[Husker] NU opponent penalties or 'something rotten in the state of Nebraska'

[Paul Dalen]

I'm a member of HuskerMax.  There was a thread yesterday about how NU had
the lowest average opponent penalties in the B12.  I did some number
crunching on it.  Here's my post to that topic.  I can't post pics to this
list, so you'll have to click the links to see the graphs.  I did the work
pretty quickly last night, and I may have takes some *ahem* liberties with
assumptions.  But in general, I think my analysis is sound.

BLUF:  There are some statistical anomalies when you compare NU’s penalties
to the average of the rest of the B12’s opponents’ penalties, and when you
compare NU’s opponent penalties to an average of the rest of the B12
penalties.



Note:  None of the averages I used in analysis include NU’s numbers.   All
stats are from 2010.  I'm assuming that the data used conform to a normal
distribution, which may or may not be true.  The data I used are found here:

http://www.teamrankings.com/college-football/stat/opponent-penalties-per-game


First, I compared NU’s per-game team penalties to an average of the rest of
the Big 12 opponent per-game penalties.  NU’s average per game penalties are
7.1, and the rest of the Big 12’s average opponent per game penalties are
6.69 with a standard deviation of .92 (n=11).


NU’s average of 7.1 converts to a z-score of .44, which equals a probability
that any random team would have a penalty average of no more than this of
.67.  To me, this says that there is no evidence at all that the refs are
calling more penalties on NU than they are on the rest of the B12 in
aggregate.



The graph below illustrates this probability.  The top of the bell curve is
the average number of Big 12 opponent penalties, and the line between the
blue and white areas is NU’s per game average penalties.  The closer to the
middle of the graph the line falls, the closer to ‘normal’ the average is.



http://lh4.ggpht.com/_elioP_aq1UY/TOSfdmk1WMI/AAAAAAAADP8/4d70P0MpyqI/s800/part%201%20penalties%20analysis.JPG


The numbers become more eyebrow-raising when you compare NU’s  average
opponent penalties per game to the average per game penalties of the rest of
the Big 12.  NU’s opponents’ average per game penalties are 4.3, and the
rest of the Big 12’s average per game penalties are 6.59 with a standard
deviation of 1.21 (n=11).


NU’s average of 4.3 converts to a z-score of -1.90, which equals a
probability that any random team would have a penalty average of no more
than this of .029.  To me, this says that there is evidence that the refs
are calling significantly fewer penalties on NU’s opponents.


The graph below highlights this.  The shaded blue area is the probability
that a random team’s opponents would be assessed an average of 4.3 penalties
per game.    As fan and as a stats nerd, it takes significant suspension of
disbelief to accept that this average is attributable solely to chance.


http://lh4.ggpht.com/_elioP_aq1UY/TOSfdmk1WMI/AAAAAAAADP8/4d70P0MpyqI/s800/part%201%20penalties%20analysis.JPG


There is one other thing to consider.   The Big 12 averages include four
teams that the Huskers have not faced yet, and these teams include the three
teams (CU, BU, A&M) with the highest per game average penalties.   If we
perform the same calculations but exclude the teams NU has not played yet,
the numbers become even more eye opening.


Comparing NU’s per-game team penalties to an average of the rest of its Big
12 opponents' per-game penalties, NU’s average per game penalties are 7.1,
and the average of the rest its Big 12 opponents' per-game penalties are
6.69 with a standard deviation of 1.03 (n=7).


NU’s average of 7.1 converts to a z-score of .40, which equals a probability
that any random team would have a penalty average of no more than this of
.66.  Again, there is no difference in the number of penalties called on NU
even when you only consider the teams NU has played.



However, when we compare NU’s  average opponent penalties per game to the
average per game penalties of the rest of its Big 12 opponents we see that
 NU’s opponents’ average per game penalties are 4.3, and the rest of the Big
12’s average per game penalties are 6.04 with a standard deviation of .61
(n=7).   NU’s average of 4.3 converts to a z-score of -2.85, which equals a
probability that any random team would have a penalty average of no more
than this is .002!


http://lh5.ggpht.com/_elioP_aq1UY/TOSftvXGtPI/AAAAAAAADQc/JxJ4c1fDv08/s800/part%203%20penalties%20analysis.JPG


While the number of penalties called on NU’s opponents seems hard to accept
as coincidence when compared to the entire Big 12, it’s almost 10 times more
likely to happen than when you look at only NU’s opponents!  In fact, the
probability is so small as to be almost invisible on the graph.  Trust me
though, there is a very small blue shaded portion above.



What’s this all mean?   To me, it’s clear that the per game average number
of penalties called on NU’s opponents is very difficult to attribute solely
to chance…which begs the question of “to what else could it be
attributable?”  I leave it to each of you to draw your own conclusions about
that…as we’ve left the realms of science and entered the more treacherous
realms of conspiracy theories.


Full data and computations are here.


https://docs.google.com/leaf?id=0By3lZgFCOqcjNzZkNmViZDctMTgxZS00ZDk4LTg3ZGMtNWZkMmNiZDcwMTU4&authkey=CMz19e4C&hl=en


Thread on HuskerMax is here:


http://www.huskermax.com/vbbs/showthread.php?10074-NU-s-oppoents-least-penalized-in-Big-12.