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Penalty Yards and Possession: On the Rocks.

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No element of SMQ's month-long Stats Relevance Watch has proven such a catalyst for debate as the consistent finding that penalty yardage has no correlation at all with winning, and that in fact teams that were penalized more than their opponent in any given game were more likely to win said game.

Mergz at Saurian Sagacity is intrigued, for one, and offers up a closer look at one possible explanation that's been tossed around on his site and elsewhere: penalties are more likely to be assessed against an offense than defense, therefore teams with greater time of possession are more likely to wind up with more penalties.

As a public service: Penalties are bad, mmkay?
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The first assumption that has to be made there is that time of possession is integral to winning itself, which the numbers show generally but Brian (with basic agreement from SMQ) also disputed effectively in October; time of possession is a complimentary factor itself, accompanying successful third down conversions and running more often with a lead.

But to address the relationship at hand: Inherent to the penalty-possession pas de deux is the assumption of a control outside of possession time, our variable: all offenses (and defenses, and special teams) must be penalized at roughly the same rate over a given period of time. If this weren't true, if some offenses (or defenses, or special teams) were more likely for whatever reason to draw a flag on any play than others, it wouldn't be possible to draw any substantive link to time of possession. If the penalty-possession correlation is true, it would be possible to establish a standard measure of "penalties per minute" based on time of possession that would look pretty similar across the board.

Since Mergz (who said he considered but did not actually implement this sort of ratio) already isolated the times of possession and average penalty yards for each team in the SEC, SMQ will start with his numbers (teams ordered by penalty yards per game):

Rank Team Penalty Yds. Time of Poss. Yds. Per Minute*
1 Florida 63.4 31:08 2.03
2 Arkansas 53.9 28:41 1.88
3 Kentucky 52.8 30:11 1.75
4 Miss. State 52.2 29:17 1.78
South Carolina 52.2 30:01 1.73
6 LSU 50.5 30:10 1.67
7 Georgia 47.0 29:31 1.59
8 Auburn 45.8 30:09 1.52
9 Alabama 42.8 32:11 1.33
10 Ole Miss 38.7 28:55 1.30
11 Tennessee 37.7 28:33 1.33
12 Vanderbilt 33.2 28:52 1.15

* - Total penalty yards per offensive minute, of course.

That is a no-go. The "per offensive minute" numbers correlate almost exactly with per game averages; where time of possession only varies about ten percent from the league's "best" number (Alabama) to its worst (Tennessee), the per game yardage difference from the top (Florida) to the bottom (Vanderbilt) varies by about 48 percent, and the "per minute" average between the same extremes varies more than 56 percent, five and a half times greater than the variance in time of possession. That's not much of a relationship.

But those are averages over an entire season, which could represent the middle ground between two poles that do tell us something, game-by-game. To test this, SMQ looked at Mergz's own Gators by game (the "per minute" penalty yards in question here are in italics; numbers in bold are games in which those numbers were within half a yard of one another):

Florida Penalty Yds. Time of Poss. Yds. Per Minute Opponent YPM Opp. Pen. Yds. Opponent TOP
So. Miss (W, 34-7) 44 28:13 1.6 2.0 64 31:47
UCF (W, 42-0) 71 32:20 2.2 1.1 30 27:40
Tennessee (W, 21-20) 65 35:04 2.0 1.4 34 24:56
Kentucky (W, 26-7) 71 26:17 2.7 2.0 66 33:43
Alabama (W, 28-13) 53 30:23 1.7 .88 26 29:27
LSU (W, 23-10) 102 32:35 3.1 1.1 30 27:25
Auburn (L, 17-27) 33 23:17 1.4 1.1 40 35:42
Georgia (W, 21-14) 75 33:58 2.1 2.0 50 25:30
Vanderbilt (W, 25-19) 53 31:55 1.7 1.2 33 28:05
So. Carolina (W, 17-16) 49 29:29 1.7 2.8 85 30:31
Fla. State (W, 21-14) 65 33:43 2.0 1.0 27 26:17
Arkansas (W, 38-28) 67 28:02 2.4 0.78 25 31:58
Ohio State (W, 41-14) 50 40:48 1.2 2.6 50 19:12

The rates are all over the place relative to total yardage, but mostly, Florida's just committing more penalties regardless its time with the ball (SMQ did Alabama's games,. The most interesting result is Auburn, the one game UF was really dominated in total time of possession, but managed to rack up almost the same amount of penalty yardage. The other very interesting result - extremely counter to the larger trend - was in the mythical championship game, when UF absolutely owned time of possession far more that any other point in the season, but penalty yards held steady and in fact were matched exaclty by Ohio State, which hardly ever had the ball; Florida's best performance, possibly the best single performance by any team all season, corresponded with its least penalized game relative to total time with the ball. Yet its second-best effort, against LSU, was the most penalty-laden of the season.

Very, very small sample size, but penalty yardage represents a very small sample size itself compared to other types of yardage and the usually larger margins that accompany those categories. Remember also that the measure is penalty yardage, not number of penalties, and that it requires three delays of game to equal one pass interference. It's enough for SMQ to assert he doesn't really buy it until proven otherwise - it's not ridiculous or out of the question, but SMQ doesn't see anything tangible that suggests a readily apparent correlation of penalty yardage with time of possession. The relationship doesn't hold at all half the time, and a possible correlation seems pretty iffy the other half, which makes it pretty random.

...yet still more functional than a lot of other relationships...
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That appears to SMQ to be the bottom line here: random. A "mystery," as Mergz puts it in his post. In Part One of the Relevance Watch, there was hardly difference between the records of the most and least penalized teams nationally, a sign of irrelevance either way; in Part Two, SMQ said the effect was "apparently nil," and as really proving otherwise would require more overwhelmingly tedious, play-by-play data mining than he's willing to attempt, that remains the de facto position for the time being.