.

Touchdowns are given four times as much weight as a completion, so touchdowns are worth 80 yards.  And interceptions are given five times as much weight as a completion, so interceptions are worth -100 yards. That’s what happens when you divide yards per attempt by 4 and multiply interception rate by 25. That’s wrong, but that’s the math behind why completions are worth 20, touchdowns are worth 80, and interceptions are worth -100 in this formula.

We could fix that with ANY/A, which puts completions at zero (or, preferably, we can give credit for passing first downs independent of completions), touchdowns at 20, and interceptions at -45. That would solve issue #3 with passer rating, but we are trying to solve issue #1.  So let’s just accept at face value that these are the weights we are working with.

The issue with the era adjustment proposed yesterday is instead of multiplying interception rate by 25, we multiply it by 60.  But that would make interceptions worth 240 yards! Remember, the passer rating formula incorporates interception rate with this calculation:

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

That result was designed, in the early ’70s, to equal 1.0. Since INT rate has dropped significantly from that time, changing the multiplier from 25 to a 60 is one way of making that formula equal 1.0.

Here’s another:

2.375 – (INT rate * 25 + 0.8)

This formula keeps the 100-yard weight on interceptions, but it adds 0.8 as a penalty to all passers.  If we use 2.3% as a hypothetical interception rate for this formula — and that was the league average for 2016 — we get 0.575 plus 0.8, which sums to 1.375.  That means the formula would once again yield an average result of 1.0.

Of course, that 0.8 number is a constant that would (despite its name) have to fluctuate each year.  In the early ’70s, that number would be roughly zero.  In 1993, when the interception rate was 3.25%, that number would have to be +0.562.  But you could generate that number in any given season if you know the league average, using the following formula:

Constant = 1.375 – 25 * LgAvgINT_Rate

Using that formula, we keep interceptions equal to -100 yards but also adjust for era.  There are some drawbacks, with one being that you artificially cap how high a modern passer can get in this variable: even with 0 interceptions, the top score possible is now around a 1.58 with a 2.3% interception rate.  On the other side, the era adjustment described yesterday — with the 60 multiplier — cut things off in the other direction, as it imposed such a high floor that some of Ryan Fitzpatrick’s excess interceptions didn’t hurt him.

What I like about this formula, though, is that it won’t change the order of the results in a given season.  By keeping the same weight of 25, as long as passers are within the lower and upper limits, this won’t shuffle the ratings (whereas changing the weight to 60 will).

So, what do you think?