Rhythm & Fatigue: The Three-and-out Dance

Be ye warned, this is going to be a bunch of idle number crunching. No game footage analysis, and no fancy-schmancy animated gifs. Just numbers.

So I have this theory:

You often hear about an offense scripting the first 20 plays of a game. Presumably, this provides a sequence of less predictable play calls because you aren't overreacting to a few results. And it should help your offense get off to a fast start because you've rehearsed those particular plays beforehand.

My theory is that teams would be better served focusing, not on the first 20 plays of the game, but the first 3 to 4 plays of each drive. Every time a team goes three-and-out, its defense has to come back out with inadequate rest, and the opposing defense goes to the bench with minimal fatigue. This effect should-- in theory, at least-- be cumulative. Failure on one drive brings a fresher defense to the next drive. A tired defense which gives up several first downs will be even more tired the next time it comes out, and so on and so on.

Getting at least one first down gives your offense a chance to get in rhythm while providing more chances to feel out the opposition for a weakness. And, of course, you can't get the second 1st down until you get the first 1st down.

Could such a simple strategic change work? I don't know. But not knowing is the best part, because it lets us do some fun, fun, math to find out! And, of course, we'll take a look at the Patriots and the Seahawks to see how they measure up, and whether or not early three-and-outs will have an impact in the Super Bowl.

What to Measure: Minimum Success on Drives

Nothing too tricky here.

If a team goes three-and-out, they'll have only three offensive plays on their drive, which we'll label as a failure.

A team that gets a first down will typically run at least 5 offensive plays, which we'll label as a success.

Four plays is questionable. It might be a result of going for it (and failing) on fourth down. It could also be a single play for 10 yards (or a defensive penalty) followed by a three-and-out, which doesn't do much for your offensive rhythm or the opponent's fatigue. So at exactly four plays, I counted a minimal success when gaining 20+ yards and gave half credit for 10-19 yards. Four plays that gain fewer than 10 yards counts as a failure.

And finally, we don't want to look at all drives. Those at the end of either half can be skewed by 2-minute drills and prevent defenses. Also, the success on later drives is more likely to be an effect of rhythm and fatigue from earlier. So to focus on Minimum Success as a cause, we'll look at just nine drives per game: Five in the first half, and four in the second half.

For example, Cincinnati Bengals drives vs Cleveland Browns, week 10; MSOD = "Minimum Success on Drive":

Drive #	Quarter	Plays	Yards	Result	MSOD
1	1	5	10	Interception	1
2	1	5	1	Punt	1
3	1	7	7	Field Goal	1
4	1	4	11	Punt	0.5
5	2	2	24	Fumble	0
6	2	don't care
7	2	don't care
8	2	don't care
9	3	7	-3	Punt	1
10	3	6	20	Punt	1
11	4	8	46	Interception	1
12	4	3	-5	Interception	0
13	4	don't care
14	4	don't care

The Bengals went three-and-out 2.5 times over 9 drives, so their whole game MSOD% would be 6.5/9 = 72.2%

Per-drive stats are hard to come by. Because I had to manually gather them game-by-game, I took a representative sample of all 2014 games for each of six teams, choosing those with a near-average SRS: Cincinnati, Arizona, Detroit, Miami, San Diego, and Minnesota. I set this aside as the "control sample" (to test the theory in general) and also gathered data for the New England Patriots and Seattle Seahawks.

We'll see below how these correlate with winning on a per-game basis. But first, let's examine how our Champions did on average:

Team	MSOD%
Sample Average	61.9%
Seahawks	64.3%
Seahawk Opponents	58.6%
Patriots	64.4%
Patriot Opponents	64.4%

That's not too surprising, really. Seattle's powerful running attack and stifling defense put them ahead of average on both sides of the ball.

On offense, the Patriots' short passing and balanced rushing attack is outstanding at attacking the first ten yards. On defense, they force fewer three-and-outs than average, a reflection of their comparative strengths: They are vulnerable to short runs, and do well limiting big gains.

What To Measure: Wins and Points

If you wanted to know how valuable completion percentage is (on both sides of the ball), you'd probably look at how it correlates with scoring. It should have the same effect on scores whether you're playing in a close game or a blowout, so by looking at total points (scored and allowed) you actually get a better idea of how it can predict wins than if you'd simply looked at wins and losses.

