Mr Ingrate
02-21-2002, 04:54 PM
Byes and Seeding
Tournament charts are usually designed for a number of players based on the power of 2. For those of you who want to know the math 2^3=8, 2^4=16, 2^5=32, 2^6=64, etc.
Software developers (I consider myself one) use this basic concept when designing their programs. They also use a technique to determine where the byes are placed and where seeded players are entered on the chart.
This consists of using a numbering sequence that not only distributes the byes on the chart as evenly as possible, but also ensures that seeded players do not meet until later rounds.
Some tournaments give their top seeds afirst round bye. A proper numbering sequence accomplishes these objectives.
Here are the numbering sequences for 8 to 128 player charts:
8 Player Chart:
1-8, 4-5, 2-7, 3-6
16 Player Chart:
1-16, 8-9, 4-13, 5-12, 2-15, 7-10, 3-14, 6-11
32 Player Chart:
1-32,16-17, 8-25, 9-24, 4-29, 13-20, 5-28, 12-21, 2-31, 15-18, 7-26, 10-23, 3-30, 14-19, 6-27, 11-22
64 Player Chart:
1-64, 32-33, 16-49, 17-48, 8-57, 25-40, 9-56, 24-41, 4-61, 29-36, 13-52, 20-45, 5-60, 28-37, 12-53, 21-44, 2-63, 31-34, 15-50, 18-47, 7-58, 26-39, 10-55, 23-42, 3-62, 30-35, 14-51, 19-46, 6-59, 27-38, 11-54, 22-43
128 Player Chart:
1-128, 64-65, 32-97, 33-96, 16-113, 49-80, 17-112, 48-81, 8-121, 57-72, 25-104, 40-89, 9-120, 56-73, 24-105, 41-88, 4-125, 61-68, 29-100, 36-93, 13-116, 52-77, 20-109, 45-84, 5-124, 60-69, 28-101, 37-92, 12-117, 53-76, 21-108, 44-85, 2-127, 63-66, 31-98, 34-95, 15-114, 50-79, 18-111, 47-82, 7-122, 58-71, 26-103, 39-90, 10-119, 55-74, 23-106, 42-87, 3-126, 62-67, 30-99, 35-94, 14-115, 51-78, 19-110, 46-83, 6-123, 59-70, 27-102, 38-91, 11-118, 54-75, 22-107, 43-86
To illustrate how the numbering sequence works, assume that we have a tournament with only 12 players entered. We use a 16 player chart as follows:
http://home.socal.rr.com/dsyrya/ccb/pt_theory.gif
Note that the byes are distributed as evenly as possible. This would hold true even if there were only 2 players.
With the proper numbering sequence, an 8 player chart can handle 2 to 8 players, a 16 player chart can handle 2 to 16 players, a 32 player chart can handle 2 to 32 players, etc.
It is possible to seed every player in a tounament. The first seed goes in the first slot, the second seed in the slot numbered two, etc. Player One (the first seed) will not meet Player Two (the second seed) until the final round assuming they win their games. The top four seeds are not scheduled to meet each other until the third round.
In order to ensure a bye for the top four seeds you have to limit entries to 4 less than the maximum allowed. In the example above the 4 byes go to the players in slots 1 to 4.
The WPBA used to seed 16 players and give them a first round bye which meant they limited entries to 48 players. Expanding to 64 entries eliminates first round byes but seeding can still be accomplished.
I know that no one asked for this, but I thought it might be useful information and it gave me a chance to play around with a few things.
Now if I could just get Ed to renumber his charts.
Tournament charts are usually designed for a number of players based on the power of 2. For those of you who want to know the math 2^3=8, 2^4=16, 2^5=32, 2^6=64, etc.
Software developers (I consider myself one) use this basic concept when designing their programs. They also use a technique to determine where the byes are placed and where seeded players are entered on the chart.
This consists of using a numbering sequence that not only distributes the byes on the chart as evenly as possible, but also ensures that seeded players do not meet until later rounds.
Some tournaments give their top seeds afirst round bye. A proper numbering sequence accomplishes these objectives.
Here are the numbering sequences for 8 to 128 player charts:
8 Player Chart:
1-8, 4-5, 2-7, 3-6
16 Player Chart:
1-16, 8-9, 4-13, 5-12, 2-15, 7-10, 3-14, 6-11
32 Player Chart:
1-32,16-17, 8-25, 9-24, 4-29, 13-20, 5-28, 12-21, 2-31, 15-18, 7-26, 10-23, 3-30, 14-19, 6-27, 11-22
64 Player Chart:
1-64, 32-33, 16-49, 17-48, 8-57, 25-40, 9-56, 24-41, 4-61, 29-36, 13-52, 20-45, 5-60, 28-37, 12-53, 21-44, 2-63, 31-34, 15-50, 18-47, 7-58, 26-39, 10-55, 23-42, 3-62, 30-35, 14-51, 19-46, 6-59, 27-38, 11-54, 22-43
128 Player Chart:
1-128, 64-65, 32-97, 33-96, 16-113, 49-80, 17-112, 48-81, 8-121, 57-72, 25-104, 40-89, 9-120, 56-73, 24-105, 41-88, 4-125, 61-68, 29-100, 36-93, 13-116, 52-77, 20-109, 45-84, 5-124, 60-69, 28-101, 37-92, 12-117, 53-76, 21-108, 44-85, 2-127, 63-66, 31-98, 34-95, 15-114, 50-79, 18-111, 47-82, 7-122, 58-71, 26-103, 39-90, 10-119, 55-74, 23-106, 42-87, 3-126, 62-67, 30-99, 35-94, 14-115, 51-78, 19-110, 46-83, 6-123, 59-70, 27-102, 38-91, 11-118, 54-75, 22-107, 43-86
To illustrate how the numbering sequence works, assume that we have a tournament with only 12 players entered. We use a 16 player chart as follows:
http://home.socal.rr.com/dsyrya/ccb/pt_theory.gif
Note that the byes are distributed as evenly as possible. This would hold true even if there were only 2 players.
With the proper numbering sequence, an 8 player chart can handle 2 to 8 players, a 16 player chart can handle 2 to 16 players, a 32 player chart can handle 2 to 32 players, etc.
It is possible to seed every player in a tounament. The first seed goes in the first slot, the second seed in the slot numbered two, etc. Player One (the first seed) will not meet Player Two (the second seed) until the final round assuming they win their games. The top four seeds are not scheduled to meet each other until the third round.
In order to ensure a bye for the top four seeds you have to limit entries to 4 less than the maximum allowed. In the example above the 4 byes go to the players in slots 1 to 4.
The WPBA used to seed 16 players and give them a first round bye which meant they limited entries to 48 players. Expanding to 64 entries eliminates first round byes but seeding can still be accomplished.
I know that no one asked for this, but I thought it might be useful information and it gave me a chance to play around with a few things.
Now if I could just get Ed to renumber his charts.