ATVS Quarterback Productivity Index 2: Electric Bugaloo

I wanted to look back over the past few years to see how sophomore QB's have performed in the SEC in contrast to their junior year.  The idea, at least, was to look at some actual data of how SEC QB's have performed in their second year after being thrust into a starting role as an underclassman.  This seemed like a perfect job for our old friend, the ATVSQBPI.

Unfortunately, while Richard devised a formula that is far more useful than the traditional quarterback rating, it wasn't very easy to gather the data.  Part of the formula ATVSQBPI uses 1st downs converted, and the task of digging through the boxscores of every quarterback in the study was quite daunting.  The use of 1st downs in the formula lessened its utility to make historic comparisons, just because of the amount of labor required to dig up the raw data to plug into the formula.

Because I wanted to use ATVSQBPI so I could rate quarterbacks all on the same scale, I decided it was time to modify the ATVSQBPI formula to make it a little easier to use.  I thank Richard for coming up with the original formula, and I do like it, but it's requirement of harder to find data lessens its utility.  I might sacrifice a little bit of the formula's expansiveness in order to make it easier to use and make useful historical comparisons like this. 

Let's look at Richard's original 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 looks like there's a lot going on there, but it's really just a modified yards/attempt rating.  I like yards/attempt because it tends to even different types of quarterbacks out.  A passer who throws it deep a lot is going to have a huge yards per completion number, but a much lower completion percentage than the classic west coast offense QB.  A quarterback who throws a lot of safe, short routes will have a high completion percentage, but a low yards/completion rating.  Yards per attempt bridges the gap between the two.  It's not perfect, but it's a good starting point. 

It also is the guiding light for the ATVSQBPI formula: how many yards is a QB worth each time he callas his own number?  The more the rating deviates from answering the simple question "how many yards is this guy worth per play," the less value it has. 

The first question is whether to keep the rushing component.  Running is a big part of a lot of quarterbacks' jobs, and I believe any QB rating that does not account for the ability to run is missing out on a big part of the position.  It might be more accurate to call it yards/play instead of yards/attempt, but it's the same concept.  How does a QB do when he calls his own number?

Also, since the NCAA counts sacks as rushing attempts, it makes the raw data easier to sift through.  We just have to look at net rushing yards, since it includes yards lost due to sack.  Adding the yards lost to sack in the original formula was redundant, and I'm tossing it overboard.  Right now, the formula looks like this:

Passer Rating = (yards passing + yards rushing)/(Number of pass attempts + rush attempts)

A lot more elegant, but still incomplete.  Richard's original formula incorporated two yardage "bonuses" and one yardage "penalty".  While I like the idea of giving a five-yard bonus for each first down, it's got two major flaws.  The first I've already discussed, it makes the formula difficult as hell to calculate due to the need to pour through each quarterbacks game-by-game stats.  The second problem is that while there is a real-life bonus to getting a first down (an extra set of downs), it's hard top pin down how many yards it is worth.  It very well could be worth five yards, it might be more, it might be less.  It's just a random bonus, and given that it lessens the utility of calculation, there's no reason to add this bonus since we don't really know what it should be worth.

Richard had a 30-yard penalty for each turnover.  Let's treat fumbles and interceptions separately, looking at interceptions first.  How many yards is an interception worth?  Well, assuming the ball is returned to the line of scrimmage, a dubious assumption but we have to start somewhere, an interception costs a team the yardage it might have continued to gain as well as the yardage in a punt.  This means that a third down pick is worth less than a first down interception, but let's remember the lesson learned from 1st down bonuses.  Keep it simple and easy to find the data.  Looking at the data Billy posted in his special teams preview, the average net punt was about 32 yards last season, giving us our penalty for an interception.  It cost the team 32 yards, so we deduct 32 yards for each pick. 

Fumbles are a bit dicier.  First, one of the principles of "football sabermetrics"  is that of fumble luck.  Fumbling is not a random event, but recovering a fumble is.  Once the ball is fumbled, it is essentially a coin toss who picks it up.  We really can only blame the QB for the first part of that event, the fumble, not whether it was recovered or not.  Secondly, we are getting back into the territory of difficult to find the raw data.  It's not as hard as first downs, but it is labor intensive to get fumble data.  Thirdly, quarterback fumbles aren't as common as interceptions.  Finally, a large portion of QB fumbles are on the center exchange.  Sure, bad snaps are a pain in the ass, but it's not really what we're trying to measure.  I feel comfortable excluding fumbles all together.  They increased accuracy of the rating would not be worth the added difficulty to get the data.

Finally, we have the touchdown bonus.  Richard's original value for each touchdown was 20.  Looking over the past few seasons of quarterback stats, the "average" quarterback throws for about 3 TD's for every 2 INT's.  That would place the value of a TD, relative to the interception in our formula, would be about 21.3.  I'm not morally opposed to fractions or anything, but I'm going to keep it at a 20-yard bonus because I'm including the quarterback's rushing touchdowns as well as passing, which would throw off the 3/2 ratio.  Besides, it's not a precise ratio anyway, it's more of a ballpark. 

So, with a little bit of tinkering, I give to you ATVSQBPI2:

Passer Rating = (yards passing + net yards rushing + 20*Number of Touchdowns - 32*Number of Interceptions)/(Number of pass attempts + rush attempts).

If Richard ever gets his internet connection back, he can continue using his original formula (you can too, if you wish to calculate it), but going forward, I'm going to be using ATVSQBPI2.  It's just going to be easier for me to use.  I don't want to devote all of my free time to finding out how many first downs Greg McElroy converted by game.  So, now that I've tinkered with the formula and made it more idiot friendly (the idiot in question being me), I can tackle the project mentioned in the first paragraph.  Coming up tomorrow, we take ATVSQBPI2 for a spin and look at how SEC QB's who started as a sophomore play as juniors.  Quick preview... Steve Spurrier hates juniors. 

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