AnAnalysis of Attendance for the Ohio Dominican University FootballTeam (ODUFT)

InstitutionAffiliation

AnAnalysis of Attendance for the Ohio Dominican University FootballTeam (ODUFT)

Thisreport provides an analysis of the football attendances for the OhioDominican University football team with an overriding objective toprovide insights concerning the determinants of match attendances andprediction of attendances. The report analyzes data for theattendances pertaining to the University Football Team for threeconsecutive seasons 2012, 2013 and 2014. Owing to the fact thatattendances pertaining to the football team are easily controllablewhen the matches are scheduled at home, this report relied on theattendances recorded when the team played at home. This is due to thefact that when the team plays away, there is a likelihood that theattendance will be influenced more by the attributes of the host teamrather than that of ODUFT. For this reason, the report sampled theten home games per season, which translates to 30 games for the threeseasons covered by the report. The 30 games therefore form the basisof this report. For purposes of analysis, the report relies ofregression analysis to obtain ordinary least squares (OLS) estimatesof the selected variables and statistical forecasting to enable theprediction of attendances. The explanatory variables adopted toexplain the variations in attendance (response variable) aretemperature, pass yards and percentage wins.

Thefirst analysis undertaken is the statistical forecasting in which aremote model is used tentatively to forecast the next attendance byhypothesizing that the next game attendance will equal the immediateprevious game attendance *ceterisparibas*.Further, a more sophisticated time series forecasting is completewith a 3-game moving average (3GMA) and a 3-game weighted movingaverage (3GWMA). Moreover, mean average deviation (MAD) is providedfor each MA. Table 1.0 below shows the remote model.

Figure1.0: The Remote Forecasting Model

Game |
Attendance |
Forecast Attendance |
MAD |

1 |
1178 |
||

2 |
10499 |
1178 |
9321 |

3 |
1927 |
10499 |
8572 |

4 |
1837 |
1927 |
90 |

5 |
843 |
1837 |
994 |

6 |
2317 |
843 |
1474 |

7 |
1630 |
2317 |
687 |

8 |
1152 |
1630 |
478 |

9 |
1073 |
1152 |
79 |

10 |
1047 |
1073 |
26 |

11 |
1000 |
1047 |
47 |

12 |
1987 |
1000 |
987 |

13 |
4335 |
1987 |
2348 |

14 |
2100 |
4335 |
2235 |

15 |
1834 |
2100 |
266 |

16 |
1548 |
1834 |
286 |

17 |
783 |
1548 |
765 |

18 |
4102 |
783 |
3319 |

19 |
1500 |
4102 |
2602 |

20 |
406 |
1500 |
1094 |

21 |
1066 |
406 |
660 |

22 |
15005 |
1066 |
13939 |

23 |
1763 |
15005 |
13242 |

24 |
1610 |
1763 |
153 |

25 |
696 |
1610 |
914 |

26 |
1267 |
696 |
571 |

27 |
1853 |
1267 |
586 |

28 |
1116 |
1853 |
737 |

29 |
1673 |
1116 |
557 |

30 |
518 |
1673 |
1155 |

31 |
518 |
||

Total |
2351.172 |

Therefore,the forecast attendance for game 31 i.e. first game of the 2015season is 518.

*Table2.0*:Moving Averages

Game |
Attendance |
3GMA |
3GWMA |
MA MAD |
WMA MAD |

1 |
1178 |
||||

2 |
10499 |
||||

3 |
1927 |
||||

4 |
1837 |
4534.667 |
4659.5 |
2697.667 |
2822.5 |

5 |
843 |
4754.333 |
3310.667 |
3911.333 |
2467.667 |

6 |
2317 |
1532.667 |
1356.667 |
784.33 |
960.333 |

7 |
1630 |
1665.667 |
1745.667 |
35.667 |
115.667 |

8 |
1152 |
1596.667 |
1727.833 |
444.667 |
575.833 |

9 |
1073 |
1699.667 |
1505.5 |
626.667 |
432.5 |

10 |
1047 |
1285 |
1192.167 |
230 |
145.167 |

11 |
1000 |
1090.667 |
1073.167 |
90.667 |
73.167 |

12 |
1987 |
1040 |
1027.833 |
947 |
959.167 |

13 |
4335 |
1344.667 |
1501.333 |
2990.333 |
2833.667 |

14 |
2100 |
2440.667 |
2996.5 |
340.667 |
896.5 |

15 |
1834 |
2807.333 |
2826.167 |
973.333 |
992.167 |

16 |
1548 |
2756.333 |
2339.5 |
1208 |
791.5 |

17 |
783 |
1827.333 |
1735.333 |
1044.333 |
952.333 |

18 |
4102 |
1388.333 |
1213.167 |
2713.667 |
2888.833 |

19 |
1500 |
2144.333 |
2570 |
644.333 |
1070 |

20 |
406 |
2128.333 |
2247.833 |
1722.333 |
1841.833 |

21 |
1066 |
2002.667 |
1386.667 |
936.667 |
320.667 |

22 |
15005 |
990.667 |
918.333 |
14014.333 |
14086.667 |

23 |
1763 |
5492.333 |
7925.5 |
3729.333 |
6162.5 |

24 |
1610 |
5944.667 |
6060.833 |
4334.667 |
4450.833 |

25 |
696 |
6126 |
3893.5 |
5430 |
3200.5 |

26 |
1267 |
1356.333 |
1178.5 |
89.333 |
88.5 |

27 |
1853 |
1191 |
1133.833 |
662 |
719.167 |

28 |
1116 |
1272 |
1464.833 |
156 |
348.833 |

29 |
1673 |
1412 |
1386.833 |
261 |
286.167 |

30 |
518 |
1547.333 |
1517.333 |
1029.333 |
999.333 |

31 |
1102.333 |
1002.667 |
|||

Total |
1927.691 |
1904.741 |

Therefore,the forecasted attendance for the 31^{st}game is 1103and 1003(after rounding off since these are people) for the 3GMA and 3GWMArespectively.

