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PredictingtheFinalScoretotheAnnualFloridavs
1.
Predicting the Final Score to the Annual Florida vs. Georgia Game Researchers: Kyle Sander and Sabrina Gayle University of North Florida ECO 3411 MW 4:30
2.
Introduction: Who is going to win the big game today? A statement said by countless college football fans around the country every Saturday. Many people believe that they can predict the outcome of any given game, and usually everybody at least throws out a guess of how badly their team is going to defeat their opponent. These overconfident, underconfident, and sometimes outlandish future telling claims are in no short supply when one of the biggest rivalry games in college football, the Florida Gators versus the Georgia Bulldogs, is on the horizon. Nicknamed “the World’s Largest Cocktail Party”, this contest of Southeastern college football heavyweights takes place annually during the last weekend of October. The event has consistently been held at a neutral sight in Everbank Field, home of the NFL’s Jaguars of Jacksonville FL. While predictions may be coming from every direction this paper is attempting to formulate a statistical model that will help predict the score of the next game with some accuracy and mathematical backing. Motivated by a previously created prediction model of the total points the Florida Gators would score on any given Bulldog game day, provided certain historical data, this new model will address the other side of the coin. How many points will the Georgia Bulldogs score on any given Gator gameday, given its own needed data requirements, and ultimately combining the two models and forming a third model with an estimation output of total combined points to be scored. The goal of these models are to enable the user to confidently predict the score of the annual Florida Georgia game, and provide a educated approximation of the combined total points. Review of Literature: Model #1: Predicting How Many Points the Florida Gators Will Score When They Play the Georgia Bulldogs: Following is the final regression model for predicting how many points the University of Florida Gators would score standing opposite the University of Georgia Bulldogs given independent variables; X1: Time variable: 19462007, X3: Florida number of points in last year’s game, X5: Florida’s Wins/Total games played before the game with Georgia, X6: Florida’s average points per game before game with Georgia, X8: Florida’s Points/Opponent Points, games before the game with Georgia, X9: Dummy variable equal to 1 if Florida won the game previous to the Georgia game, X10: Florida’s number of Wins/Total number of games in previous season, X11: Florida’s position in ranking the week before to game with Georgia (AP Poll), and X13: Difference of Florida and Georgia’s ranking (X12X11). One previous Florida Gator coach and two previous Georgia Bulldog coaches were added to the model, however as they no longer coach at their respective Universities, no effect is felt on the predicted output.
3.
The model is linear and predicted a final scoring total of 24.70621 points, which can be reasonably rounded down to 24, for the 2015 Florida Gators as they geared up to play the Georgia Bulldogs. With alpha set at .05, the 95% confidence interval is between 13.23777 and 36.17464. The Florida Gator football team actually scored 27 points when they played the Georgia Bulldogs on Oct.31 of this year(2015), lending support to the success of this prediction model. With the prediction output provided by this first model being within such close proximity of the actual points scored by the Florida Gators against Georgia has sparked curiosity into further investigating predictions models, more specifically creating a more comprehensive process of predicting the outcome of the game to be played next year by molding a second model with the anticipated function of predicting Georgia’s score at the end of the competition. Finally a third model will be created from a mixture of the Florida and Georgia point models to reliably predict the total amount of points to be scored by the two teams additively.
4.
Model #2: Model Predicting How Many Points the Georgia Bulldogs Will Score When Playing the Florida Gators: Data Description: Beneath is a listing, starting with the dependent variable, followed by the 23 independent variables originally considered for the second model, designed with the function of predicting the University of Georgia Bulldogs final score, standing opposite the Florida Gators. Y: Georgia number of points in the game that year (model 1: Florida number of points in the game that year) X1: Time variable: 19462007 X2: Dummy variable equal to 1 if Florida won the game the previous year X3: Georgia number of points in last year’s game X4: Florida number of points in the game that year (model 1: Georgia number of points in the game that year) X5: Florida’s Wins/Total games played before the game with Georgia X6: Florida’s average points per game before game with Georgia X7: Average points per game for teams playing against Florida before game with Georgia X8: Florida’s Points/Opponent Points, games before the game with Georgia X9: Dummy variable equal to 1 if Florida won the game previous to the Georgia game X10: Florida’s number of Wins/Total number of games in previous season X11: Florida’s position in ranking the week before to game with Georgia (AP Poll) X12: Georgia’s position in ranking the week before to game with Florida (AP Poll) X13: Difference of Florida and Georgia’s ranking (X12X11) X14: Georgia’s Wins/Total number of games before the game with Florida X15: Georgia’s Win/Total number of games previous season X16: Dummy variable equal to 1 if Georgia won the game previous to the Florida game X17: Dummy variable equal to 1 if Florida went to a Bowl, or won a Championship (SEC or National) that year
5.
