Working out Brackets.
Whenever you want to organize a knockout competition of some sort you need to create 'brackets'. The fundamental bracket, for two players/entries, is shown on the left (fig.1)
To make a 4 entry bracket you would use two of these. To make brackets for 8 you would use two 4 entry brackets. To make brackets for 16 you would use two 8 entry brackets. To make brackets for 32 you would use two 16 entry brackets. Etc.
As you can see you need to keep doubling up (2, 4, 8, 16, 32, 64, 128, 256, ..... ). Creating brackets for exactly these number of entries, the magic numbers, is easy. The problem is creating brackets for an awkward number of entries like 13, or 26, or 58, etc.
The Magic Numbers
Magic numbers for brackets are 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, etc. They are simple to remember as each number is exactly double the one before it. EG. 2x2=4, 4x2=8, 8x2=16, 16x2=32, 32x2=64, etc.
Once you know the magic numbers it is easy to create your bracket using 'byes'. You simply count the number of entries and use the first magic number higher than it to create your bracket. Put in the 'byes' then start adding your entries in the blanks.
For example. If you have 13 entries the next magic number is 16.
- 1/ Create a bracket for 16 entries.
- 2/ Subtract 13 from 16 to find out how many byes there will be. In this case 16-13=3 (3 byes)
- 3/ Write the 3 byes into your bracket on alternate lines. Start at the top (see fig.2 left)
- 4/ Write in the entries (teams or players) into the blanks, as they are drawn out of the hat. (see left: fig.2)
Creating a losers (AKA. Second Chance) bracket as well
The idea here is to make sure everyone can play at least two matches. If you get knocked out in the first match you play then you get a second chance in the losers bracket.
To create a losers or second chance bracket that works with your main bracket is easy enough most of the time. For the example above (13 entries) use the magic number below the number entries. In this case you would create a bracket for 8.
If you have an even number of entries divide by two to find out how many losers you will have. If you have an odd number of entries, add 1, then divide by two to find out the maximum number losers you will have.
In this case we have 13 entries so 13+1=14 and 14/2 = 7. (7 losers) Because we have an odd number of entries, we might end up with either 6 or 7 losers in the second chance table. (see fig.3 left: 'loser 7 or bye')
- 1/ Create a bracket for 8 entries.
- 2/ Subtract (number of losers) 7 from 8 to find out how many byes there will be. In this case 8-7=1 (1 bye)
- 3/ Write the byes into your bracket in sensible places (see fig.3 left)
- 4/ Write the losers into the blanks if they lose their first match in the main bracket. (see fig.3 left)
Sometimes loser brackets get confusing when a lot of 'byes' are required. This final example shows how to create loser brackets for awkward numbers. In this example for 10 entries you would create a loser bracket for 8. Number of losers is 10/2=5 (5 losers)
- 1/ Create a bracket for 8 entries.
- 2/ Subtract (number of losers) 5 from 8 to find out how many byes there will be. In this case 8-5=3 (3 byes)
- 3/ Write the byes into your bracket in sensible places. (see left)
- 4/ Write the losers into the blanks when/if they lose their first match in the main bracket. (see fig.4 left)
Cleaning up your brackets
To finish off your bracket you need to clean it up a bit. All entries with a bye can be advanced and the original construction bracket lines erased. The bracket below (fig.5) shows the finished loser bracket for (fig.4, 10 entries, 5 losers)
fig.5 Above : Example of a finished loser bracket.
NOTE: The losers are normally filled in as they lose. This causes least delay in playing.
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