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Tuesday, October 06, 2009

Are UGA fans crazy or are we being penalized more?

Georgia fans are quick to point out that it seems that UGA is being penalized more than in recent memory. Plenty of reasons are proffered for why this might be the case - ranging from poor coaching and preparation, to lack of discipline by the players, to a conspiracy by the referees.

Where does the conspiracy theory come from? The 2007 UGA-Florida game was marked by the entire UGA team charging the end zone for a celebration of the first touchdown scored by the team. Of course the celebration drew a penalty and the ire of UF fans. It might have also drawn the ire of the Zebras who might not yet put it behind them. Why would the officials care about the event? Because it let them know in no uncertain terms (from their perspective) that they were not in control of the game.

To test whether there has been any systematic change in the number of penalties UGA football incurs per game, I broke my standard 10 minute rule for an econometrics-based post (mainly because I am truly interested in the problem). So here are the results of about one hour of data gathering from the NCAA web site, getting the data into Stata, and some preliminary study.

First, here are some time lines of the following: penalties per game, penalty yards per game, yards per penalty. Each observation is a game and the sample period runs from the first game in 2000 through the LSU game of 2009. The red line indicates the first game after the 2007 UGA-UF game when the celebration under consideration occurred:







The ocular estimator suggests that the number of penalties seems to be increasing after the 2007 UGA-UF game, maybe a slight increase in in penalty yards per game, but not change in the yards per penalty incurred (I note that the spike in the yards per penalty graph is the 2001 home game against Houston in which we had one penalty for 62 yards).

I took the penalties per game and looked at the breakdown by year


. xi: reg penalties i.year
i.year _Iyear_2000-2009 (naturally coded; _Iyear_2000 omitted)

Source | SS df MS Number of obs = 119
-------------+------------------------------ F( 9, 109) = 1.79
Model | 145.614209 9 16.1793566 Prob > F = 0.0777
Residual | 984.116883 109 9.02859526 R-squared = 0.1289
-------------+------------------------------ Adj R-squared = 0.0570
Total | 1129.73109 118 9.57399231 Root MSE = 3.0048

------------------------------------------------------------------------------
penalties | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Iyear_2001 | 2.090909 1.281235 1.63 0.106 -.4484568 4.630275
_Iyear_2002 | 1.216783 1.230971 0.99 0.325 -1.222961 3.656527
_Iyear_2003 | 2.123377 1.210653 1.75 0.082 -.2760986 4.522852
_Iyear_2004 | 1.909091 1.254258 1.52 0.131 -.5768086 4.39499
_Iyear_2005 | .1398601 1.230971 0.11 0.910 -2.299884 2.579604
_Iyear_2006 | -.2337662 1.210653 -0.19 0.847 -2.633241 2.165709
_Iyear_2007 | .5757576 1.254258 0.46 0.647 -1.910142 3.061657
_Iyear_2008 | 2.832168 1.230971 2.30 0.023 .392424 5.271912
_Iyear_2009 | 3.075758 1.524975 2.02 0.046 .0533077 6.098207
_cons | 6.090909 .9059699 6.72 0.000 4.295306 7.886512


What do these results suggest? The column identified with "Coef" is the number of additional penalties per game (on average) incurred in the various years above and beyond that incurred on average in the 2000 season. In 2000 (the year associated with the _cons) UGA average 6 penalties per game. In 2001 and 2003 there was a slight (but not statistically significant) increase in penalties per game: just around 2 more per game on average.

However, starting in 2008 and continuing in 2009 there were approximately 3 more penalties per game against UGA. These results are statistically significant and robust, suggesting that something happened after the 2007 season.

Of course, the skeptic would suggest that there are plenty of reasons for this to be the case. Perhaps the coaching and discipline started to slip, perhaps the quality of the opponents changed, perhaps the games were tighter, etc., I am a skeptical empiricist as well so I decided to delve a little deeper.