But that analysis treats completion percentage as an independent variable. You can toss every game, every drive, every pass into the same statistical bucket. It's all cause and no effect. With MSOD, we are explicitly looking not at the effect on immediate scoring, but a cumulative effect throughout a single game.

So the cause we want to measure is neither MSOD for a series nor MSOD throughout the course of a season, but total MSOD confined to a single game. And for the effect we don't want to ignore points altogether, but we want to put more weight on winning and losing.

Which brings us to the simple (I hope) concept of win value:

Win Value = point differential + (8 for a win) - (8 for a loss)

Why eight points? Because it's the maximum value of a single score. That way, a single meaningless score late in the game (either by the losing team or the winning team) cannot double or halve the win value.

Results

Because MSOD only affects offense and defense, we'll check its correlation next to some other, more general, offensive & defensive performance statistics. All of these stats are taken from the same sample, so if any game outcomes are radically affected by special teams play, it should affect the predictive power of all the stats equally.

Yardage differential: Simply offensive scrimmage yards minus defensive scrimmage yards. This should set the standard for best possible correlation with scoring.

First down differential: Team first downs minus opponent first downs. If MSOD is just a limited way of measuring first downs, this should expose it.

Turnover differential: Often cited as a key variable in winning games; we'll see how it stacks up.

MSOD differential: The difference in success percentage between the two teams. The first two drives of the game and the first drive of the 3rd quarter are all given one-and-a-half weight (to better reflect the hypothesis of cumulative effect).

9-drive yardage differential: Just for fun, this is a comparison of yardage gained on the same 9 drives that MSOD is measuring.

SAMPLE	Measured Stat	Correlation to   Win Value	Correlation   to Wins	Wins Straight-up (Record for Leader)
Control	Yards differential	0.710	0.636	0.808
Control	First Down diff	0.566	0.519	0.720
Control	Turnover diff	0.531	0.459	0.699
Control	MSOD diff	0.549	0.496	0.779
Control	9 drive yards diff	0.742	0.650	0.786
				W-L if   better	W-L if   tied	W-L if   worse
Patriots	Yards differential	0.713	0.574	10 - 0	0 - 0	4 - 4
Patriots	First Down diff	0.701	0.582	11 - 0	1 - 0	2 - 4
Patriots	Turnover diff	0.532	0.360	9 - 2	3 - 1	2 - 1
Patriots	MSOD diff	0.645	0.563	7 - 0	3 - 0	4 - 4
Patriots	9 drive yards diff	0.841	0.775	11 - 1	0 - 0	3 - 3
Seahawks	Yards differential	0.619	0.445	13 - 2	0 - 0	1 - 2
Seahawks	First Down diff	0.481	0.461	12 - 2	1 - 0	1 - 2
Seahawks	Turnover diff	0.076	0.019	7 - 2	4 - 1	3 - 1
Seahawks	MSOD diff	0.584	0.440	10 - 2	1-0	3 - 2
Seahawks	9 drive yards diff	0.603	0.404	13 - 2	0 - 0	1 - 2

I've slapped the whole mess of numbers up there so you can draw your own conclusions. Here are mine:

The basic hypothesis is questionable. The total yards differential across the same 9 drives that MSOD examines is better at predicting game outcomes. Which is to say, two three-and-outs along with one 80-yard drive is superior at producing wins to three 15-yard drives that end in a punt. But...

MSOD contains the least amount of information (save perhaps turnover differential) out of all the statistical measures above. Its roughly half the data from about a third of all plays. Yet it correlates with win value almost as well as total first down differential. And I still think it would be a better focus for scripting plays, but until I get a phone call from an NFL franchise that wants a strategy analyst, that's just my opinion.

Predicting a winner straight-up, MSOD was as good as anything, with the team having a superior MSOD winning 77.9% of the time. That the straight-up prediction is so much better than the correlation suggests that perhaps MSOD differential works well for close games and small differences (as opposed to yardage differential, which is more informative with bigger gaps). On the other hand, winning teams tend to win most statistical measures across the board, so MSOD may not be that special.

The Seahawks

Compared to the control sample, Seattle had weaker correlations for yardage differential, first down differential, turnover differential, and 9-drive-yardage differential. Some of that is due to erratic special teams play.

