Football in the 90s

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Football in the 90s

• Curtis Olswold
• University of Iowa
• 22S Honors Project

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Sunday Afternoon Ritual

• A teams strategy, or tactical approach to a game
  is not unique.
• There are three dominant types of offense that
  exist in the NFL
• 1) Pass oriented
• 2) Run oriented
• 3) Balanced (Run and Pass oriented)

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(No Transcript)
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Purpose

• Construct a model to predict the points a team
  scores.
• Determine the probability that a team wins given
  certain factors.
• Investigate whether or not there exists a
  significant difference in the points a team
  scores by year and week.

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Why Am I Doing This?

• Determine what and how certain variables affect
  the amount of points a team scores
• How effective the variables are at determining
  the outcome of the game
• Win or Lose
• Rules change almost annually in the NFL to
  increase the amount of points a team scores, is
  it really working?

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The Variables

• Score
• Rushing Yards
• Passing Yards
• Completions
• Outcome

• Passing Attempts
• Rushing Attempts
• Interceptions
• Fumbles

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The Sample

• A random sample was drawn from the population of
  every regular season week from the 1990 season to
  the 1999 season.
• Individual team names were not identified
• From each week of each year, a sample of 5 teams
  were randomly chosen. This gave a sample of 850
  observations.

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Regression Model

• Score 4.92593
• 0.15441 (Rushing Attempts)
• 0.05858 (Rushing Yards)
• - 0.43734 (Passing Attempts)
• 0.20470 (Pass Completions)
• 0.08080 (Passing Yards)
• - 0.56074 (Intereceptions)
• - 1.09088 (Fumbles)

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Statistics of the Model

• R2 is the proportion of variability in Score that
  is explained by the model.
• Adjusted R2 is a measure of how efficient the
  predictor variables are Penalizes for
  overcomplicating the model.
• For this model
• R-Square 0.5020
• Adj R-Sq 0.4978
• This indicates the model explains over 50 of the
  variability in score and is not overly complex

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Significance of Predictors

Parameter Standard Variable DF
Estimate Error t Value Pr t
Intercept 1 4.92593 1.66448
2.96 0.0032 ratt 1 0.15441
0.04725 3.27 0.0011 ryds
1 0.05858 0.00785 7.47
0.06043 -7.24 0.20470 0.10039 2.04 0.0418
pyds 1 0.08080 0.00534
15.12 0.23748 -2.36 0.0184 fumble
1 -1.09088 0.25782 -4.23 11
Interpretation of Significance

• Every parameter is significantly different from
  zero. This means that each of the variables
  constructively adds to the precision of the
  model.
• The significance level is 0.05, meaning there is
  only a 5 chance of wrongly rejecting the
  hypothesis that the parameter is zero, or does
  not help in prediction.

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Interpretation of the Model

• For every rush attempt a team makes, the model
  predicts they will score 3/20 of a point.
• Every yard that a team gains on the ground
  suggests 3/50 of a point increase.
• When a rush attempt results in a fumble, the
  teams score will decrease by 1 and 9/100 of a
  point.

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Interpretation of the Model

• As a team throws the ball more, for each pass
  attempt, they will decrease their score by 11/25
  of a point.
• However, for every completion, they will increase
  their point total by 1/5 of a point.
• For every yard that is gained from the completion
  of a pass, a teams score increases by 2/25 of a
  point.
• If a pass attempt is intercepted, then their
  points scored will decrease by just over ½ of a
  point.

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Interpretation of the Model

• All of this can be summed up quite simply A
• rushing team is superior to a passing team.This
  is
• magnified if the team is able to gain substantial
• yardage per rush. Conversely, if a team passes
• many times, but completes a good percentage of
• them for good yardage, the effects of the pass
• attempt statistic are not as prevalent.

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Examples of Prediction

• Actual Predicted
• Score Value
• 19 22.4272
• 24 26.3893
• 13 5.8283
• 14 8.6153
• 11 14.5838
• 13 14.6197
• 20 24.8587
• 45 31.7385
• 20 15.1015

• 95 Confidence Level
• for the Mean
• 21.1840 23.6705
• 24.8230 27.9555
• 4.3773 7.2793
• 6.3462 10.8845
• 13.7462 15.4215
• 13.3944 15.8451
• 23.7494 25.9680
• 30.6684 32.8086
• 13.7705 16.4324

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Explanation of the Predictions

• The above are the predictions for 9 observations
  of the sample.
• Obviously, none are exact, which should not be
  expected.
• They are, however, relatively close to the actual
  values.