{aside}
I note that this analysis is preliminary and somewhat naive. I have not identified what type of penalties are being called and when, I have not identified who was on the officiating crew for the game, I have not identified who was on the opponent's team and what their style of play and penalty history was leading up to the game. There is probably a lot more that could be done on this, and I might try do so some of the work, but I have to get ready to teach my graduate econometrics class.
{\aside}

The next step is to create a set of variables that try to minimally describe the conditions under which UGA was playing (and the referees were officiating) to see if there are any issues that would explain the increase in penalties per game in 2008 and 2009.

I defined a series of variables:

  • POSTFLORIDA: A dummy variable that takes a value of one after the 2007 UGA-UF game
  • DIAA: A dummy variable that takes a value of one if UGA is playing a Division IAA opponent;
  • SEC: A dummy variable that takes a value of one if UGA is playing an SEC opponent;
  • RIVAL: A dummy variable that takes a value of one if UGA is playing a rival, which I define as: Georgia Tech, Florida, Tennessee, Auburn, Clemson;
  • BOWL: A dummy variable that takes a value of one if UGA is playing in a bowl game;
  • GAPCTPTS: The percentage of the end-of-game points scored by UGA (value of 0.5 indicates that UGA won).

    {aside}
    I also have information on the attendance to the game, the date of the game, etc. It turns out that these variables didn't matter in the subsequent analysis.
    {\aside}

    These variables were used to explain per-game penalties with the following results:

    . prais penalties postflorida diaa sec rival bowl gapctpts,r

    Iteration 0: rho = 0.0000
    Iteration 1: rho = -0.0888
    Iteration 2: rho = -0.0923
    Iteration 3: rho = -0.0925
    Iteration 4: rho = -0.0925
    Iteration 5: rho = -0.0925

    Prais-Winsten AR(1) regression -- iterated estimates

    Linear regression Number of obs = 119
    F( 7, 112) = 135.60
    Prob > F = 0.0000
    R-squared = 0.1165
    Root MSE = 2.9983

    ------------------------------------------------------------------------------
    | Semi-robust
    penalties | Coef. Std. Err. t P>|t| [95% Conf. Interval]
    -------------+----------------------------------------------------------------
    postflorida | 1.429894 .6325056 2.26 0.026 .1766651 2.683123
    diaa | -3.524105 1.408917 -2.50 0.014 -6.315694 -.7325169
    sec | .0508761 .7586802 0.07 0.947 -1.452352 1.554104
    rival | .1654104 .5729116 0.29 0.773 -.9697405 1.300561
    bowl | .1898674 1.254325 0.15 0.880 -2.295417 2.675151
    gapctpts | 4.283429 1.625689 2.63 0.010 1.062335 7.504523
    _cons | 4.526006 1.318731 3.43 0.001 1.913111 7.138902
    -------------+----------------------------------------------------------------
    rho | -.0924945
    ------------------------------------------------------------------------------
    Durbin-Watson statistic (original) 2.170573
    Durbin-Watson statistic (transformed) 1.973597


    The results are robust to various estimators, so I went with the Prais-Winsten standard errors which controls for first-order auto-correlation which the DW statistic suggests might be in the data (albeit with a negative AR(1) coefficient suggesting that the penalties being assessed against UGA follows an oscillating process).

    The results suggest that controlling for type of opponent and the status of the game explains about half of the increase in the post-Florida celebration rate of penalties incurred by UGA as the parameter on POSTFLORIDA falls by about half of what it was for the 2008 and 2009 seasons.

    The other results suggest that Georgia has 3.5 penalties fewer against Division IAA opponents (smaller, less qualified opponents do not generate as many "mistakes"?), there is no discernible change in the number of penalties if playing an SEC team, Rival, or in a Bowl game. If UGA scores all the points in the game they obtain 4 more penalties per game but if the game is close, so that UGA scores just over or under 50% of all the points, UGA incurs about 2 more penalties per game, on average.

    When using the other measures as dependent variables the results are not statistically significant.