Theessence of the procedures undertaken above is to espouse the expectedcrowd in the forthcoming match. The analysis done here so far needsto be interpreted with caution since the outcomes are only validbased on attendance. This kind of projecting outcomes based on thepast records is known as time series forecasting and the techniquemakes a major assumption in predicting outcomes in that the past willrepeat, *CeterisParibus*.The remote model presented in table 1.0 is a very simplistic model,which forecasts the attendance of the next game based on theattendance in the preceding game. For instance, since game serializedas 1 had an attendance of 1178, the model predicts that game 2 willrecord an attendance of 1178 but this deviates from the actualattendance by 9321! The deviation is almost eight times more than thepredicted figure. This shows that the remote model is not a rigoroustechnique. The greater deviation could be attributable to otherfactors other than previous attendance such as the type of opponent,the trend in the attendance, temperature and other special variables.This calls for a more robust technique.

Thisis the reason that prompted the report to adopt the moving average(MA) technique whose results are presented in table 2.0. Thistechnique is more rigorous since it takes into account the trend inthe match attendances thereby smoothing for the effects of anyirregularities thereof. Given that the total number of games coveredby the survey numbered only 30, the report used a 3-game movingaverage. The implication of this is that the prediction of the nextgame becomes a function of the preceding three games. The idea wasthat the three game margins are enough to smoothen for the effects ofirregularities and expose any unusual phenomena that can influencethe attendance of the next game. The outcomes of advanced MAtechniques are always expected to be fairly accurate relative tothose of the remote model (Box et al, 2011: Montgomery et al, 2015).True to this, the method predicts that the attendance for the 31^{st}game will be 1103, which is more reasonable given the observed trend.Moreover, the MAD reduces considerably to 1927 from 2351.172 recordedusing the remote model. This signifies a considerable increase inpredictive accuracy.

However,to ensure rigor, there was need to adjust for the effect of time ininfluencing the outcomes of the next game as far as attendance isconcerned. In order to take care of this, the report adopted the useof weighted average technique that was similar to the moving averagetechnique only that it allocated weights to the preceding games. Theallocation of weights was structured in such a way that the mostrecent game got more weight and the magnitude of the weight decreasesgradually in depending on the chronology of games factored inforecasting the next game. In this report, the weights were 1, 2 and3 since a 3-game moving average had been adopted. As expected, theoutcomes of this technique are even more accurate predicting theattendance of the 31^{st}game to be 1003 with a MAD of 1904.741, which is much lower comparedto that of the 3GMA.

Theweighted moving average technique is thus more accurate of thetechniques used so far. However, as rigorous as it is, the model doesnot take into account other factors other than those related to timelike the temperature, percentage wins and other factors. For thisreason, it was necessary to develop a regression model to examine thesignificance of these factors in determining the volume of matchattendance. The model adopted was as shown below.

*Attendanceof next game = ʄ (temperature, pass yards, percentage wins, recordsfrom wins, OSU home, ODU home)*

Thedata relating to OSU home, ODU home and records from were entered asdummy variable. (See Appendix 1). The outcomes of the regressionmodel are summarized below.

*Figure3.0*:Summary Output

Interpretationof results and Implications

TheOLS coefficients are all significant (greater than zero). Thisimplies that all the factors examined provide significant informationabout the attendance of the next game.

Temperature:A unit increase in temperature, leads to a decreaseinmatch attendance by 19 people (18.7076 in the table) on averageholding pass yards, percentage wins and record, ODU home and OSU homeconstant.

Passyards:A unit increase in the pass yards of the opponent team leads to anincrease in match attendance by 2 people (1.023) on average, holdingtemperature, percentage wins and record, ODU home and OSU homeconstant.

Percentagewins:An increase in opponent wins by a percentage leads to a decrease inmatch attendance by 5558 on average, holding temperature, pass yardsand record, ODU home and OSU home constant.

Recordfor Wins:A record of a win in favor of ODU leads to an increase in matchattendance by 5540 on average, holding temperature, pass yards andrecord, ODU home and OSU home constant. This implies that when theteam records better performance, the attendance is likely to increaseby a great margin. This seems to be the major factor that influencesmatch attendance.

However,the R^{2}for the model is0.25implying that the factors covered in the model only explain 25% ofthe variations in match attendance. This shows that the model is anot a very good fit since only 25% of the variations in matchattendance are explained by temperature, pass yards, percentage winsand record, ODU home and OSU home constant at the 95% confidenceinterval. The F significance is 0.26 > 0.05 confirming that themodel is indeed not a very good one. To improve on this, it isnecessary to gather more data and include other significant factorslike festive seasons and ticket prices. Nevertheless, the model isgood enough to indicate the likely effects of the different factorscovered on match attendance. Errors inherent in data collection andencoding can at times impair the predictability of the model thoughit can hardly alter the bearing of such models (Kleinbaum et al,2013). This model can be used alongside the forecasting techniquesto determine factors influencing match attendance as well as forecastthe future attendance.

References

Box,G. E., Jenkins, G. M., & Reinsel, G. C. (2011). *Timeseries analysis: forecasting and control*(Vol. 734). John Wiley & Sons.

Kleinbaum,D., Kupper, L., Nizam, A., & Rosenberg, E. (2013). *Appliedregression analysis and other multivariable methods*.Cengage Learning.

Montgomery,D. C., Jennings, C. L., & Kulahci, M. (2015). *Introductionto time series analysis and forecasting*.John Wiley & Sons.

Appendix1: Data Entry (Note the dummy variables)