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Residual Error vs. Predicted
Test of First and Second Moment Specification DF
Chi-Square Pr ChiSq
35 37.52 0.3543
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Diagnostic Checking

• Residual, or Prediction Error
• 1) Constant Variance
• The plot shows that the variance is
  slightly shaped like a
• megaphone.
• The Cook and Weisberg1 formal test
  indicates that the
• null hypothesis of constant variance
  cannot be rejected.
• 2) Normality
• The regression coefficients do not rely
  upon residual
• normality assumption to be asymptotically
  normal2.

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Diagnostics Continued

• Variance
• Inflation
• 0
• 2.71820
• 2.49829
• 4.37648
• 5.67120
• 2.57837
• 1.18387
• 1.02425

• The Variance Inflation is a measure of the
  multicollinearity (linear relationship among 2 or
  more predictors) of the variables.
• None of these indicates severe multicollinearity.

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Example of a Run vs. Pass Oriented Offense

• If a team rushes the ball 35 times in a game
  gaining 150 yards with 1 fumble, passes 12 times
  for 115 yards and no interceptions, then on
  average it will score 23.5 points. If they throw
  an interception then the points scored reduces to
  22.9.
• Now suppose a team rushes 12 times for 75 yards
  without fumbling, passes 35 times, completing 19
  for 315 yards with 2 interceptions. They will
  average 24.085 points.

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Example of a Balanced Offense

• For a team that rushes the ball 25 times for 110
  yards with 1 fumble, passes 22 times and
  completing 12 for 145 yards and 2 interceptions
  will score on average 17.57 points per game.
• If they only throw one interception, then the
  points scored becomes 18.13.

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Statistical Comparison of Offenses

• Definitions
• 1) An offense is run oriented if its attempts
• are 1.5 times or greater than its pass
• attempts.
• 2) An offense is pass oriented if its pass
  attempts
• are 1.5 times or more than its rush
  attempts.
• 3) If a teams passing and rushing attempts are
• anywhere within 1.5 of each other, then
  it is
• balanced.

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The ANOVA Procedure Tukey's Studentized Range
(HSD) Test for score This test controls the Type
I experimentwise error rate.
Alpha
0.05 Error Degrees of
Freedom 847 Error
Mean Square 89.94897
Critical Value of Studentized Range
3.32034 Comparisons significant at the 0.05 level
indicated by .
Difference
orient Between Simultaneous 95
Comparison Means
Confidence Limits Run -
Bala 5.2083 2.8845 7.5320
Run - Pass 9.2933
6.7978 11.7888 Bala -
Pass 4.0850 2.3737 5.7963

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Interpretation of Comparisons

• There is a difference between the orientations of
  teams.
• In fact, they are all different from each other!
• Run oriented teams will actually score more
  points than both pass oriented and balanced
  offenses.
• Balanced offenses score more often than pass
  oriented teams.
• Why? Possibly due to the fact that more time is
  used by running the football than by passing.

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Determining the Probability of Winning the Game

• A win is given a value of 1. If a team ties or
  loses, they are given a value of 0.
• The only variables that are in a coachs
  immediate control are whether they run or pass
  the ball on offense.
• For this reason, only rushing and passing
  attempts will be used as independent variables.

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Distribution of Wins and Losses
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Frequencies of Game Outcomes

Cumulative Cumulative Outcome
Frequency Percent Frequency
Percent Loss 426
50.12 426 50.12 Tie
23 2.71
449 52.82 Win
401 47.18 850
100.00
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Method of Analysis

• Logistic Regression will be used to model the
  probability that a team wins.
• The form of the model is
• (eß0 ß1 rushes ß2 passes)
• (1 eß0 ß1 rushes ß2 passes)

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Estimation of Parameters
Analysis of Maximum Likelihood Estimates

Standard Parameter DF Estimate Error
Chi-Square Pr ChiSq Intercept 1
-2.1140 0.5403 15.3082
0.0119 112.5931 1 -0.0481 0.0107 20.1301
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Interpretation of the Model

• Both Rushing and Passing Attempts are significant
  factors in determining the probability of winning
  a game.
• The parameter estimates are in the form of the
  natural logarithm.
• Odds Ratios will give more insight into how the
  model is affected by rushing and passing.

