The Seattle Seahawks are the third most penalized team in the NFL (penalties per game accepted against). Pete Carroll has brought up the penalty disparity between the Seahawks and their opponents several times in the last few weeks. His detractors would argue that the disparity is because the Seahawks are so wont to get flagged. He refined his argument this week to suggest that he is not so much complaining about the calls against the Seahawks, but rather the lack of calls that are made against the Seahawks' opponents.

As dedicated fans, we see one specific trend - pre-snap penalties on offense (offsides, illegal motion, and illegal formation) - which accounts for a disproportionate number of the Seahawks' penalties, and probably is the difference between being around league average versus the third most penalized team in the league. The "tendency" towards this class of penalties is intrinsic to our team this season (due to OL injuries, lack of continuity), and by this point in the season we expect that, regardless of opponent, we will accumulate enough of these penalties to make the total count above average on any given game day.

What's harder to figure out is why the Seahawks' vast array of opponents would draw fewer flags when playing Seattle than they would draw playing any other team in the league. And indeed, the Seahawks' opponents are getting flagged for fewer penalties against Seattle than they are when playing anyone else. The Seahawks have played 12 different opponents this season. 5 of these teams have their lowest penalty count of the season in their game against the Seahawks. 9 (75%) of these teams achieved one of their three best penalty counts of the year in their game against the Seahawks. Only 1 of 12 teams (GB) has been penalized more than their season average when facing the Seahawks.

****For purposes of clarity, all statistics are obtained from NFL.com and pro-football-reference.com and include Thanksgiving day games of week 13 only (26 teams with 11 games, 6 teams with 12 games). For the purposes of penalty counts, I only considered accepted penalties - declined or offsetting penalties are not included. Penalty yards only include enforced yards (and not yards lost due to a negated play).****

League wide, there have been 2,384 penalties (damn that's a lot of yellow) for 20,060 yards (11.4 miles) in 358 games. That's a league wide per team per game average of 6.66 penalties for 56.0 yards.

For brevity, I will use the acronyms PAO (penalties accepted against opponent) and PYAO (penalty yards accepted against opponent), and will mostly use these terms in regards to per game averages. Averaged over 12 games, the Seahawks have accepted a paltry 4.3 penalties (PAO) for 34.7 yards (PYAO) against their opponents.

To put that in perspective, for the other 31 teams, the range of PAO per game is 5.7 - 8.5 and the range of PYAO is 44.3 - 72.5 yards.

Here is a table of all 32 teams and their respective PAO and PYAO, ranked from highest PAO (most penalties accepted against opposing team, aka most referee help) to lowest PAO (least referee help):

Rank Team PAO/g PYAO/g 1 Washington Redskins 8.5 69.3 2 San Francisco 49ers 7.8 59.7 3 San Diego Chargers 7.8 62.7 4 Arizona Cardinals 7.7 72.5 5 Minnesota Vikings 7.6 65.8 6 Philadelphia Eagles 7.6 68.5 7 Oakland Raiders 7.5 61.5 8 Jacksonville Jaguars 7.3 55.5 9 Baltimore Ravens 7.0 63.5 10 Chicago Bears 7.0 64.3 11 Tampa Bay Buccaneers 6.9 60.0 12 New Orleans Saints 6.8 58.6 13 Detroit Lions 6.8 54.0 14 Green Bay Packers 6.7 68.3 15 Miami Dolphins 6.6 60.2 16 Cincinnati Bengals 6.6 55.6 17 Kansas City Chiefs 6.5 54.3 18 Carolina Panthers 6.5 53.8 19 Buffalo Bills 6.5 51.6 20 Atlanta Falcons 6.4 52.3 21 St. Louis Rams 6.4 48.2 22 New York Giants 6.3 55.8 23 Houston Texans 6.3 50.4 24 Cleveland Browns 6.2 49.0 25 New England Patriots 6.2 52.4 26 Tennessee Titans 6.1 48.2 27 Pittsburgh Steelers 6.1 54.1 28 Indianapolis Colts 5.9 50.0 29 Dallas Cowboys 5.8 46.3 30 New York Jets 5.7 48.7 31 Denver Broncos 5.7 44.3 32 Seattle Seahawks 4.3 34.7

At a quick glance, there does not appear to be bias regarding: win total (Cards and Skins near the top, Broncos and Jets at the bottom), DVOA (see win total), media market size, or geographic location. The only trend I might see is that a few teams that have win totals greater than expected given their DVOA are at the top end of the scale - would it be surprising to anyone that having a PAO/PYAO advantage would lead to a better record than expected?

Back to the story at hand. The 1.4 PAO gap between the Seahawks (the team least helped by referees) and the Broncos (the 2nd least helped team), is the same magnitude as the gap from the 2nd least helped team to the 23rd least/9th most helped teams (tie, Bears and Ravens), and is the same magnitude as the difference from the 23rd least/9th most helped team to the #1 ref loved team (Redskins). That sounds a little extreme, doesn't it? But, "How extreme?" you ask.

How is this illustration?

To really answer "How extreme?", we can determine the probability of these events based the number of standard deviations from the mean (z-score). The league average is 6.66 PAO (standard deviation +/- 0.82) for 56.0 PYAO (SD +/- 8.3) per game. The second worst team in terms of PYAO and PAO are the Broncos who have a per game PYAO of 44.3 yards, 1.41 SD below the mean, and per game PAO of 5.73, 1.13 SD below the mean.

Using an online calculator, we determine the odds (P value) of a team achieving these z-scores at 0.079 (7.9%) for PYAO and 0.129 (12.9%) for PAO. To phrase it another way, the expectation is that around 1 in 12 teams (PYAO) and 1 in 8 teams (PAO) should receive "referee help" equal to or less than Denver has. To be fair, it seems like Denver has seen its opponents get flagged for significantly fewer penalties than most of the league, but the results fall within the realm of reasonable statistical variation (P value not less than 0.05).

Let's take a look at the Seahawks. The Seahawks have z-scores of -2.566 for PYAO and -2.939 for PAO. The probability of achieving that PYAO in an unbiased environment is 0.005144 (0.51%), or 1 out of 194 times. Even worse, the probability of achieving a PAO 2.939 SD below average is 0.001646 (0.16%), or 1 out of 607 times. In a 32 team league, we should expect a team to get as few penalties on its opponent as the Seahawks have so far this season once every 19 seasons.

To calculate the probability another way, in an unbiased environment, one would expect a teams' opponents to have more than their average number of penalties in about half their games and less than their average number of penalties in about half their games. Essentially a coin flip each game. The Seahawks have played 12 games and their opponents have had fewer than average penalties in 11 of those games; the probability of that happening 0.00293 (0.29%), easily in the same range as our P-values obtained from z-scores above.

These P-values are well below 0.05, the standard accepted norm for a statistically significant variation from the mean. This means that the incredibly low rate of penalties called against the Seahawks opponents has an explanation other than random variation.

There are two possibilities to explain these results. The first is that Seahawks opponents are committing fewer penalties against the Seahawks than they do against all other team (regardless of home/away). If the Seahawks were really bad, one might postulate that their opponents could succeed without pushing the boundaries of the rules and thus get fewer penalties, but the Seahawks are not bad. If teams were really focused the week they played the Seahawks (defending champions), they might play more disciplined football, but the 2013 Baltimore Ravens (defending champs) had the highest PAO in the league.

The second possibility is that the opposing teams are committing just as many penalties as they normally do, but that the referees are not calling them. Is there any explanation other than blatant league and referee bias?

POW!