Computerizing Division 3 Tennis Rankings John Goldis Scientific Computing Spring 2003

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Computerizing Division 3Tennis RankingsJohn
Goldis Scientific ComputingSpring 2003
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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

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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

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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?

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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

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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 teams best wins.
  Thus all teams essentially play the same number
  of matches

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Modeling Problems

• There are 30 ranked teams each of which plays
  about 20-30 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

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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

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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

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Conclusion

• The final rankings can be seen at
  www.mountainace.com/tennis/final.html
• 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