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Beyond the Box Score: The '+' Concept

When I started entering all this play-by-play data, one of my main goals was simply to apply some of the basic sabermetric ideas to football.  I mean, if they make sense in one sport, they should make sense in another, no?  The idea behind my 'EqPts' (and therefore PPP) measure came from two baseball measures: 'EqR', the Equivalent Runs concept that take a series of offensive stats and determines how many runs those stats should have produced on average, and Expected Runs, the matrix that shows you, on average, how many runs you can expect out of specific "__ runners on, __ outs" situations.  And of course the S&P (Success Rate + PPP) measure was an obvious rip-off of OPS.

Well, the next one I'm going to rip off (actually, I prefer co-opt) is the '+' concept.  The idea of an Adjusted ERA or Adjusted OPS figure (also known as ERA+ or OPS+) starts with saying, basically, that not every 3.68 ERA (or 0.890 OPS) is created equal.  Was it during the deadball era?  Was it in a hitter's park or the Polo Grounds?  You try to put everybody on as even a playing field as possible to evaluate their stats.  That idea should work for football too, right?

Last year Colt Brennan threw for 416 yards and 6 TDs against Northern Colorado on September 1, while Tim Tebow threw for 304 yards and 2 TDs (and 15.8 EqPts) against a decent South Carolina defense on November 10. By all basic statistical accounts, Brennan's stats were insanely good and easily better than Tebow's performance against SC. However...could Brennan have put up Tebow's numbers against SC? What would Tebow have done against Northern Colorado?  In a nutshell, the goal of the '+' concept is, for me, to adjust for what's expected against different opponents.

For every major measure I use, both the ones I created and the ones I, uhh, co-opted--Success Rate, PPP, S&P, Line Yards/Sack Rates, etc.--you could create '+' measures that compare an offense's or defense's performance to what their opponents typically averaged.  And here's how we're going to do it, using a blurb from my Buffalo BTBS piece as an illustration:

Let's take [Buffalo's] October 4 matchup against Ohio, a game they won 31-10. For that game (without taking turnovers into account) they put up a 0.780 S&P and scored 30.3 EqPts, while Ohio garnered a .576 S&P and 12.0 EqPts. How did that compare to what an average opponent did against Ohio? Ohio gave up 22.0 EqPts per game and a 0.704 S&P while gaining 18.3 EqPts and a 0.665 S&P. So Buffalo gained 1.66 times more than the average Ohio opponent gained, 166% of normal. Ever heard of the OPS+ measure? Basically it compares people to averages, with a score of 100 more-or-less meaning that the person gained exactly 100% of what was expected. So if we use this concept, we can say that Buffalo's offense put up an EqPts+ measure of 166 against Ohio, meaning they gained 166% of what Ohio normally gave up. Get it? They also put up a 110.9 S&P+.

Meanwhile, if you flip the equation, you can come up with a defensive score as well. (You have to flip the equation so a good defensive performance also results in a score above 100.) Buffalo's defensive scores against Ohio were a 109.6 EqPts+ and a 115.6 S&P+.

So to summarize that in pretty bullet points...

  • For every game they play, a team's output (offensive and defensive) is compared to the expected output considering the team they're playing.
  • 100 = dead average.  Over 100 = good, under 100 = bad.
  • The purpose of this is to give (or take away) credit for teams' statistics based on the quality of their opponents.  Technically you could do this same thing with rushing yards, points (the real kind), or anything else, but since I've been doing all this measuring of EqPts, success rates, etc., and since I'm very much sold on the quality of these measurements, by god we're going to use them.
  • The trick here is that, for each game played, there are two sets of offensive ratings and two sets of defensive ratings.  Why two?  Well, taking into consideration the Buffalo-Ohio game above, Buffalo got an offensive score for their performance against Ohio's averages and a defensive score for their performance against Ohio's averages.  However, Ohio also got offensive/defensive scores compared to Buffalo's averages (a 47.3 EqPts+ on offense and a 51.8 EqPts+ score on defense, if you're scoring at home...or if you're alone).  The key is that Ohio's score isn't simply an inverse of Buffalo's score.  If that's still not clear, I'll illustrate with more examples, but for now we'll move on.

So what's the point of doing all of this?  Quite simply, we can more accurately measure how good teams really were.  The best way to illustrate that is to show you some rankings.  I have lots of '+' measures to choose from, and I haven't yet figured out the most accurate one to use, but let's just run through some for now.