    Looking at the points scored by UGA and its opponents over the sample period:

    . xi:reg ugascore i.year
    i.year _Iyear_2000-2009 (naturally coded; _Iyear_2000 omitted)

    Source | SS df MS Number of obs = 119
    -------------+------------------------------ F( 9, 109) = 0.56
    Model | 819.673503 9 91.0748337 Prob > F = 0.8241
    Residual | 17612.024 109 161.578202 R-squared = 0.0445
    -------------+------------------------------ Adj R-squared = -0.0344
    Total | 18431.6975 118 156.200826 Root MSE = 12.711

    ------------------------------------------------------------------------------
    ugascore | Coef. Std. Err. t P>|t| [95% Conf. Interval]
    -------------+----------------------------------------------------------------
    _Iyear_2001 | 1.909091 5.420134 0.35 0.725 -8.833439 12.65162
    _Iyear_2002 | 5.888112 5.207497 1.13 0.261 -4.432977 16.2092
    _Iyear_2003 | -.7987013 5.121545 -0.16 0.876 -10.94944 9.352035
    _Iyear_2004 | 2.022727 5.306013 0.38 0.704 -8.493619 12.53907
    _Iyear_2005 | 1.965035 5.207497 0.38 0.707 -8.356054 12.28612
    _Iyear_2006 | -.8701299 5.121545 -0.17 0.865 -11.02087 9.280607
    _Iyear_2007 | 5.189394 5.306013 0.98 0.330 -5.326952 15.70574
    _Iyear_2008 | 6.041958 5.207497 1.16 0.248 -4.279131 16.36305
    _Iyear_2009 | -.0606061 6.45125 -0.01 0.993 -12.84677 12.72556
    _cons | 26.72727 3.832614 6.97 0.000 19.13116 34.32339
    ------------------------------------------------------------------------------

    . xi:reg oppscore i.year
    i.year _Iyear_2000-2009 (naturally coded; _Iyear_2000 omitted)

    Source | SS df MS Number of obs = 119
    -------------+------------------------------ F( 9, 109) = 1.59
    Model | 1459.27826 9 162.142029 Prob > F = 0.1275
    Residual | 11126.9402 109 102.08202 R-squared = 0.1159
    -------------+------------------------------ Adj R-squared = 0.0429
    Total | 12586.2185 118 106.662869 Root MSE = 10.104

    ------------------------------------------------------------------------------
    oppscore | Coef. Std. Err. t P>|t| [95% Conf. Interval]
    -------------+----------------------------------------------------------------
    _Iyear_2001 | .9090909 4.308174 0.21 0.833 -7.629571 9.447753
    _Iyear_2002 | -2.692308 4.13916 -0.65 0.517 -10.89599 5.511373
    _Iyear_2003 | -4.5 4.070842 -1.11 0.271 -12.56828 3.568277
    _Iyear_2004 | -1 4.217466 -0.24 0.813 -9.35888 7.35888
    _Iyear_2005 | -2.923077 4.13916 -0.71 0.482 -11.12676 5.280604
    _Iyear_2006 | 1.071429 4.070842 0.26 0.793 -6.996848 9.139706
    _Iyear_2007 | 3 4.217466 0.71 0.478 -5.35888 11.35888
    _Iyear_2008 | 6.384615 4.13916 1.54 0.126 -1.819065 14.5883
    _Iyear_2009 | 7.166667 5.127753 1.40 0.165 -2.996374 17.32971
    _cons | 18 3.046339 5.91 0.000 11.96225 24.03775

    There is not much here. The upper panel suggests that the average points scored by UGA over the sample period was 27 points per game but with no discernible change in average scoring year to year. UGA opponents scored an average of 18 points per game with a similar lack of discernible change in average scoring from year to year.

    This suggests that the conspiracy goes to penalties but does not materially effect the scoring of UGA or its opponents. If the referees are engaged in a cabal they would not want to draw attention to themselves by changing the average points scored/allowed. On the other hand, if the referees ARE NOT engaged in a cabal then there would be no change in the average points scored/allowed. On the other hand if the increased number of penalties are attributed to mistakes or small issues then they might not have a big impact on the scoring of the two teams - which would be why the LSU and perhaps the Ok. State outcomes were so obviously outrages to UGA fans. In the past, the increase in penalties hasn't seemed to cost UGA in terms of average scoring on either side of the ball.