X18: Dummy variable equal to 1 if Georgia went to a Bowl, or won a Championship (SEC or National) that year X19: Maximum temperature the day of the game X20: Minimum temperature the day of the game X21: Average temperature the day of the game X22: Rain precipitation the day of the game X23: Average wind speed during the day of the game Determining Significance: In choosing what independent variables should be used in morphing this model a decision rule was created. Any X variable that had a correlation coefficient equal to or greater than .20, after a correlation coefficient test provided by statistical software had run, would be included in the continuing data set. The following chart is the output of the correlation command when entered into Stata Statistical Software. When reflecting on the information provided by the preceding chart, and comparing each independent variable's correlation coefficient to the decision rule of 0.20, variables that have
6.
been deemed significant and will be utilized in our model as we continue forward include; x1, x4, x7, x8, x12, x13, x14, x15, x16, and x17. Explanation of Chosen Independent Variables: x1: Time Variable (19462007):positive correlation 0.2052: As time moved forward and the game of football matured, superior coaching tactics and more powerful athletes have created an atmosphere where average scores have been increasing over the decades, for which the Florida Georgia game has contributed. x4: Florida Points in game that year(derived from the Florida Gator point estimation model): negative correlation 0.2307: As an opposing team continues to score, or as Florida’s football team continues to score on Georgia’s team as applied to this model, feelings of defeat can start setting in, deflating a team’s spirit and drive to compete. This has the potential of being a doubleedge sword as the opposing team, sensing the thrill of victory and having an elevated level of determination, will continue pushing for more points except now against a team more like conquered foes than intense competitors, making the task far easier. x7: Average points per game for teams playing against florida before game with Georgia: positive correlation 0.4157: Logically the higher an average amount of points scored against a team by its competition the less capable that team's defense would appear to be. Removing outside possibilities such as a team plagued with injuries only to have their MVP’s return for this competition or an extreme outlier in the data skewing it to reflect a higher average than could be reasonably justified, when prior opponents have a high points per game average against a particular team, a reasonable conclusion can be drawn that the chances of future opponents scoring a hefty amount of points is more probable. Simply, if Florida is giving up large amounts of points to its opponents every week then they are not very good competitively speaking and will more than likely give up a large amount of points to Georgia’s team as well. x8: Florida’s points/Opponents points, games before the games with Georgia: negative correlation 0.2620: The greater amount of points the Florida football team scores divided by the amount of points their opponents score against them provides a ratio variable that helps reflect the overall team's skill and capabilities to outscore opposing competition. The higher the ratio, which can be increased by scoring more points and driving the numerator up or allowing less adverse points to be scored compressing the denominator down all other factors held constant, is a sign of a team that wins games. The higher the ratio given by this division of Florida’s points scored and allowed, the better and more rounded team the Georgia Bulldogs are most likely facing. x12: Georgia’s position in rankings the week before the game with Florida (AP Poll): negative correlation 0.3768: One would think that being ranked higher than your opponent the week before a rivalry game would provide that team with an advantage, however this has been proven untrue in the case of the Georgia Bulldogs.In a rivalry football game as big as Florida
7.
