CITTT CLUB PLAY SYSTEM JED YANG First Draft October 14, 2007 http://clubs.caltech.edu/~tabletennis/ccps.pdf Abstract. We claim that the quality of table tennis club play can be increased if players are grouped together by skill level and encouraged to switch partners. To that end, we introduce a system aimed at realizing this style of club play. We give a brief summary and describe the general logistics of a typical day, then we explain in more detail how each step of the system is to be accomplished. 1. Motivation Table tennis is a fine sport. Playing with people of drastically different levels could prove frustrating at times. This is evident in the rating system employed in the USATT tournaments. To encourage people playing with different partners of the same skill level, we shall adopt the following system. 2. Synopsis Players are divided into ordered partitions of size 4 by skill level. Each partition holds a round robin, which consists of 6 matches. The result of the round robin in each partition determines the relative ranking of the four players. The first and the fourth player will pair up and play the second and the third player in a doubles match. Combining the results from the singles and the doubles matches, a final ranking of the four players are determined. The first place of each partition (except the first partition) will advance and exchange ranking with the last place of the previous partition for the next club play. 3. Definitions The Coordinator is a nonempty set of people in charge of the CITTT Club Play System. The Coordinator is expected to keep the best interest of everyone else in mind. The Coordinator is allowed to participate as players. A game is a standard game up to 11 points. A match is a 1
CITTT CLUB PLAY SYSTEM 2 standard match where the players attempt to win 3 games first. If all the players agree, they may reduce a match to best 2 out of 3 instead of 3 out of 5 in the interest of time, physical fatigue, and the like. A round robin is a collection of matches where every player in the round robin plays one match against everyone else. With n people in a round robin, there will be ( ) n 2 = 1n(n 1) matches played. A partition is a 2 collection of (usually) 4 players. 4. Logistics: A Typical Day The CITTT Club Play System will be employed on Sundays from 16:00 to 18:00 in the Brown Gym. Players are expected to arrive between 16:00 and 16:15. Players shall check in with the Coordinator. Then players may warm up in any pairing they wish until 16:30. The Coordinator will produce the partition for the day (see Paritition Determination ) from those who have checked in according to the rankings from the previous week (see Grand Ranking ). At 16:30, each partition should commence round robin. If enough tables are present, each partition will be assinged two tables so two simulatenous matches can proceed. Otherwise, some partitions may have to share the third table, or use only one table for the singles matches. Each partition will be given a score sheet. The players are responsible in filling out the sheet including their names and scores of each game. It is important to record the points of each game because it is used to break ties. After all singles matches have been played, the ranking should be determined according to the Round Robin Ranking section by the players. If there is difficulty in resolving ties, ask the Coordinator for help. The first and the fourth player shall now pair up and play a doubles match against the second and the third player. Return the score sheet to the Coordinator before departure. If there are time remaining, players may play against anyone, including players of different partitions, until 18:00, when the club play period officially ends. 5. Partition Determination The Coordinator will use the grand ranking from the previous club play (see Grand Ranking ) to determine the partitions for a club play. The Coordinator shall list the players who have checked in today according to the order in the grand ranking. The first set of four players will be placed in the first partition, and the second set of four players will be in the second partition, and so on. The Coordinator reserves the right to shrink any partition in the interest of a more homogeneous distribution of the number of players in the partitions.