    Finally I looked at how penalties influenced the odds that UGA would win a particular game. I reduced the model by a few of the variables used before because they were perfect predictors, etc. Here is what I found:


    probit gawin penalties fumbles sec rival flpenalties

    Iteration 0: log likelihood = -63.723551
    Iteration 1: log likelihood = -50.628893
    Iteration 2: log likelihood = -49.687793
    Iteration 3: log likelihood = -49.658957
    Iteration 4: log likelihood = -49.65892

    Probit regression Number of obs = 119
    LR chi2(5) = 28.13
    Prob > chi2 = 0.0000
    Log likelihood = -49.65892 Pseudo R2 = 0.2207

    ------------------------------------------------------------------------------
    gawin | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    -------------+----------------------------------------------------------------
    penalties | .176218 .0619769 2.84 0.004 .0547455 .2976905
    fumbles | -.2502459 .1420188 -1.76 0.078 -.5285975 .0281058
    sec | -.9432742 .3609628 -2.61 0.009 -1.650748 -.2358002
    rival | -1.070402 .3042725 -3.52 0.000 -1.666765 -.4740385
    flpenalties | -.0898959 .046037 -1.95 0.051 -.1801267 .0003349
    _cons | 1.218159 .4913581 2.48 0.013 .2551144 2.181203
    ------------------------------------------------------------------------------

    . mfx compute

    Marginal effects after probit
    y = Pr(gawin) (predict)
    = .84125799
    ------------------------------------------------------------------------------
    variable | dy/dx Std. Err. z P>|z| [ 95% C.I. ] X
    ---------+--------------------------------------------------------------------
    penaltiess | .0426549 .01366 3.12 0.002 .01588 .06943 7.36975
    fumbles | -.0605739 .03351 -1.81 0.071 -.126245 .005097 1.61345
    sec* | -.1971101 .0623 -3.16 0.002 -.319218 -.075002 .655462
    rival* | -.3032896 .09203 -3.30 0.001 -.483659 -.12292 .319328
    flpenaties | -.02176 .01063 -2.05 0.041 -.0426 -.00092 1.70588
    ------------------------------------------------------------------------------
    (*) dy/dx is for discrete change of dummy variable from 0 to 1

    The bottom panel reports the marginal impact of certain variables on the probability that UGA wins a game during the sample period. For example, for every penalty above the average of 7 over the sample period, UGA gained a 4% increase in the odds of winning. However, for every fumble above the average of 1.6 UGA's odds of winning fell by 6%. Everything else equal an SEC team lowers UGA's odds of winning by about 20% (SEC opponents are that much better), and rival games lower UGA's odds of winning by about 30% (which might be why they are rivals?). The last row shows that penalties incurred after the 2007 Florida game are reducing the odds that UGA will win.

    Whereas before the 2007 FL event UGA penalties helped the team win (perhaps by being smart defensive penalties or intimidation penalties that let the offense or the defense perform better), after the 2007 FL game this is less the case. In fact, the benefit of UGA penalties in terms of the odds of winning have fallen by almost 50%.

    Thus while UGA fans might recognize more penalties, which seems to be supported by the data, it does not seem that the referees are materially altering the outcomes of the games after the 2007 UF game. However, it seems that the penalties that are being called against UGA are subtly reducing the odds that we will win.

    What is causing this reduction? Is it dumber penalties? Is it smarter opponents? Is it referee bias/mistakes? What I have to do next is figure out how to discern between the three.

    Labels: ,

    Comments:
    How was there a 62 yard penalty in college?
     
    Good question. It could be a typo in the NCAA data - I just lifted the data from them.

    In 2001 was pass interference enforced at the point of the foul?
     
    Hi... Looking ways to market your blog? try this: http://bit.ly/instantvisitors
     
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