versus Georgia where the two teams have played each other countless times, the idea of one team being favored and thought of as better by a national ranking system such as the AP Poll can set a fire in the soul of the underdog and create an unquenchable yearning to prove everybody wrong. With a game packed full of pride and emotion, what might be thought of as an advantage in a higher AP Poll ranking can, and usually does, make Florida a hungrier and more dangerous opponent. x13: Difference of Florida and Georgia’s ranking (X12X11): negative correlation 0.3172: When the difference between Florida and Georgia’s rankings begin growing further apart and this predictant variables value increases, it is logical to assume that one team is performing better than the other that particular year. This is causing the better performing team to move higher in the rankings and adversely the lesser performing team to drop. Over the history of both the Florida and Georgia football programs, Florida has traditionally been the higher ranked team. This then explains Georgia’s negative correlation between how many points they score against Florida as this independent variable rises. If this variable is higher than usual then more times than not Florida is the higher ranked and better performing team that Georgia will probably have a difficult time acquiring points against. x14: Georgia’s Wins/Total number of games before the game with Florida: positive correlation 0.3837: The more wins a team has, and the longer that winning streak continues the closer this ratio variable will move towards one(1). A ratio that reveals more as times continues to move forward and games continue to be played. As each week's results become incorporated into the data set and applied to this variable’s formula, the more reliable the representation from ratio will become. The Florida versus Georgia game is held on the same weekend every year, the last weekend of October, which allows the metric time during the early months of the season to acquire data through the Georgia Bulldogs prior contest schedule. Adding to its appeal, the average number of games played each season preceding the Florida Georgia matchup is equivalent, providing consistent time parameters for more reliable data comparison from one year to the next. x15: Georgia’s Win/Total number of games previous season: positive correlation 0.2143: Though this ratio is often used to show the success of a program over multiple seasons similar to that which the University of Florida and the University of Georgia football programs have enjoyed. However, this does not mean that this predictor variable does not provide useful information for creating an estimation model for a game less than a week away. When a team is very dominant it is most often because they have distinct advantage whether it be superior coaching or top notch athletes. What is nice about both of these advantages is that they carry over year to year, and attract new top of the line talent. The higher win percentage Georgia has at the end of its season, the more talent will gravitate towards their program and provide more advantages for their following season. X16: Dummy variable equal to 1 if Georgia won the game previous to the Florida game: positive correlation 0.2336: With a win previous to a rival game, a confident winning attitude will often be felt dwelling among that victorious team. When the Georgia Bulldog football team has a previous weeks victory under their belt when entering into sporting battle with the Florida Gators
8.
an extra emotional lift, in combination with a proper winning mentality, will stimulate and provide a positive driver of effort often translating into extra point accumulation on the scoreboard. X17: Dummy variable equal to 1 if Florida went to a Bowl, or won a Championship (SEC or National) that year: positive correlation 0.3761: This independent variable appears to be confusing at first glance. One could wonder why this predictor variable is positively correlated to the Georgia Bulldog team when it was the Florida Gators who either went to a bowl game or won a championship, and would lead one to the perception that Florida had a better team the season before and as a result should have more talent and stronger coaching tactics overflowing to the current season's campaign. It can become even more bewildering when one considers that independent variable x18, the dummy variable equal to one if Georgia went to a bowl, or won a championship was not found to have a high enough correlation to the dependent variable to be included in this prediction model formation. The key to understanding the correlation between this predictor variable and the number of points that the Georgia football team is going to score is going back and looking at the original raw data. Georgia, without fail, has consecutively attended either a bowl or championship game for the past 22 years. In that same amount of time Florida has missed only five years where they did not match Georgia in attending of one of these prestiges end of the year competitions. In the 1960’s, 70’s, 80’s neither team made it to an impressive number of bowl or championship games First Linear Regression Results for Model Predicting How Many Points the Georgia Bulldogs Will Score When Playing the Florida Gators: With understanding of the independent variables to be used in the regression model, the first regression results are displayed below.
9.
Adding a New Independent Variable: Longtime Georgia Head Coach Richt (2001present): Unlike the Florida Gators who currently have a first year coach in Jim McElwain, the Bulldogs have had the same man at the helm of the team for almost 15 years. Mark Richt has a long coaching history stooped in Georgia tradition. The effects that one coach can have on a program, especially when one has been present for as long as Coach Richt, it is appropriate to create a dummy variable representing the years he has spent coaching the Bulldogs to discover exactly what kind of effect he has had. Null and Alternative Hypothesis: H0: Coach Richt does not add significance to the prediction model as an independent variable. H1: Coach Richt does add significance to the prediction model as an independent variable. Ftest = {[SSE(reduced) SSE(full)]/1} / [SSE(full) /(np1)] Ftest = [(5355.230095184.01082) / 1] / (5184.01082 / 57) Ftest = (171.21927) / (90.94755825) Ftest = 1.882615359
10.
