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Mr Ingrate
02-21-2002, 05:54 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.

Troy
02-21-2002, 06:58 PM
Where have I seen this before ?????

Mr Ingrate
02-21-2002, 07:08 PM
Hi Troy,

Yah, kind of like my response to you on the other board. It is actually part of the documentation for my new version of the Tournament Director, if I ever get it done. I just added a graphic to make it more visual.

Troy
02-21-2002, 08:19 PM
Well Dave, the graphic is a great addition.

Tom_In_Cincy
02-21-2002, 10:09 PM
Great post and nice bracket pic.

Of course this all changes when you go from Single Elimination to Double. Seeded players can and do end up playing each other prior to the finals.

Mr Ingrate
02-21-2002, 10:29 PM
Tom,

Doesn't matter. They still won't meet until the end IF they win their matches. Seeding is set up with the assumption that the top seeds will win as expected. So even with double elimination they still won't meet until the end. The only difference between a single elimination and the winner's side of the double elimination is that the loser's side winner gets to come back and play the winner's side in a final.

Early losses could result in top seeds meeting in the loser's side early on in the tournament.