On Quantifying the Topsy-Turvyness of a College
Football Season: Understanding the TT factor
Autar Kaw
December 21, 2007
Football Season: Understanding the TT factor
Autar Kaw
December 21, 2007
| Understanding the TT factor Page 1 2 3 4 What is the TT factor? The TT factor is a simple way to measure the topsy-turvyness of the college football season. There are two factors: Week TT factor: It is a measure of the topsy-turvyness from week to week. Season TT factor: It is a measure of the topsy-turvyness of the season so far. How is the Week TT factor calculated? The method to find the Week TT Factor is based on comparing the AP poll rankings of schools from the current week to that of the previous week. The difference in the rankings of each school in the top 25 from the current week to the previous week is squared. All the squares of the differences in the rankings are added together. A square root of the resulting number is taken and multiplied by 4. The only reason why the number is multiplied by 4 is to let the TT factor have a better scale - similar to the quarterback ratings. How is the Season TT factor calculated? The Season TT factor is calculated after each week to gage how topsy-turvy the season has been so far. The Season TT factor is calculated using weighted averages of the Week TT factors. As the season progresses, the Week TT factors are given more weight in the calculation of the Season TT factor because toward the end of the season, an upset of a ranked team is more topsy-turvy than an upset in the beginning of the season when the strength of a ranked team is less established. The weight given to each Week TT factor in the Season TT factor formula is equal to 1+ 1/10 x Week number of the season. For example, the weight given to the Week TT factor of fourth week is 1+1/10x4=1.4. Some statisticians may question the reasoning behind the weighted average. For them the difference between a Season TT factor with and without weight is shown not to be significant as given in the table below. Why are the differences in rankings squared in the calculation of the TT factor? The reason for squaring the difference is because losses such as those of No. 5 Michigan to an unranked team should be weighed higher than a case of a No. 2 team losing to a No. 4 team. Also, the difference squared is always a positive number. How is the Week TT factor calculated if a team was unranked in the previous week? A team that was unranked in the previous week and gets ranked in the current week is assumed as being the No. 26 team in the previous week. A higher number is not used to avoid over-inflating the TT factor. What is the highest possible Week TT factor? The highest possible Week TT factor would be if all the ranked teams from the previous week dropped from the rankings. The highest possible Week TT factor is approximately 300 (actual value is 297.3214). What is the lowest possible Week TT factor? The lowest possible Week TT factor would be if all the rankings stayed unchanged from the previous week. Since in this case, the difference in ranking would be zero for all teams, the lowest possible Week TT factor is zero. What is the significance of TT factor of 91 or more? The average Week TT factor for 2002-2007 seasons is 68 and the standard deviation is 23. So, one standard deviation more than the average TT factor is 68+23=91. What is the significance of TT factor of 45 or less? The average Week TT factor for 2002-2007 seasons is 68 and the standard deviation is 23. So, one standard deviation less than the average TT factor is 68-23=45. Next: The TT factors for the 2007 college football season |
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