Ftest Critical Value = 4 Pvalue of 0.175 > alpha .05 We do not reject the null hypothesis in saying that Mark Richt is not statistically significant as an independent variable in our model. However, because he is the current coach and a true staple in the Georgia football program, and perhaps just for fun, Mark Richt will remain in the model. Compare linear model with log linear model: We want to make sure that the functional form of the model is the most appropriate for displaying the most comprehensive results. To accomplish this objective a comparison should be made between the linear model and the log linear model. Variables that do not contain many negative or zero values were converted to logarithm form, followed by the creation of a new regression model with these generated logarithm variables taking the place of their original counterparts. Hypothesis: H0: Linear Model: Y is a linear function of the regressors X1, X4, X7, X8, X12,X13, X14, X15, X16, X17, and CoachRicht. H1: LogLinear Model: lnY is a linear function of logs of regressors lnX1, lnX4, lnX7, lnX8, lnX12, lnX14 and lnX15. Z1 was generated and a regression was ran using the linear model and including Z1. Z1=ln(yhat)[predicted(lnyhat)]
11.
We then generated Z2 and ran a loglinear regression model including Z2. According to the MWD test, the log linear model is a better fit for the data because; Z1 in the linear model is significant and Z2 in the log linear model is not. Therefore we reject H0, and accept H1: LogLinear Model: lnY is a linear function of logs of regressors lnX 1, lnX4, lnX7, lnX8, lnX12, lnX14 and lnX15.
12.
Note: Seven observations were lost from the data set for they were not able to be converted into logarithmic form; four observations were lost from Y and three observations were lost from X4. Checking the model for heteroscedasticity: Now that it has been determined to use the loglinear model, we want to make sure that there is no heteroscedasticity. Hypothesis: H0: The variance of the residuals is homogenous. H1: The variance of the residuals is not homogeneous. . rvfplot, yline(0) The above graph presents a good visual representation of the homogeneous distribution of the residuals and their distance from the fitted values. This visual test tells us that we do not have heteroscedasticity affecting our model. A BuschPagan/Godfrey test was also ran to confirm these results, however for the sake of saving room the results were left out.
13.
Check for multicollinearity: Finally the model must be checked for multicollinearity by performing a VIF (variance inflation factor test). Following are the test results. When studying the independent variables and their resulting VIF scores above, it is apparent that none have a VIF score greater than 10 (the rule of thumb score to signal possible multicollinearity), or even half of ten. Therefore it can be confidently concluded that this model does not have any multicollinearity affecting its predictor variables. Final Regression for Predicting How Many Points the Georgia Bulldogs Will Score When Playing the Florida Gators: Now the final regression that should provide the best possible predictive results can be displayed and are located on the following page.
14.
Final Regression Equation: lny=120.2667+16.13238lnX10.0839627lnX4+0.2003266lnX70.4081254lnX8+0.1083383lnX 120.0008402X13+0.4111577lnX140.1080464lnX15+0.283221X16+0.1924116X170.188235c oachricht+error Estimated Score: After plugging in values and predicted values for this year, the model predicts Georgia will score 21.31428 against the Florida Gators. Created 95% confidence interval: Mean of Variable Score: 21.31428 Standard Deviation of Variable Score: 5.976003148 Z score for a 95% Confidence: 1.96 95% Confidence Interval for Variable Score: 21.3148 (5.976003148)(1.96) = 9.601834 21.3148 + (5.976003148)(1.96) = 33.02777 95CI: (9.602 < 21.315 < 33.028)
15.
Model #3: Predicting the Total Points Scored By Both the Florida Gators and the Georgia Bulldogs When Playing one another: Data Description: The data set and variables within that were used for the first, model predicting Florida Gator score and the second predicting the Georgia Bulldog tally when these two programs collide every year. The dependent variable (Y), will now be the product of; the first models Y:Florida’s number of points in the game that year, and the Y of the second model: Georgia’s number of points in the game that year. Both of these now combined variables will be fully represented as model three’s Y, resulting in the dismissal of independent variable x4. Determining Significance: Sifting through the correlation stata results the decision rule of an independent variable requiring possession of a correlation coefficient greater than 0.25 to be included in the prediction model number three, the summed total of points scored by the Florida Gators and the Georgia Bulldogs. Independent variables that have surpassed the decision rule and will serve in model number three include; X1, X6, X7, X10, X11, and X16. Explanation of Chosen Independent Variables: X1:Time Variable(19462014): positive correlation 0.5231: With time the game of football has matured. Both players and coaches have become increasingly skilled which is reflected in the average points scored per game slowly climbing over the years.
