I'll be the first to tell you that I enjoy numbers. Numbers aren't my life, but they can expose things are just so plainly obvious that it would be foolish to overlook them as a useful tool in sports. I'm an outsider when it comes to the world of sports stats and ratings for the most part. I honestly have no idea what's already been written or espoused upon, particularly in the world of football. It's entirely possible that I've come up with something that's already been done, but at the same time it could also trigger a collective, "Now why didn't I think of that earlier?"
I remember when this revelation here first hit me. Two years ago, after a series of particularly frustrating Friday nights coaching on an offensively-starved team, I was sitting in the office with my fellow coaches bemoaning our pathetic offense letting down our stout defense yet again (although, given the number of two-way players, it was kind of nonsensical). After a lengthy pause at some point, I said, "You know what the problem is? Our defense is as gloriously efficient as it gets, and our offense is as inefficient as it gets. We'll never make the playoffs is we can't get over 100% combined." The eyes of my fellow coaches lit up, at which point I went up to the board and doodled out two formulas. Once I had explained them, they all rolled their eyes and discussed other things. Math, you see, apparently has no business in the world of football.
Ready? Here they are. I call them OER and DER, mostly because it's less unwieldy than OSTER and DeSTER. The trade-off is that OSTER and DeSTER can be used as words, while OER and DER is a little tougher.
OER (Offensive Efficiency Rating) / OSTER (Offense and Special Teams Efficiency Rating)
(Total offensive points scored + kick return points scored) / (Adjusted offensive possessions * 7) + (number of two-point conversions attempted) = OER/OSTER
DER (Defensive Efficiency Rating) / DeSTER (Defense and Special Teams Efficiency Rating)
(Total defensive points allowed - punt return points scored) / (opponent's adjusted offensive possessions * 7) + (number of two-point conversions attempted) = DER/DeSTER
The basis of the formula is "adjusted offensive possessions". An adjusted offensive possession is defined as one in which scoring is attempted; thus, a possession that ends with killing the clock by taking a knee wouldn't count. If a team recovers an onside kick with :07 left and takes a knee, that's not considered an adjusted offensive possession. If the same team takes over with a three-point lead and 4:08 on the clock and they manage to kill it (ending with taking a knee), that's also not considered an adjusted offensive possession. A team that receives a kickoff and fumbles on the return would be charged with an offensive possession. And so on.
Here's a quick example. Team A wins a game 42-37. They had 11 offensive possessions, although the quarterback took a knee to kill the clock to end both the first and second half. They scored touchdowns on six possessions, with four converted extra points, one converted two-point conversion, and one missed two-point conversion.
AOP (adjusted offensive possession) -- 11 possessions - 2 clock-killers = 9 AOP TOTAL POINTS SCORED -- 42 TOTAL 2-POINT CONVERSIONS ATTEMPTED -- 2 Thus...
(42 offensive points + 0 return points) / (9 [AOP] * 7) + (2 two-point conversions attempted) 42 / 63 + 2 42 / 65 0.646, expressed as a percent 64.6% OER
But now, you ask, is it possible to have a negative number? Certainly. If a team allows more defensive points than it scores on offense, they can have a negative number. If a team scores 14 points but allows two interceptions to be returned for touchdowns and a punt return for a touchdown, they'll have a negative number.
What you'll find an overwhelming majority of the time is that the team with the higher OER is the victor, thus making it the one stat (that isn't "total points") that most strongly correlates to victory.
The best teams will have a combined OER and DER of over 100, average teams will be around 100, and the bad ones will be less than 100.