An Inside Look at QB Rating

I have spent some time over the last few days trying to reconcile the true reasoning behind the stat that is know as “QB Rating” or “Passing Efficiency”. In most of sports, statistics have a pretty straight-forward, easy-to-figure-out meaning. But if you ask some true football fans how you calculate QB rating, you’re likely to get some dumbfounded looks or nonsensical explanations.

So I went on a mission – to explain the meaning of the elusive quarterback rating statistic. I warn you in advance – the following is mathematically analytical and perhaps highly boring.

The first thing that you need to know is that QB Rating is that it is calculated differently in college than it is in the NFL. It’s a pretty significant difference that you would probably notice if you simply saw the leaders in the category for both leagues. The top QB’s in college can have a rating up around 160 while the NFL leaders are generally slightly over 100.

So why the stark differences? You would expect a stat to be consistent from one level to the next, but these are completely different. Let’s begin with college.

NCAA QB RATING CALCULATION

Here is the formula for calculating QB Rating in College Football:

(8.4 x Yards) + (330 x TDs) + (100 x COMP) – (200 x INT)
---------------------------------------------------------------
                                         ATT


Now, in English.

This formula consists of 4 factors based on an individual passing stat. In order to give each stat a relevant level of importance, they are converted into a multiple. Then all 4 multiples are added together and divided by the number of attempts.

The factors involved are as follows:

Yards Passing. Each yard is given a value of 8.4.
Touchdowns. Each TD is given a value of 300
Completions. Each completion is given a value of 100.
Interceptions. Each INT is given a value of -200.

The NCAA formula tries to assign a value of importance to each of these 4 categories. For example, one TD Pass is equivalent to about 39 passing yards, and 3.3 completions. A completion is equivalent to about 12 yards passing. Two completions can offset 1 interception. A TD Pass is 1.65 times more valuable than an interception is detrimental.

If you thought the NCAA formula was confusing, then hold onto your calculators... because the NFL formula is a doozy.

NFL QB RATING CALCULATION

The NFL version of QB rating consists of four slightly different factors that are calculated separately and then entered into a formula. The formula looks like this:

     Sum of 4 Factors
------------------------- x 100
                6


The four factors each revolve around a specific stat:

1) Completion Percentage Factor
2) Yards Per Attempt Factor
3) TD Passes Per Attempt Factor
4) Interceptions Per Attempt Factor

There are two rules that are enforced when calculating any factor.

Rule #1 - the maximum result in any factor calculation is 2.375.  Therefore, if you calculate anything higher than 2.375, the number is reduced to 2.375.

Rule #2 - the minimum result in any factor calculation is 0. Therefore, if you calculate any negative number, you merely consider it zero.

From this point you'll notice that since the factors are the variable component of the formula and they are all summed, in order to produce a more positive result you would want these factors to come out as high as possible (up to the maximum of 2.375). So let's take a look at the factor calculations:

1) Completion Percentage Factor

((Comp % x 100) -30) x .05

So if you had a 100% completion percentage, the calculated value would equate to 3.5. This value would then be reduced to 2.375 (the maximum it can be under the aforementioned rule). In fact, any completion percentage between 77.5% and 100% will produce a value at or above 2.375. This means that anytime a QB achieves a completion percentage of 77.5 or greater, they will receive the maximum amount for this factor.

By subtracting 30 in the formula, it creates a situation where any completion percentage lower than 30% will produce a negative number. This of course means that the factor would be set at the minimum value of zero.

So generally speaking, for the Completion Percentage Factor:
-A completion % of 0-30% will produce a 0 result
-A completion % of 77.5% - 100% will produce a 2.375%
-A completion percentage > 30%, but less than 77.5% will generate some number between 0 and 2.375.

2) Yards Per Attempt Factor

(Yards Per Attempt - 3) x .25

Taking the same analytical look at this factor you would deduce the following:
-An average yards per attempt of 12.5 or greater would earn the maximum of 2.375.
-An average yards per attempt of 3 yards or less would earn the minimum of 0.
-Any yards per attempt of 3-12.5 yards will generate some number between 0 and 2.375.

3) TD Passes Per Attempt Factor

TDs Per Attempt x 20

In this factor:
-A QB needs to throw one TD pass at least every 8.42 attempts in order to max out at 2.375.
-If a QB doesn’t throw a TD pass, the value of the factor will be 0.
-If a QB throws a TD for every 8.42 attempts or more, the formula will generate some number between 0 and 2.375.

4) Interceptions Per Attempt Factor

2.375 - (INT per Attempt x 25)

Interceptions are handled a little differently, since they are a negative stat – the less you have, the better. The interception factor starts a QB at the maximum level of 2.375 and then reduces the number based on the interceptions thrown per attempt. In this factor:

-If a QB doesn’t throw any interceptions, the value of the factor will be the maximum of 2.375.
-If a QB throws an interception every 10.53 passes or worse, not only will he probably be looking for a job, but his calculation for the interception factor will be zero.
-As long as a QB doesn’t throw an interception for better than 10.53 attempts, the formula will generate some number between 0 and 2.375.


One relationship that differs from the NCAA formula is that touchdowns-per-attempt are multiplied by 20, while interceptions-per-attempt are multiplied by 25 (before being subtracted from 2.375). In other words, the interception is treated as being 1.25 times more detrimental than the TD Pass is considered beneficial, which is a complete reversal of the NCAA formula.

Once calculated, all of the factors are then added up and plugged into the original formula.

If the QB had an awful game and every factor was the minimum of zero, then his QB rating would obviously be zero. A list of such occurrences can be found here.

On the other hand, if the QB maxed out at 2.375 for each factor, his QB Rating would calculate out to 158.3. That means a completion percentage of at least 77.5%, at least 12.5 yards per completion, at least one TD pass per every 8.42 attempts and no interceptions. In these rare instances where a 158.3 is posted, it would be considered a perfect passing game for the QB. A list of such occurrences can be found here.

My initial reaction to these statistics is that this whole thing is insane!

QB Rating seems like just an arbitrary way to commingle multiple statistics into one number based on an arbitrary scale. It doesn't necessarily tell you which signal-caller is better. It's just another semi-meaningful statistic along with the rest of them.

In upcoming weeks, I’ll take an even closer look at this and other statistics and discuss how much stock we should put in these fantasy football numbers. For now, all this math is hurting my brain... I need a nap.