CITTT CLUB PLAY SYSTEM 3 6. Round Robin Ranking The round robin ranking is a ranking of the players in a partition calculated after the round robin is played. It is used to determine the pairing for the doubles match. The players are responsible in calculating the round robin ranking. However, if difficulty arises, seek help from the Coordinator. Mathematical Aside. Determining the ranking of the players in a round robin is a non-trivial task. In general, with n players, we may represent the result as a mathematical tournament, which is an orientation on the complete graph with n vertices. A tournament is strongly connected if for any two distinct vertices there is a directed path from one to the other. When such tournament is strongly connected, then the tournament is vertex-pancyclic, and in particular, Hamiltonian. A proof can be found in [1]. If you are interested in these combinatorics problems and the generalization to hypertournaments, see [3]. With four players, there are four possible results in a round robin. The number of matches won for the four players, listed descending in magnitude could be (i) 3, 2, 1, 0; (ii) 3, 1, 1, 1; (iii) 2, 2, 2, 0; or (iv) 2, 2, 1, 1. The ranking is clear in (i). For both (ii) and (iii), there is a 3-way tie in each. For (iv), there are two 2-way ties. To break a k-way tie, we consider the ( k 2) matches played amonst the k players, without regard to the other n k players, where n is the number of players. For each player in the k-way tie, we consider the sum of the number of games won within these ( k 2) matches. If a k -way tie remains (with 1 < k k), we consider only the ( k 2) matches played amonst those k players, and use the sum of the number of points. If a k -way tie remains (with 1 < k k ), a random number generator will be used to determine the ranking. An acceptable random number generator is the guess which hand holds the ball method used to determine who serves first. If there are less than four players in a round robin, the ranking is easier to calculate and should be a straightforward exercise in applying the principles described in the previous paragraph.
CITTT CLUB PLAY SYSTEM 4 7. Partition Ranking The partition ranking is a ranking of the players in a partition calculated after both the round robin and the doubles match is played. It is used to determine the final ranking for the purposes of trading players to form the partition for next week. The players are not responsible to calculate the partition ranking. For each partition, a player receives 2 points for winning a singles match, and 1 point for winning the doubles match. The maximum points a player can receive is therefore 7, and the minimum is 0. The sum of the points of the four players is therefore 14. The point value is used to determine the ranking within each partition. If there are ties, they are broken by referring to the round robin ranking of the individuals in the tie. 8. Grand Ranking: Player Exchange The Coordinator will maintain a grand ranking of players. The slots of the players in attendence will be used to update the ranking, while those not in attendence will be left in place. The players are filled into the list first by the ordering of the partitions then by the partition ranking within each partition. The first player of each partition (except the first partition) will advance and trade position with the last player of the previous partition. The Coordinator reserves the right to arbitrarily permute the grand ranking in the interest of maintaing a resonable grand ranking. 9. Late Arrival Players who arrive after 16:30 will be placed arbitrarily according to the following guideline: The player will be (i) added to a partition if there exists a partition needing an extra player and the skill levels are suitable; (ii) asked to temporarily play with the third player waiting for a match if there is a partition with only three players; (iii) asked to play with another late arrival player; or (iv) asked to wait. This is not to punish the late arrival player, but rather to keep the process running as smoothly as possible, while encouraging players to show up on time. To that end, in the case of (iv), if a partition has finished, we ask an odd number of players from the partition to voluntarily step down and let the late arrival player enjoy some table tennis. In general, the late arrival player will not be eligible in participating
CITTT CLUB PLAY SYSTEM 5 in the player exchange. However, at the discretion of the Coordinator, with the best interest of fairness in mind, the late arrival player may enter the player exchange. 10. Early Departure Players have the right to depart early due to physical fatigue or any other reason. The Coordinator will exercise best judgement when updating the grand ranking. 11. New Players When new players join the club for the first time, they are encouraged to attempt to find someone at the approximate level and warm up. The Coordinator will observe their levels of play and attempt to insert the new players appropriately into the grand ranking. This procedure will also be in effect the first time this CITTT Club Play System is employed. Please be considerate to the decisions of the Coordinator. If you feel you are placed in the wrong partition, you should be able to make your way up or down the ranking to the appropriate partition in a matter of weeks. 12. Concluding Remarks The CITTT Club Play System is newly proposed and may contain areas admiting improvement. Please be patient as we try to make the system better for everyone. In the mean time, please channel your suggestions to us by emailing tabletennis@clubs.caltech.edu. This document can be found on our club webpage [2]. References [1] J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications, Springer-Verlag, London (2001). [2] Jed Yang, CITTT Club Play System, manuscript, 2007, http://clubs.caltech.edu/~tabletennis/ccps.pdf. [3] Jed Yang, Vertex-pancyclicity of hypertournaments, manuscript, 2006, http://www.htam.org/surf/pancyclic.pdf.