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I was looking over the year-end stats for pass offense and defense earlier today, just to see where the Falcons sort of rank in certain areas.

I was focusing mainly on completion percentage, yards per attempt, 1st downs per attempt, big (20+ yd) plays per attempt, sack rate, and quarterback rating.

Atlanta grades well in 5 of those 6 categories, ranking in the Top 7. They led the league in completion % and 1st down rate. The lone category where they performed poorly was big plays, where they were 29th in the league.

Defensively, the Falcons fared much worse, ranking average or below average in all but 1 category. They were 16th in completion% and 1st down rate, 21st in YPA and big plays, 27th in sack rate. But they were 5th in opponent passer rating.

And after looking over the numbers, I started thinking about whether these numbers really mean anything. So I wanted to see how they correlated with wins. So I calculated the correlation coefficient for each. And just for the sake of comparison, I also calculated it for these 6 categories as well as points scored/allowed, passing yards, touchdowns, and interceptions.

I'm sure it wouldn't take most people more than 1 guess what correlated the most with wins, it was points scored. It had a coefficient of 0.792. The closer you are to 1.0, the higher/closer the correlation, the closer you are to 0, the lower the correlation. But what I thought was interesting was that QB rating came in second at 0.730. Also interesting was that 1st down rate was at 0.706.

Interceptions had a negative correlation of -0.652, which means that as you throw more interceptions, the less likely you are going to win.

After that, it proceeded as such:

Completion Percentage: 0.628
Yards Per Attempt: 0.625
Touchdowns: 0.552
Big Plays/Attempt: 0.342
Yards: 0.231
Sack Rate: -0.170

Now that's all for offense. I did the same for defense. And while the correlations did follow the same basic order, they were much less stronger.

Points Allowed: -0.736
Passer Rating: -0.539
Interceptions: 0.424
Yards Per Attempt: -0.382
Sack Rate: 0.375
1st down Rate: -0.324
Touchdowns: -0.308
Completion Pct: -0.251
Big Plays/Attempt: -0.182
Yards: -0.010

Several observations:

- Obviously, this is by no means a comprehensive study, and sweeping conclusions would require at least 10, if not 20 or more years of date. And obviously, it'd be interesting to factor in postseason success and whether that changes things. And of course the fact that this is only measuring passing still leaves about 40% of the game unaccounted for.

- But it is interesting that passing yards is still used as a measure of quality of a defense, yet it has the flimsiest correlation to wins, at least this year it did. Looking at yards allowed, it's practically zero, basically meaning that it has almost no relation to winning football games.

- It's interesting that getting 1st downs on offense throwing the ball has a fairly high correlation, but giving them up on defense doesn't have that much of a correlation.

- Interesting to see how sack rate on defense correlates better with winning (and more so than several other categories), but correlates very poorly on offense in terms of sacks allowed.

- Also seems to suggest that Cold Hard Football Facts way of looking at team's offensive/defensive passer ratings as their main tool of measurement is not as iffy as I originally thought. Outside points scored, their probably isn't a better way to really judge the good teams from the bad ones.

- Also that the positive correlation between scoring points and winning is stronger than the negative correlation of allowing points and winning. But obviously, it's not a huge discrepancy. But if you had to choose between having an elite scoring offense, or an elite shutdown defense, you would probably win more (regular season) games.

Did you calculate the correlation coefficient for each team, or just the Falcons?

The league as a whole.

Some of those numbers are kind of surprising then... It would seem that, "opportunistic," and, "bend don't break," is the name of the game on defense.

Good analysis. I've read/done several of these over the years, and passer rating is always very highly correlated with winning, so I don't think that's an aberration. It's not the perfect measure, but it does capture how well the passing game is working (mostly) and that mostly covers who wins. Adjusted yards/attempt also correlates very highly with winning.

