<https://smashboards.com/threads/how-do-i-manage-time-for-a-round-robin-pool-toing.361341/>
<http://schema.org/articleBody>
"In the second half of this two-part article, I'll discuss how to manage time specifically with round-robin pools. This is a very popular starting format at Smash tournaments because of the seeding foundation it builds transitioning into a final bracket, the extra competitive playing time it provides to all players, and the creative control it offers to organizers (we'll talk more about the advantages and disadvantages of round robin pools in a future article dedicated to tournament formats). Round-robin pools are a staple of Smash tournaments, but time management of the format is often butchered.\n\nAs usual, think about some of the expected values for your event before proceeding. The answers to these questions will serve as the parameters for your time estimate.\n\nEntrants: How many entrants do I expect per pool?\nSetups: How many full setups do I expect to be available per pool?\nTime: How many minutes do I expect the average set to require?\n\nLet’s jump right into it. Due to the number of parameters involved with estimating time for round robin pools, I'll present the solution first and then explain it later.\n\nThe time required to run a round robin pool is:\nkt(n(n-1))/2s\n\nwhere \nk = efficiency factor\nt = average time per set\nn = number of players in the pool\ns = number of setups available in the pool\n\nFor those of you who are interested in how this formula is derived, see below for an explanation. For those of you who trust that the formula works and want to go straight to some examples, skip ahead.\n\n\nFormula Explanation\n\nn(n-1)/2 is an expression that represents the number of total sets that have to be played in a round robin given n players in the pool. Consider the classic handshake problem: if you're in a room with n people and everyone has to shake hands once with everyone else, how many handshakes occur overall? This is pretty much the exact same question as: if you're in a pool with n players and everyone has to play each other in one set, how many sets occur overall? Plenty of documentation exists on how this formula is derived, and you can read up on it [1][2][3] if you're curious.\n\nn(n-1)/2 is multiplied by the variable t, which represents the average time per set. We are essentially taking the number of total sets and multiplying it by the time per set to obtain an expected value for the time required overall, or the time required to play out every set in the pool one after the other.\n\ntn(n-1)/2 is multiplied again by the efficiency factor k, which represents the multiplier coefficient that accounts for downtime between sets. If the average set takes 10 minutes but players experience an average downtime of 5 minutes per set, then the efficiency factor k would be 1.5 to account for the extra time between sets. Well-run tournaments often achieve an efficiency factor close to 1, while poorly-run tournaments often have an efficiency factor that exceeds 2. Use your TOing experience to come up with a reliable empirical value for k to use at your tournaments.\n\nktn(n-1)/2 is then divided by the variable s, which represents the number of setups available in the pool. Since more setups means more sets can be played concurrently instead of one after the other, we can divide the overall expected time by s to account for the decrease in consecutive sets that have to be played until pool completion. Keep in mind there is an upper limit to s represented by s' = min(s,floor(n/2)) which accounts for the fact that after a certain point, additional setups do not help decrease time required (for example, 3+ setups for a pool with 4 players).\n\n\nThe Handshake Problem illustrated in grid format (left) and geometric format (right).\n\n\nExample #1\n\nYou're at a small Melee tourney with the standard ruleset and you see a round robin that contains 6 players in it, with 2 available setups to use for the pool.\n\nLet\nk = 1\nt = 10 minutes per set\nn = 6 players in the pool\ns = 2 setups available in the pool\n\nTime required to run this round robin pool:\n\n= kt(n(n-1))/2s\n= (1)(10 mins)(6(6-1) players) / (2(2 setups))\n= (1)(10)(6(6-1))/(2)(2)\n= 75 minutes\n= 1 hour 15 minutes\n\n A six-person round robin pool.\n\n\nExample #2\n\nYou're at a large Brawl tourney with the standard ruleset and you see a round robin that contains 8 players in it, with 2 available setups to use for the pool.\n\nLet\nk = 1.5\nt = 10 minutes per set\nn = 8 players in the pool\ns = 2 setups available in the pool\n\nTime required to run this round robin pool:\n\n= kt(n(n-1))/2s\n= (1.5)(10 mins)(8(8-1) players) / (2(2 setups))\n= (1.5)(10)(8(8-1))/(2)(2)\n= 210 minutes\n= 3 hours 30 minutes\n\n An eight-person round robin pool.\n\n\nExample #3\n\nYou're at a large Project M tourney with the standard ruleset and you see a round robin that contains 10 players in it, with 6 available setups to use for the pool.\n\nLet\nk = 1.2\nt = 10 minutes per set\nn = 10 players in the pool\ns = 6 setups available in the pool => 5 setups *\n\n* Be careful here! Even though 6 setups are available, only 5 setups can be used concurrently since there are 10 players in the pool and each set requires 2 of them at once. The sixth setup does not help reduce time. Because of this, s = 5 in this example.\n\nTime required to run this round robin pool:\n\n= kt(n(n-1))/2s\n= (1.2)(10 mins)(10(10-1) players) / (2(5 setups))\n= (1.2)(10)(10(10-1))/(2)(5)\n= 108 minutes\n= 1 hour 48 minutes\n\n\n A ten-person round robin pool.\n\n\nFood for Thought\n\n* This article’s scope is limited to that of time management within one round robin pool. We'll talk more about round robin pools -- advantages and disadvantages, how to determine the number of pools to run and number of players to advance, and more -- in a future article dedicated to tournament formats. In any case, if you’re a new TO, you’re advised to evaluate the setups situation at a tournament and calculate the time required manually before looking too far ahead.\n\n* Be careful scaling up the number of players per pool. While the number of players grows linearly, the time required grows at a more unforgiving rate. In Example #1, an increase from 6 players to 7 players results in an increase in time required from 75 minutes to 105 minutes. In the same example, an increase from 7 players to 8 players results in an increase in time required from 105 minutes to 140 minutes.\n\n* Waves are extremely useful. For TOing purposes, assume the definition of a wave to be a period of time in which only a subset of your entrants have tourney obligations. Multiple waves allow events to be broken down into chunks that contain a subset of the entrants, such that TOs have to manage a smaller number of entrants at any given time and players have to be present for a smaller period of time while still playing the same number of matches.\n\n* Pay attention to setup utilization. To calculate a round robin pool's setup utilization, divide the number of setups by the number of available sets. If a pool of 8 players has 2 setups to work with, the setup utilization is (2 setups) / (4 available sets) = 0.5 = 50% setup utilization. You want this number to be as close to 1 (or 100%) as possible. Splitting your pools into multiple waves allows you to accomplish this. Number of setups remains constant throughout, but you control the number of pools happening at any given time.\n\n--\n\nJuggleguy is a national tournament organizer, Melee It On Me team member, and Smashboards contributor. You can follow him on Twitter: @JuggleRob"
<https://smashboards.com/threads/how-do-i-manage-time-for-a-round-robin-pool-toing.361341/#post-17088926>