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# PLAYING THE NUMBERS GAME: Measuring Running Back Efficiency

Billyzane returns with another of his weekly columns looking at the numbers of the game we love. --PB--

 Obligatory picture of Mike Leach. Pirates!
Remember last week, when I calculated some statistical correlations with winning football games?  Of course you do.  I also tried to argue (I believe somewhat effectively) that rushing for more yards than your opponent is more an effect of winning games rather than a cause of winning games.  If that’s correct (and really even if it’s not), traditional rushing statistics are inherently flawed.

Claiming that total rushing yards by a team or by an individual back is a dispositive indication of the strength of a running back or rushing attack is ludicrous, and any learned football fan will tell you so.  If a team runs every down of every game, of course they will end up with more net rushing yards than, say, Texas Tech.  But does that mean that this run-only team is a better at rushing than our pirate friends to the West?  Not necessarily.

We need to know more than just raw rushing statistics.  We need to know something about the efficiency of that rushing.  So what do we have?  The most common efficiency statistic is, quite predictably, the easiest to calculate: yards per carry.  Divide total yards by number of carries and voila!  Efficiency!  And sure, this is a lot better than total yards because it doesn’t care how many carries you get per game – only what you do when you get those carries.

And that is where most commentaries on the efficiency of running backs end.  But is that enough?

You know me well enough by now to realize that I believe the answer is no.  Why not?  Because some yards are inherently more important than other yards.  For instance, if it’s 4th down and 2, and a running back rushes for 2 yards, that’s a pretty successful run.  But if in that same situation a running back rushes for 4 yards, is it twice as important as rushing for 2 yards?  Of course not.  It’s certainly marginally better, but on fourth down, all that really matters is getting a first down, which 2 yards accomplishes just as well as 4 yards.  But on first down and 10, 4 yards is much more valuable than 2 yards.  Yards have different values depending on the situation.

Armed with all these seemingly brilliant thoughts, I decided to construct my own equally brilliant metric to accurately determine the efficiency of a running back (or team rushing attack) based on the principle that not every yard is equal in value.  In an effort to figure out a way of determining the values to be assigned to the yards gained in certain situations, I did a google search to see if anyone had done something remotely similar to this before.

Much to my dismay, I found the oldest tenet of my intellectual life proved yet again: everything I ever wanted to do has already been done.  I subsequently wrote in my notes: "Football Outsiders knows fucking everything."  Here’s a link to an article of theirs titled Introducing Running Back Success Rate and dated 8/16/04.  Three freaking years ago!  What a bunch of jerks.  [As a side note, and hurt feelings aside, Football Outsiders is the absolute most cutting edge football website there ever was or ever will be.  It’s geared mostly towards the NFL, but if you care at all about understanding the game beyond the plays themselves, you can’t NOT read it.]

The Running Back Success Rate Statistic

Here’s how Football outsiders breaks down "Running Back Success Rate":
• A play counts as a "Success" if it gains 40% of yards to go on first down, 60% of yards to go on second down, and 100% of yards to go on third or fourth down.
• If the team is behind by more than a touchdown in the fourth quarter, the benchmarks switch to 50%/65%/100%.
• If the team is ahead by any amount in the fourth quarter, the benchmarks switch to 30%/50%/100%.

For instance, regularly, if it’s 1st and 10, a rush of 4 yards or more is a success and less than 4 is a failure.  On 2nd and 10, a rush of 6 yards or more is a success, and less is a failure.  For a rush on 3rd or 4th down, anything less than a first down (or a touchdown in an "and goal" situation) is considered a failure.  The metric also takes into consideration and accounts for the fact that yards become more or less important not just based on the situation of that specific play but also based on the situation of the game as a whole.  For instance, when you’re ahead in the 4th quarter, yards on the early downs don’t matter as much as killing time.  Thus, the definition of "success" is less stringent: 30% of yards to go on 1st down, etc.  The inverse is the case if your team is behind in the fourth quarter.

 The bane of my existence.

Thus, as Football Outsiders notes, when it’s 3rd and 1 and a running back dives for 2 yards, that’s a very successful run and is rewarded as such by this metric whereas he is penalized by the "yards per carry" metric.  This statistic, then, will give you a much better idea than yards per carry of how efficient a running back is at achieving "success" in the situations in which he finds himself within a game.

But Football Outsiders designed this metric very specifically to measure NFL running backs based on the intricacies of the pro game, which are often times quite divergent from those of the college game.  So to reconfigure this statistic for college football, I needed to take a look at what’s different between college and pro football.  Yardage is the same, so I think I’m fine leaving "success" as based on the 40/60/100 splits.  I’m also fine with the other splits (50/65/100 for a team trying to come back and 30/50/100 for a team trying to protect a lead).  But what’s different about college football from the pros is 1) how much more easily points are scored and 2) the circumstances under which a team’s predominant goal is to kill time.

As to difference 1), I have decided to change the success splits to 50/65/100 not when a team is behind by 7+ points in the fourth quarter, but rather when a team is behind by 11-21 points in the fourth quarter or 7+ points on any drive that begins more than halfway through the 4th quarter.  I think this better jibes with the relative ease of scoring points in college as opposed to the pros (due in part to college clock rules and in part to the comparative lack of consistency displayed by most college teams).  I don’t think being 10 points down in the first half of the fourth quarter is cause for a full-on "comeback mentality."  Ten points in a quarter isn’t an unreasonable expectation for a team using regular standards for what constitutes "success."

