A Look at the 'And The Valley Shook Quarterback Productivity Index'

A month ago, a couple of gracious commenters agreed to help out  with compiling the data for a new feature I will be running, chronicling the And The Valley Shook Quarterback Productivity Index, or ATVSQBPI for short.  it is a replacement for the woefully inadequate "Passer Rating" statistic, which has come to criticism here.  I told you I'd go into this in more detail at another time, and here it is.

The passer rating is a great idea for a statistic.  The idea is to combine a number of important passing statistic into an index that can be ranked and evaluated.  The problem is that the college passer rating is not calculated in an intelligent way.  Here is the formula used to measure college quarterbacks (the formula for pro quarterbacks is different):

(100*Completions/attempts) + (8.4*yards/attempts) + (330*Touchdowns/attempts) - (200*Interceptions/attempt) = Passer rating

This looks all fine and dandy, but if you do a little algebra, it comes out like this:

8.4*(Yards passing + 11.9*Completions + 39.3*Touchdowns - 23.8*Interceptions)/(Number of attempts) = Passer Rating

If you think about it, this makes no sense at all.

It amounts to a measure of yards per attempt, which is a really nice core of a useful statistic, but then it adds some bonuses and penalties, which would be really nice features, if the bonuses and penalties made sense.  In this formula, you add a bonus of 11.9 yards for a completion and 39.3 yards for a touchdown pass, while penalizing a quarterback 23.8 yards for an interception.

Why reward the quarterback at all for merely completing a pass?  With this formula, it is actually better to complete a pass for a big loss than to throw it away.  

Illustration #1:  Quarterback #1 takes two consecutive throws.  The first is a screen pass on 1st and 10 that is stopped for -1 yards.  The second is a pass over the middle on 2nd and 11 to a tight end which goes for 6 yards.  Quarterback #2 takes two consecutive throws.  The first is a deep out that falls incomplete on 1st and 10.  On 2nd and 10, he hits the wideout on a 12-yard curl for a first down.  On those two throws, QB#1 has a passer rating of 120.96, while QB#2 has a passer rating of 100.38, but QB#2 has clearly helped his team a lot more.

Better still?  Take a sack, because it does not increase your number of attempts.

That brings up the second problem.  It does not account for a running quarterback.  It ignores the running and scrambling aspect entirely.  It makes the same mistake that football statisticians have always made: it does not include sacks and scrambles as part of the passing game.

Illustration #2:  Quarterback #1 drops back to pass twice.  The first time, the offensive line fails, and the rush gets to the quarterback.  He pulls down the ball and is sacked for a 5 yard loss, bringing up 3rd and 13.  On the second play, he completes a 10 yard pass, bringing up 4th and 3.  Quarterback #2 drops back to pass twice.  The first time, the offensive line fails and the rush gets to the quarterback.  He throws the ball away, bringing up 3rd and 8.  On the second play, he completes a 10 yard pass.  QB#1 has a passer rating of 183.96 while QB#2 has a passer rating of 91.98, but QB#2 has kept his offense on the field, while QB#1's team has had to punt.

The third problem here is that the bonus for a touchdown and the penalty for an interception are way out of balance.  If you add in the bonus merely for completing a pass, there is over a 50 yard bonus for completing a touchdown pass, while the penalty for an interception is less than half that.  This insufficiently penalizes interceptions relative to touchdown passes, and if you want an example of what that does to a passer rating, look at Jarrett Lee's stats from last year.  Despite his very high rate of interceptions, his passer rating was actually pretty darn good, one of the better passer ratings in the conference.

A few years ago, I developed my own.  Here is my formula:

Passer Rating = (yards passing + yards rushing - yards lost by sack + 5*(First down completions and runs) + 20*Number of Touchdowns - 30*Number of Turnovers)/(Number of pass attempts + rush attempts).

It's the same general idea.  It's based on a yards/attempt measure (but without that strange 8.4 multiplier that makes it difficult to understand), with bonuses and penalties.  There is no bonus merely for completing a pass.  There is a 5 yard bonus for getting your team a 1st down, a 20 yard bonus for getting your team a touchdown either by pass or run, a 30 yard penalty for throwing an interception or fumbling the ball away, and it includes rushing statistics.

With this formula, it is better to throw the ball away than to take a sack.  Better still is to scramble for a few yards.  It is significantly better to get 11 yards on 3rd and 10 than it is to get 9.  Having an equal number of touchdowns and interceptions is a bad thing with this rating, while before it was a good thing.

This, therefore, is actually very useful.  It includes more of the qualities that makes a quarterback good.  It gives sane bonuses to good results and sane penalties to bad results.  The traditional passer rating is so woefully inadequate and so easily correctible that I am amazed that those people who actually know what it is still use it on a regular basis.  

The ATVSQBPI is a stat that we will be keeping up with week-to-week as the season progresses.  In the past, I did not really have the ability to go in and see how many first downs a quarterback accounted for.  It's a statistic that is not kept (WHY!?) and you have to go into a play-by-play summary and actually physically count them.  It's not hard, but it's a little time-consuming.  Thanks to CCTV and RGI12, and anyone else who wants to chip in, we will get this done this year.