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§ This page is for tennis players who play doubles in groups with no fixed membership or court assignment. Herein we provide support for two aspects of managing the affairs of such groups.
The Scheduling Problem In doubles groups with no fixed membership, anyone can show up on a typical day and play, and usually after one set partners switch to a new combination according to a preferred scheme. Some groups use a winnersplaywinners and losersplaylosers approach. Others prefer a round robin method. The former is, of course, selfexplanatory and requires no further attention. The round robin method can leave a group leader in need of a fair schedule that treats all player equally. Or rather as many schedules as there are player and court combinations, since there can be many and a particular round robin schedule is specific to the number of players and available courts. This can be especially trying if the number of players isn't an exact multiple of four, and people must sit out and then substitute back in as play proceeds. Round robin schedulers can be found on Internet. Typically, each player is assigned a number, and the schedule determines who plays with and against other players and on which court for a certain round. The process repeats for the next round, and so on. As an example, in an eight player, two court schedule, there are seven rounds and each player plays with every other player once and against every other player twice. This schedule is fair and balanced for all. However, Internet schedulers are not necessarily wellbehaved when handling cases more complex than exact multiples of four players, i.e. those involving player substitution. Too often, when there are substitutes the substitution order is random and unbalanced, and is certain to be perceived as unfair. Consider what players want from a schedule. An ideal schedule would partner each player once and each opponent no more than twice, if possible. And when there are excess players, they should substitute in a fixed sequential order. If this last criterion is not observed, players will perceive the substitution process as unfair. What is needed, then, is a selection of schedules for many arrangements of players and courts, including cases that are not exact multiples of four players and that allow substitutes to rotate in sequentially. Because available automated schedulers often do not produce such round robins, many schedules conforming to the above criteria must be hand crafted, a difficult process, and as a result some may be a little less than perfect.
The schedules that follow give first priority to preserving a strict numerical order in the rotation sequence of substitutes. Second priority is partnering a player with another only once in a cycle if at all possible. The last priority is to limit each player to two appearances as opponent if possible. However, it has not always been possible to fulfill the third condition. The schedules provided below range from five players on one court to sixteen players on four courts, with many combinations in between. The schedules are provided in the form of 2sided PDFs, suitable for printing and sized minimaly for retaining in a tennis bag. They may be taped for durability.
Whose Turn Is It? Another problem arises when deciding whose turn it is to open a new can of balls. People being what they are, unless there is a set ball assignment schedule some players will remain silent and others will be stuck with more than their share of that expense. Groups with fixed membership and play schedules, for example groups who play contract time, can assign balls on a fair basis built around the contract schedule. But for irregular groups, where it is not known from one session to the next exactly who will show up, the problem is multifaceted, requiring tracking not only the obvious factor of how frequently, or infrequently, a player has provided balls but also the more subtle aspect of how many players are on court per session. The first factor, ball opening frequency, is straightforward  someone must track days played (D) and ball provided (B) by each player. Implicit in that data is the obligation that if someone hasn't contributed recently, i.e. if their average days played played per balls provided (D/B) is high, their turn should be coming up again soon. Actually, in order for for an assessment to predict whose turn it is at the next, yet to be played session, the term should be (D+1)/B To clarify the players on court situation, consider two examples. First, imagine a group of exactly four players (P) on a single court (C). A fair ball rotation for this group (P/C=4) would have each player supplying new balls every fourth day. Now add a fifth player (P/C=5). Four would play and one sit out each set; after which the substitute would rotate back in, and a different player would sit out  a repeating pattern. In this case, each player should supply new balls every fifth day. In the fixed examples above, players provided balls at a rate based on the number of players on court (P/C), with the individual who has gone the longest without opening (highest D/B value) being eligible next. (Note that lower values of P/C lead to more frequent ball openings, an inverse relationship.) However, for an open group the situation is not so simple. The number of players showing up on a particular day can vary, and the P/C metric will be specific to players present and courts in use on that day. Over time, an individual player's average P/C will become unique. This added complication means that to fully describe a player's situation we must a) track days played, balls contributed, and courts in use, b) compute a (D+1)/B value for each player, and c) compute the (weighted) average P/C for each player. With these latter two items of information, a metric can be devised to determine whose turn it is to next ante up!
Based on the above, the per player metric below determines who should provide balls next, with the highest value being next in line. Adj_{P/C} D/B = Avg_{WA} P/C * (D+1)/B ÷ P/C_{WA} Where: Adj _{P/C} D/B = A player's D/B metric adjusted for the weighted average of players per court (P/C_{WA}). (D+1)/B = A player's total days played divided by total balls provided. One day is added to make it predictive. P/C_{WA} = The player's weighted average of players per court for sessions played by that player. Avg_{WA} P/C = The weighted average of players per court across all active players. In the above formula, (D+1)/B is the sum of days played, plus one extra day to predict for the next session to be played, divided by the sum of balls provided by a player. The P/C_{WA} term adjusts for players on court; it is a per player weighted average, with weight porportional to the number of players participating per day. Since P/C has an inverse relationship to ball opening frequency the correct adjustment is to divide (D+1)/B by P/C_{WA}. Finally, multiplying the result by Avg_{WA} P/C , the weighted average of all active players (some players may be in inactive status due to injury, vacation, work status, etc.), sets the answer to units of days per balls opened and scales the metric to the order of nominal D/B. Keeping track of all this can be done with a spreadsheet labeled across the top with player names and down the side with play dates. Participation and ball supply checkoffs are marked in appropriate cells and summed in auxiliary columns, which are used to compute the statistics described above. 
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