On defense, scoring D and turnovers being high correlation makes sense. I'm a bit surprised by yards. I know sometimes this just reflects garbage 4th quarter yards, but it still seems a D that forces a lot more 3 and outs or 15 yard drives is less likely to suffer a lapse than a team that routinely lets teams drive 60 yards an then prays for a red zone stop.

Neat stuff.

Did some additional number crutching. Wanted to look at net yards per attempt (which factors in sacks/sack yardage), adjusted yards per attempt (which basically gives yardage credit for TDs and penalizes for INTs), and adjusted net yards per attempt (combo of the two). I also wanted to look at run offense and run defense as well to see how it stacked up.

So I had to get the sack yardage numbers to do this. What was interesting that I found out is that how many yards you give up due to sacks is much more important than the number of sacks.

The negative correlation of just sack yardage alone for passing offense is -0.313. As posted above, the correlation for sack rate is -0.170. I also thought I'd look at just raw sack numbers, which also posted a higher negative correlation than sack rate (which factors in # of attempts): -0.305. I would have figured sack rate was more important. Basically that suggests that if you have a team that gives up 30 sacks, it will likely be better than a team that gives up 40 sacks, even if the team that gave up 40 sacks threw the ball many more times to have a lower sack rate.

For defense here are the numbers:

Sack Yards: 0.513
Sack (raw): 0.506
Sack Rate: 0.375

But here are the NYA, AYA, and ANYA correlations for both offense and defense:

Offensive NYA: 0.580
Offensive AYA: 0.695
Offensive ANYA: 0.671

Defensive NYA: -0.412
Defensive AYA: -0.529
Defensive ANYA: -0.541

Obviously AYA and ANYA are probably close enough where the difference is negligible and would need more years of data to really get a definitive answer on which is superior.

That would make Offensive AYA that 3rd most important passing stat after passer rating and 1st down % (go figure).

What is interesting though is that raw sacks, sack yards, defensive AYA, and defensive ANYA all hover around the same importance as defensvie passer rating. Again, would need more years worth of data to see if any clear pattern emerges.

I also wanted to crunch the numbers for running too:

Offensive Correlations:

Rush Attempts: 0.474
Rushing TDs: 0.457
Fumbles (per attempt): -0.376
Rushing Yards: 0.311
Rushing 1st down Rate: 0.286
Fumbles (raw): -0.248
20+ runs (raw): 0.187
20+ runs (per attempt): 0.081
Yards Per Carry: 0.079

Defensive Correlations:

Rush Attempts: -0.639
Rushing Yards: -0.488
Rushing TDs: -0.476
Fumbles (per attempt): 0.431
Fumbles (raw): 0.333
Rushing 1st down rate: -0.220
20+ runs (raw): -0.215
Yards Per Carry: -0.115
20+ runs (per attempt): -0.056


What's interesting about the run defense is that attempts have the highest correlation, likely due to the fact that teams tend to run more when they have a lead. And what's interesting is the disparity between offense and defense, where the correlation is higher (or furthest from zero) with defensive run attempts. The more teams run against you, the less likely you'll win.

Look at how fumbles matter, which again turnovers are key. But look at how low YPC is. At least in terms of judging the quality of teams in 2012, it is largely a useless statistic.

So the conclusion I guess to take from all of this is this is how you want to build/coach your team:

Basically being a team that can score in the redzone, and prevent scoring in the redzone is important. You want to be able to move the chains by throwing it, but you also want to be able to run the ball late in games to protect a lead. You want to create turnovers, and limit your own, and also get pressure on the opposing QB.

So I guess if the Falcons want to increase their chances of winning, then improving their running game and pass rush should be priorities. I think everyone would agree that the eyeball test tells us those were key areas to improve, and it seems stats back it up.

More good info.

I don't know how easy the data is to find (don't know which sources you used) but if you take 1st half rushing, or 1st 3 quarters rushing (attempts, ypc, yards) you get rid of the "you run when you're winning and milking a lead effect" and it helps show which aspects of running contribute to winning instead of result from winning.