Technical
How to Derive the Process Given the Draw
Dr Ian Vincent reveals the mechanism for deriving the matches in the Process-half of a Draw and Process competition.
The numbers in the process table can be derived from the draw by the following algorithm:
- Deduct 1 from the Draw position (i.e. label the players from 0 to 2(N-1))
- Express the result in binary.
- Reverse the order of the bits.
- Convert back to decimal
- Add one, to give the position of that player in the Process.
Thus in the example of the seeding positions quoted for the 16 player draw:
Draw Position |
Subtract 1 |
Convert to Binary |
Reverse Digits |
Convert to Decimal |
Add 1 = Process Position |
|---|---|---|---|---|---|
1 |
0 |
0000 |
0000 |
0 |
1 |
6 |
5 |
0101 |
1010 |
10 |
11 |
11 |
10 |
1010 |
0101 |
5 |
6 |
16 |
15 |
1111 |
1111 |
15 |
16 |
This shows the underlying symmetry between the two draws and illustrates why 6 and 11 are special: they are an inverse pair the maximal distance apart from 1 and 16. Other inverse pairs, such as 0111 (8) and 1110 (15) have one of their members too close to one of the top two seeds.
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