Computerizing Division 3 Tennis Rankings John Goldis Scientific Computing Spring 2003

Background Info ITA (Intercollegiate Tennis Association) has been thinking about computerizing division 3 rankings Currently the rankings are determined by a committee of coaches This is obviously problematic since coaches try to promote their teams

Division1 vs. Division3 In Division1(d1) there is a lot of national play. In Division3(d3) there is insufficient funding for teams to travel, so very little national play. In d1 the schedule is much longer than in d3 so that each ranked team plays every other ranked team. In d3 there are an equal number of teams total but due to a shorter season not all ranked teams play each other. These two issues create some problems

Objectives Can I create a system to computerize rankings? What kind of system would work best and most efficiently to compute these rankings? How will these rankings compare to the official rankings released by the ITA?

Problems For d1 a computerized system exists. It is easy to make such a system because a variable number of points can be given to a team for a victory and since every ranked team plays every other ranked team the number of points that a team has at the end of some time period can be used to re-rank the teams. In d3 this is a problem since not all teams play all other teams and there is more emphasis on regional play. Even then not all teams play all the teams in their region. Thus different teams could have a different number of points but be ranked equally. Due to this problem a model needs to be created to modify the d1 point system to account for different regions being of different size and to put more emphasis on regional play while still rewarding wins on the national level

Possible Modifications Use a similar point system as in d1 but give fewer points for wins on a national level. Create a constant to scale points of teams in regions that have few ranked teams. Create another constant to increment the points of teams in smaller regions. Count only some number of each team’s best wins. Thus all teams essentially play the same number of matches

Modeling Problems There are 30 ranked teams each of which plays about matches, which would take too long to enter into the database Since some regions only have one or two ranked teams so I simplified the problem by creating only two regions. I then put all the east ranked schools in one region and all the west ranked schools in the other

Observations/Results Since there has been no previous work in this area, most of my conclusions came from guess and check methods. After trying different combinations of modifications I determined that assigning less points for national play and introducing the two constants described in the previous slide gave the best results

The Point System For Inter-Region Play Win against a team ranked 1-5: 30 points Win against a team ranked 6-8: 25 points Win against a team ranked 9-12: 20 points Win against a team ranked 13-16: 15 points Win against a team ranked 17-20: 10 points Win against a team ranked 21-30: 5 points For National Play Win against a team ranked 1-5: 20 points Win against a team ranked 6-8: 12 points Win against a team ranked 9-12: 8 points Win against a team ranked 13-16: 6 points Win against a team ranked 17-20: 4 points Win against a team ranked 21-30: 2 points the constant dealing with the fewer ranked teams in different regions was determined to be 1.3 the constant dealing with regions having less teams was determined to be 20

Conclusion The final rankings can be seen at Based on the results for the time being it would be best to use my computerized rankings as an initial template that should be modified by a committee This is not an ideal solution but it expedites the ranking process which may allow for more frequent releases of them