EqPts+ (Offense)

1. Florida (172.45 avg)
2. Oregon (159.16)
3. Louisville (156.05)
4. West Virginia (155.88)
5. Tulsa (154.83)
6. Kentucky (151.31)
7. Missouri (151.02)
8. Texas Tech (150.68)
9. LSU (149.22)
10. Navy (148.74)

Now, none of the names on that list are particularly surprising, but how do these rankings compare to pure scoring and yardage rankings?

Florida: #3 scoring offense, #14 total offense
Oregon: #12 scoring offense, #10 total offense
Louisville: #18 scoring offense, #6 total offense
West Virginia: #9 scoring offense, #15 total offense
Tulsa: #6 scoring offense, #1 total offense
Kentucky: #15 scoring offense, #24 total offense
Missouri: #8 scoring offense, #5 total offense
Texas Tech: #7 scoring offense, #2 total offense
LSU: #11 scoring offense, #26 total offense
Navy: #10 scoring offense, #22 total offense

And what about some of the teams who ranked high in the 'regular' rankings but didn't appear in the top 10 above?

Hawaii: #1 scoring offense, #3 total offense...#12 in EqPts+
Kansas: #2 scoring offense, #19 in EqPts+
Boise State: #4 scoring offense, #18 in EqPts+
Houston: #4 total offense, #37 in EqPts+
Oklahoma: #5 scoring offense, #14 in EqPts+

As you would expect, teams with tougher slates--i.e. a lot of SEC teams--were held in higher regard using the '+' concept.

So what about the S&P+ measure?  That takes efficiency and explosiveness into account instead of simply explosiveness.

S&P+ (Offense)

1. Florida (again!) (156.69)
2. West Virginia (134.71)
3. Navy (131.61)
4. Texas Tech (130.81)
5. Louisville (129.48)
6. Hawaii (129.07)
7. Oregon (128.11)
8. Missouri (127.30)
9. LSU (126.82)
10. California (125.07)

So first of all...kudos to Florida and to Heisman voters.  I admit it--they nailed it with Tim Tebow.  I'm a Mizzou (and therefore Chase Daniel) fan, so naturally I'm supposed to think that Tebow is overrated and Daniel should have won the Heisman.  I was rather unimpressed with the '20 TDs passing, 20 rushing' thing (if Mizzou had only called QB keepers inside the 5, Daniel would have that many rushing TDs too), matter what I thought of that particular distinction, Tebow QB'd what was simply the best offense in the country according to these numbers, and since he basically was the rushing game...yeah, Tebow gets some dap.

And just for fun...

Rushing EqPts+ (Offense)

1. Navy
2. West Virginia
3. Oregon
4. LSU
5. Florida

Some dap for Navy there as well...of course they put up big-time rushing numbers running Paul Johnson's option system, but they apparently did it against a series of respectable rushing defenses.  This should make Georgia Tech fans happy.

Passing EqPts+ (Offense)

1. Louisville
2. Texas Tech
3. Hawaii
4. Tulsa
5. Florida

Again, no surprising names here...though it's doubly impressive that Florida was in the Top 5 in both.

Quick sidebar: a few interesting conclusions were reached about the 'national averages' post I wrote last week, including this one from SMQ:

I welcome this, personally, as an empirical base that bolsters my usual emphasis on keeping the entire playbook open: outside of talent, predictability is the number one killer of offenses, and defenses that stop the run and make offenses one-dimensional are, well, see above.

The 'above' being a youtube video of Auburn sacking Alabama roughly 176 times.  Well, an EDSBS commenter made an interesting point--Florida was one of the most predictable teams in the country, and yet they were by far the most successful.  I figure there are two main explanations for that.  1) Execution matters.  Call it the Remember the Titans Postulate.  Even if they know what's coming, they still have to stop you from doing it.  2) Down yardage matters.  Florida was able to succeed on third downs because they kept things manageable on third downs.  Not even Superman Tebow would succeed very often if most of his third downs were 3rd-and-9's instead of 3rd-and-3's.  It does go to show how interesting football is, though.  There are a million things that have to happen for you to succeed or fail.  Though I guess you don't need a bunch of new statistics to reach that forget I said anything.

Anyway...on to defense.  I should mention that, while I have no problem sharing the rankings, there's a caveat: I still have some tinkering to do with these numbers.  For one thing, it's very much possible for an offense to put up like 0.32 EqPts in a given game.  Since you're flipping the equation now, the opposing team's offensive average is in the numerator, and the 0.32 would be in the denominator.  If you take that team's average (say, 15.0) and divide it by their 0.32 output for that game, you're going to get an insanely high defensive EqPts+ score (4687.5, to be exact), and obviously that can skew averages. 