Regarding difference 2), the nature of college football (great talent disparities between many teams) leads to many more blowouts than in the NFL and a need for college teams to scale back the offensive attack and try to kill the clock much earlier by using plain vanilla rushing plays.  So I think we should use to 30/50/100 success splits when a team is up 7+ points in the 4th quarter AND we should use it in the 3rd quarter when a team has certifiably blown out the other and has obviously let up (by, say, inserting the backups and not passing at all).

Now, I’m trying to formulate this statistic with your collective wisdom, so any thoughts on whether you think this metric is properly constructed or not are welcome.  Are the splits for what constitutes "success" an accurate representation of what "success" should be?  How about when the different splits are used?  Should there be any other splits (perhaps based on which yard line the play starts on)?

Beyond Running Back Success Rate

There’s definitely some value to this success rate because it tells us one specific thing about a running back (or team rushing attack).  To wit, how effective is a running back at accomplishing the very specific, bare-minimum goals of each play?   But I still thought to myself, "That’s not all there is, though.  What about someone who runs for 20 yards on 3rd and 1 as opposed to 2 yards?  Sure, they were both equally successful at gaining the first down in front of them, but the one guy ran for 18 more yards!  That’s worth something.  I’ve got you, Football Outsiders!"

As it turns out, I didn’t have Football Outsiders.  Aaron Schatz is clearly smarter than me and has more free time than me, meaning he’s thought of everything I will ever think of (I’m not bitter though – not at all).  They equate Running Back Success Rate with batting average in baseball, which as any baseball fan knows tells you one important thing about the effectiveness of a hitter, but which tells you far from the whole story.  The trick is trying to develop a statistic that’s closer to the football equivalent of OPS than batting average.

Football Outsiders did just that, creating "Defense-adjusted Value Over Average," or DVOA.  This is too complicated to explain here and it’s so heavily NFL-centric as to be virtually useless for college football.  If you’re interested, here’s a short explanation and a long explanation.  But what I’m going to attempt to do is create something similar (though admittedly taking into account fewer variables) for college football.  And I’m going to need your help.

Here’s what I’ve decided to do so far in constructing this statistic:
(1) I’ve decided to measure efficiency based on a play-by-play basis rather than a drive-by-drive basis because I think it affords more flexibility in isolating certain situations to see, for instance, how one particular player rushes by down or by other game situation.
(2) For each rushing attempt, 1 point is awarded for a "success" using the above metric and 0 points for anything other than success.
(3) When using the 40/60/100 or 50/65/100 split in the success rate statistic (i.e. normal situations), each yard gained on a play is worth 1/10 of a point (1 point for every 10 yards), positive or negative, which is added to the success point (if there is one) to get a value for the run.
(4) When using the 40/60/100 or 50/65/100 split, the maximum yardage points that can be accumulated are 3 (equivalent to 30 yards).  Any rush beyond 30 yards still nets only 3 yardage points.
(5) When using the 30/50/100 split (i.e. trying to hold a lead and/or kill time), each yard gained on a play is worth 1/20 of a point (1 point for every 20 yards), positive or negative, which is added to the success point (if there is one) to get a value for the run.
(6) When using the 30/50/100 split, the maximum yardage points that can be accumulated is 1 (equivalent to 10 yards).  Any rush beyond 10 yards still nets only 1 yardage point.

Thus, on a normal 1st and 10, a rush for 4 yards will garner 1 success point and .4 yardage points, such that the run will have a value of 1.4.  Fleshing this out, remember our example of the difference between a 4-yard run and a 2-yard run on 3rd down and 1?  I said that a 4-yard run isn’t anywhere close to twice as important as a 2-yard run because getting the first down is what’s most important on that play.  With this system, a 2-yard rush is worth 1.2 points and a 4-yard run is worth 1.4 points, which I think is a much more accurate representation of the value differential of these two runs.

The reason for number (6) is that, when you’re trying to kill clock, yardage beyond a first down is virtually irrelevant and perhaps even counter-productive (because there’s less yards with which to eat up time).  The reason for number (4) is that beyond 30 yards any yards gained are not the product of running back capability, but rather of the yard line on which the play starts.  I’m willing to change this rule for some other rule that accounts for this problem of the varying lines of scrimmage, but I haven’t figured out how to do it yet.  That’s where you guys come in.  Any ideas?

Additionally, are there any other things I should be taking into account?  What about fumbles?  Touchdowns?  I’m inclined to not give a bonus for touchdowns because there’s nothing special about being the person who physically gets the ball in the endzone.  If you’re a short-yardage/goal-line specialist RB, the measure of your value is pretty adequately measured by your success rate statistic.  But I’m open to arguments for why I’m wrong.

One other possibility: yards in excess of what is required for "success" are more important on 1st and 2nd down than they are on 3rd and 4th.  Should the value of yards beyond what’s needed for success be weighted differently according to what down it is?  How so?

A Plea for Help

This running back statistic-thing is going to be a season-long project.  I hope to come up with an adequate metric soon, which I will find interesting to no end.  But the intellectual exercise of coming up with a statistic isn’t all that interesting to most people (we call these people "normal").  All of us want to see a practical application, so I want to compare Texas backs to each other, perhaps over several years, and I want to compare all the national standouts for this season using the statistic.

Sadly, this requires work.  Even sadder, I just started my big firm job and will have much less time to do stuff like this.  So the moral of the story is, I need help.  If any of you guys (particularly those of you still in school with lots of free time – don’t pretend you’re busy, I’m not too old to remember college) have any interest in this sort of thing, please let me know.  What’s in it for you?  Um...satisfaction; your name on the main column of BON (very exciting for me the first time); you can help me write the follow-up piece to this.  Hopefully, at least 1 or 2 of you can help me out.