But-- again compared to the control sample-- Seattle had a stronger correlation for MSOD differential.

Among the five games where they lost the MSOD battle were losses to the Chargers and to the Cowboys. Fatigue was a factor in both games. San Diego wore down the Seahawks on a brutally hot (94 F) day, and the Cowboys sealed their win with two scoring drives in the 4th quarter.

Seattle's three other games with a negative MSOD differential were all decided by less than seven points (13-9 over Carolina, 30-24 over Oakland, and 28-22 over the Packers).

On the flip side, Seattle's five games with the best positive MSOD differential include victories over Green Bay in the regular season (36-16), St. Louis (20-6), San Francisco (17-7), Arizona (35-6), and Carolina in the Divisional Round (31-17). What's more, it could easily be argued that these lopsided final scores were the more the product of rhythm and fatigue than jumping on an early lead. Over those five games, Seattle had an average halftime lead of just 9.6 to 7.2. But they outscored their opponents by a combined 73-13 in the fourth quarter.

PREDICTION: If the Seahawks force some three-and-outs in the Super Bowl, and are able to move the ball at least a little bit on each drive (whether they score or not), expect them to have no trouble flexing their muscle late in the game-- whether it's turning a close game into a blowout or overcoming a deficit.

If Seattle has a negative MSOD differential, expect the defense to suffer the most against New England's highly efficient short-range attack. The offense should be fine, and they can win, but if they trail on the scoreboard they'll need to start their comeback in the 3rd quarter before the Patriots have a chance to put the game away by killing clock.

The Patriots

For MSOD differential, New England had the strongest correlation of all teams. Part of that is due to a number of blowout games that the Patriots dominated throughout, games where rhythm & fatigue may have contributed to a lopsided score but were irrelevant to the final outcome.

More intriguing are the eight games where the Patriots had a negative MSOD differential, which includes all four of their losses. The Dolphins in week 1 moved the ball consistently, but three first-half turnovers gave the Patriots a 20-10 halftime lead. When the Dolphins stopped turning the ball over in the second half, they outscored the Patriots 23-0, largely by running the ball.

The Packers in week 13 had at least minimum success on every single offensive drive and forced a pair of three-and-outs. Although the Packers managed just 3 points in the second half, their offense was able to kill clock and their defense stayed fresh enough to stifle the Patriots' comeback attempt.

New England managed two narrow wins when their MSOD differential was negative (27-25 over the Jets, and 35-31 over the Ravens in the Divisional Round). But they also enjoyed two blowout wins under the same conditions.

So what happened there?

In a 34-9 pasting of Detroit and a 41-13 defeat of Miami, the Patriots had 4 touchdown drives of 3 plays or less. These are drives which fail to create rhythm & fatigue, at least according to the MSOD measurement (by design). The Patriots also came up big on special teams, with an 81-yard kickoff return and a touchdown on a blocked field goal.

PREDICTION: The Patriots' defense does not force many three-and-outs, but they don't need to. They're comfortable preventing big plays and relying on their offense to give them a needed rest. If the offense fails, the defense can become vulnerable late in the game to a determined rushing attack.

New England's offense, meanwhile, is clearly at its best when they move the chains consistently:

Opponent	first downs	Yards	Points
Indianapolis Colts	33	503	42
Chicago Bears	32	487	51
Cincinnati Bengals	30	505	43
Denver Broncos	29	398	43
Detroit Lions	29	439	34
Baltimore Ravens	29	422	35
Indianapolis Colts	28	397	45
San Diego Chargers	24	397	23
Miami Dolphins	23	395	41
Buffalo Bills	22	396	37
Oakland Raiders	21	297	16
Miami Dolphins	20	315	20
Green Bay Packers	20	320	21
New York Jets	19	231	17
Minnesota Vikings	16	292	30
New York Jets	16	323	27
Buffalo Bills	14	260	9
Kansas City Chiefs	13	290	14

Patriots correlation coefficients:
First downs to yards: 0.8983
First downs to points: 0.8165

Seahawks correlation coefficients, data not shown on table:
First downs to yards: 0.7288
First downs to points: 0.4466

If the Patriots go three-and-out too often, they will be in trouble on both sides of the ball. They've proven they can win under those circumstances, but it will require big plays on offense and probably some help from special teams.