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Fit of the Model
Hosmer and Lemeshow Goodness-of-Fit
Test Chi-Square DF
Pr ChiSq 9.2815 8
0.3191
This shows that there is not evidence for lack of
model fit.
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Odds Ratios

• Point 95 Wald
• Effect Estimate Confidence Limits
• ratt 1.134 1.108 1.161
• patt 0.953 0.933 0.973

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Interpretation of the Odds Ratios

• For a one attempt increase in Rushing Attempts,
  the odds in favor of winning are multiplied by
  1.134.
• For every one Pass Attempt, the odds in favor of
  winning are multiplied by 0.953.

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Conversion into Probabilities

• The equation for the probability of winning a
  game
• P(Win) 1 / ( 1 eß0 ß1 rushes ß2 passes)
• This yields
• P(Win) 1 / (1 e 2.114 .1259 rushes
  -.0481 passes)

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Some Examples

• For a team rushing 25 times and passing 25 times,
  the model yields a probability of .458 that they
  will win the game, or a 45.8 chance they will
  win.
• If a team rushes 35 times and passes only 15
  times, their probability of winning is .827, or
  nearly an 83 chance of victory.
• Now, say that team rushes only 15 times and
  passes 35 times, the probability changes to .129
  or a 13 chance of winning.

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What the Model Does Not Suggest

• Given the model predicts a higher success rate if
  a team rushes the ball, it may seem that a team
  should never pass. If this is done, the model
  gives a 98.5 chance of victory for 50 rushes and
  no passes.
• Obviously, if the other team knows you are never
  going to pass, you wont be able to move the ball
  10 yards on 3 plays very consistently. This
  shows how real world circumstances arent always
  modeled perfectly.

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Another Consideration

• The model also does not take into account middle
  of the game strategies. In other words, the
  farther you are behind, the more passes your team
  will attempt. Why? Less time is taken off of
  the game clock by passing.

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Does the Year and Week affect Points Scored?

• Year in and year out rules are changed to
  increase scoring.
• Rule changes include
• 2 point conversions allowed
• Defensive Line Encroachment Rules
• The 5-Yard Bump Rule on Receivers
• Etc.

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2 Way ANOVA for Points Scored, Year and Week
Sum
of Source DF Squares
Mean Square F Value Pr F Model
25 321.405283 12.856211
1.11 0.3186 Error 824
9509.705603 11.540905 C Total
849 9831.110886
R-Square Coeff Var Root MSE tscore
Mean 0.032693 38.39034
3.397191 8.849077 Source
DF Type III SS Mean Square F Value
Pr F year 9
133.2107197 14.8011911 1.28 0.2423
week 16 188.1945631
11.7621602 1.02 0.4333
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Interpretation of the 2 Way ANOVA

• The model indicates there is not sufficient
  evidence to conclude that Year and Week have no
  effect on how many points are scored.
• This means that for any given week in any given
  year, the points scored by a team is not
  affected, in this model.

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Conclusion

• All 3 statistical models point towards Rushing
• Attempts as being the important statistic in
• determining the points a team scores, and
  whether
• or not they win the game.
• Ball control is thus the essence to winning a
• football game. This is most readily seen by a
• team that rushes with consistency. A team is
• in better position to win if they can run and
• pass only occasionally.

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References
(1) Applied Linear Regression, 2nd Edition,
pp.135-136 Sanford Weisberg Publisher John
Wiley and Sons, 1985 (2) Applied Linear
Statistical Models, 4th Edition, pp.
54-55 Neter, Kutner, Nachtsteim,
Wasserman Publisher Irwin (Chicago) 1996 (3)
Professor Kate Cowles University of Iowa
Department of Statistics and Actuarial
Science (4) Data collected from
http//www.mrncaa.com