# Passer Rating Explained 2021

(A quick note. I’ve been getting a number of questions about what the numbers actually represent. Because the formula was derived from a regression model using points as the dependent variable, the final rating loosely represents the number of points likely being scored above or below the number of points scored if an “average” quarterback was playing in place of the indicated player. I.e. If Drew Brees has a rating of 7, that means that he is responsible for the Saints scoring 7 more points than they would have scored with an average QB in his place.)

You may have read in my review of the current QB rating that I think the current QB rating system could use a few tweaks.

I have created a ranking that better reflects a quarterback’s performance. Below is the background and explanation of my new rating – as well as the formula itself and an example from week 6.

Background and Explanation

I recently put together a regression model to determine the quarterback statistics that most drive the number of points an offense scores in any given game. The model showed that yards per attempt is by far the biggest driver of points scored.

At the end of the day, a quarterback’s job is to score points. The model also suggested that interception percentage plays a role, but not nearly as great as Y/A.

TD % also correlates, but, in my mind, TD % is what Brian Burke at AdvancedNFLStats.com would call an “intermediate outcome”. This means that a player who’s good at other things (e.g. moving the ball down the field) is likely to get more TD opportunities and, therefore, more TD passes.

Using the aforementioned regression model as a base, I have create a new rating system that I believe is a better indicator of a quarterback’s success.

The rating takes into account four factors – with different weights being applied to each:

1. The quarterback’s yards per attempt (adjusted for sack yardage)
2. The opponent’s average yards per attempt in other games played in the current season (adjusted for sack yardage)
3. Interception percentage
4. Touchdown percentage

The Y/A statistics were given higher weights than Int %.

Because of the my statements above about TD %, this statistic was given only a nominal weight to reward exceptional games.

The biggest differences between this rating and the “traditional” rating are:

1. Completion % has been removed as a factor
2. Significantly different weights were given to the factors that were included
3. Quality of opponent was factored into the calculation
4. Sack yardage was included in the Y/A calculation

The Formula

* Y/A Differential – Y/A minus the opponent’s average Y/A yielded (times a factor of 2.5 – as determined by the regression model) MINUS
* Int % TIMES 50 PLUS
* TD % TIMES 20

It can also be stated as:

((Y/A – OPP Avg Y/A) * 2.5) – (Int % * 50) + (TD % * 20)

Notes: The opponent’s Y/A is bounded at a maximum of 7.2 and a minimum of 5.2. This is done because because a team’s average Y/A yielded could be greatly affected by a single game (I call this the “Peyton manning” effect) – especially early in the season.

The Formula Applied

To explain the formula, let’s use the examples of Tom Brady and Drew Brees (see table below) in week 6.

The calculation went as follows

Rating = ((Y/A – OPP Avg Y/A) * 2.5) – (Int % * 50) + (TD % * 20)

Brees = ((12.3 – 5.2) * 2.5) – (0 * 50) + (.133 * 20) = 20.41

Brady = ((10.4 – 6.9) * 2.5) – (0 * 50) + (.176 * 20) = 12.27

Brees superior rating was largely driven by the quality of the opponent. The Giants were the top ranked defense and actually had a Y/A against – when adjusted for sacks – of 3.4. As discussed earlier, this figure was bound at 5.2. This gave Brees a Y/A differential of 7.1.

Brady, on the other hand, was playing a team with an average Y/A yielded of 6.9. Combine his slightly lower Y/A with an opponent who was significantly inferior to the Giants, and you get a Y/A differential of 3.45 – about half of Brees’ differential.

Week 6 Stat Lines:  Tom Brady vs. Drew Brees

Week 6 Stat Lines:  Opponents (As of Week 6)