The first thing I did was put a cap on scores.  For all '+' numbers so far, no particular unit's game score can be higher than 300.  I have to do some further tinkering, as that still leads to a lot of 300's (and therefore higher averages than on the offensive side of the equation), but here's what we've got so far.

EqPts+ (Defense)

1. Ohio State (216.02)
2. USC (200.94)
3. Kansas (193.43)
4. LSU (187.53)
5. Hawaii (180.24)
6. Boise State (179.52)
7. Oklahoma (171.53)
8. Texas (171.08)
9. Texas Tech (170.65)
10. Arizona State (168.49)

Beyond the first 4 teams and OU, that's not exactly what you would have considered a murderer's row of defenses there.

S&P+ (Defense)

1. Ohio State (182.64)
2. USC (161.45)
3. LSU (161.18)
4. Virginia Tech (156.96)
5. Rutgers (156.62)
6. Oregon State (156.51)
7. Oklahoma (150.14)
8. Penn State (149.37)
9. Boise State (148.44)
10. Arizona State (146.95)

These numbers as a whole run a little lower, and that makes me a bit more comfortable about them, but...those are still a lot of the same teams there.  With either measure, tOSU is by far #1, which suggests that they at least somewhat earned their good fortune last year despite a horrendously weak schedule.  They will probably remain #1 no matter what kind of tweaking I do, so...good for them, I guess.

Rushing EqPts+ (Defense)

1. West Virginia (#18 in plain old rushing yards allowed per game)
2. Texas (#6)
3. Florida (#10)
4. Air Force (#45)
5. Navy (#81)

Passing EqPts+ (Defense)

1. Texas Tech (#12 in passing yards allowed per game)
2. Hawaii (#37)
3. Ohio State (#1)
4. Rutgers (#5)
5. Kansas (#49)

Now...this is pretty damn interesting, really.  Teams with good rushing games (WV, AFA, Navy) came out of nowhere to place at the top of the rushing defense list, while pass happy teams (Tech, Hawaii) were at the top of the passing defense list.  Of course, this is measuring EqPts Allowed in those areas...teams playing Tech and Hawaii were likely to run the ball a lot (and therefore avoid passing) to keep the ball out of Tech/Hawaii's hands.  So let's check out S&P+...since it looks a per-play average instead of a per-game average.

Rushing S&P+ (Defense)

1. Ohio State (#3 in rushing yards allowed)
2. Oregon State (#1)
3. UCLA (#14)
4. Penn State (#7)
5. Wyoming??? (#27)

Passing S&P+ (Defense)

1. Ohio State (#1 in passing yards allowed)
2. Rutgers (#5)
3. Utah (#11)
4. Arkansas (#23)
5. Virginia Tech (#31)

Okay, this is better.  I obviously don't need these numbers to precisely resemble the yards per game stats--why the hell would I be doing all this if that were the case?--but it is certainly strange that these numbers could be so drastically different.  At least the offensive numbers were in the same ballpark.  Any ideas as to what I should maybe do different are welcome.


So what I've just done with some basic S&P and EqPts numbers, I could do this with every stat in the catalog...S&P+ by down, quarter, field position, etc.  Line Yards/Sack Rates, etc. And to some degree, I'm going to do just that (though I don't yet know what I'll find that will be interesting enough to share!).  There are four purposes to all of this.  

1) This could obviously be interesting form an evaluative perspective.  It's always fun trying to come up with more and more precise ways of evaluating and ranking teams.

2) It could be even more interesting from a predictive perspective. The only thing more fun than ranking teams is making accurate predictions, am I right? Of course, the main problem is, with only one year of data it's somewhat impossible to actually know what's predictive and what just seems like it should be predictive. We'll all be discovering together which tools are and are not good forecasting tools.

3) It will make for a more informed experience while watching football...which is just awesome.  It was fun watching Mizzou games last year, knowing that an opponent's best quarter is Q2, or little things like that.  It will be even more fun this year, knowing even more.

4) Judging by the response generated by my last post, it's become clear to me that there are quite a few pockets of stat nerds out there--stat nerds who enjoy the practicality and usefulness of said stats (instead of just their number-y goodness), which is even better--and this is an excellent opportunity to build something of a communicative community based around college football stats.  I'm just going to keep on writing these posts and asking for opinions and new ideas and seeing where this goes.