16.
X6:Florida’s average points before the game with Georgia:positive correlation 0.4731: Florida’s average number of points in games prior to Georgia is a measure of Florida's offensive scoring power. Higher the average, more points Florida will put on the board accordingly. X7:Average points per game for teams playing against Florida before game with Georgia:positive correlation 0.4350: When averaging opponents points against Florida before the Georgia game, you can formulate an idea of Florida’s defense, and the difficulty Georgia will face in trying to score. The more points opposing teams put on the scoreboard, the more points Georgia predictably will. X10:Florida’s number of wins/total number of games in the previous season:positive correlation 0.3735: This ratio shows the Florida Gators previous season's success. If the Florida Gators had a winning season the year before they are retaining more talent in their coaches and players, along with attracting new talent in players and coaches who want to be associated with a winning program. X11:Florida’s position in the rankings (AP) the week before the game with Georgia:negative correlation 0.2526: When Florida has traditionally been ranked high it has always had a very difficult defense for opposing teams to score against. Since model three is predicting combined scores, a stellar defense will hinder the scoring ability for one team (in this case Georgia), lowering the combined score. X16:Dummy variable equal to one if Georgia won the game previous to Florida:positive correlation 0.3181: As in model two, if Georgia was victorious in their previous game they as a team will be bringing a great deal of confidence into the Florida contest, enhancing the number of points they will score. First Linear Regression:
17.
Compare linear model with log linear model: Hypothesis for MWD test: H0: Linear Model: Y is a linear function of the regressors X1, X6, X7, X10, X11,and X16. H1: LogLinear Model: lnY is a linear function of logs of regressors lnX1, lnX6, lnX7, lnX10, lnX11,and X16. The pvalue for Z1 is greater than alpha of .05 and not significant, therefore we do not reject the null hypothesis: H0: Linear Model: Y is a linear function of the regressors X1, X6, X7, X10, X11,and X16. According to the MWD test the linear model displays a better representation of our data. Checking the model for heteroscedasticity: Hypothesis: H0: The variance of the residuals is homogenous. H1: The variance of the residuals is not homogeneous. rvfplot, yline(0)
18.
A BuschPagan/Godfrey test was also ran to confirm these results, however for the sake of saving room the results were left out. Check for multicollinearity: All of the VIF values displayed in the chart are substantially less than 10, therefore we can confidently say the model does not have multicollinearity affecting it.
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Final Regression: Estimated Score: The model predicts that in the 2015 Florida versus Georgia game the combined score of both teams will be 48.1837, which can be rounded down to 48. 95% Confidence Interval: Mean of Variable Ymodel3: 39.0740529 Standard Deviation of Variable Ymodel3: 14.8198499 Z score for a 95% Confidence: 1.96 95% Confidence Interval for Variable Ymodel3: 39.0740529 (14.8198499)(1.96) = 10.027147096 39.0740529 + (14.8198499)(1.96)) = 68.120958704 Discussion and Conclusion: With these models anyone could provide three separate predictions on the annual Florida Georgia game. How many many points each team will score individually, thus being able to predict a winner and the margin of victory, along with how many combined points the two rivals will score together. It is worth noting that this is a prediction model, and because football scores generally have large variances from one game to the next and from year to year it is expected, and shown in the models by their large error terms and relatively low rsquares, that scores can be quite
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different than predicted. With that said models like these are used all the time by professionals in the business of sports forecasting and provide a great deal of insight when making educated estimations on competitive outcomes. As two individuals, and Florida Gator fans, who annually enjoy placing cordial bets with friends and family we hope to apply these models to real life next year and prosperously predict the outcome to this yearly clash of college football titans. Bibliography: 1. http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter2/statareg2.htm 2. www.georgiadogs.com 3.
www.gatorzone.com 4. http://www.intellicast.com/Local/History.aspx?location=USFL0228 5. http://onlinestatbook.com/2/estimation/mean.html
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