Building Lower Brackets

A friend asked me for a 48 bracket for a tournament he’ll be running next month. The tourney will have a main flight, a consolation, and a last chance. He wants to pay two places in the main, and two more in the consolation.

Rather than just giving you the bracket I came up with, let me show you the process by which the bracket was built. The will take a few posts. For the first one, I’ll begin the process, and then digress to show how second brackets are built for a 64 main.

The first thing to note is that my friend couldn’t use an off-the-shelf bracket from my printable brackets page, even for the consolation. There is a 48 bracket there, but it’s a double elimination. And, as you’ll see, the difference between a double elimination and a main flight with consolation differs substantially when you decide to pay two places in the main.

So the first thing to do is to look at the upper bracket (for which you can use my stock bracket): 48Upper. What you need is the sizes of the drop groups, by round. Here you see there are 16 matches in the A round, another 16 in the B, 8 in the C, 4 in the D, and 2 in the E. Because you’re paying two places, you won’t drop the lone F. So the sequence is this: {16, 16, 8, 4, 2}.

Now, if you were running your 48-player tourney on a full 64 bracket, the drops would be like this: {32, 16, 8, 4, 2}. Let me start the next step by showing how you use this sequence to derive two different lower brackets, one shifted, and one unshifted.

In general, you strongly prefer to drop each set into its own round, with consolidation rounds where needed to even things out. With a conventional, unshifted bracket, it happens like this:

32 > 16
16, 16 > 16 > 8
8, 8 > 8 > 4
4, 4 > 4 > 2
2, 2 > 2 > 1

This structure is A.B.|.C.|.D.|.E.| in standard notation. The number of “>” signs is the number of rounds to be played, and each new line shows the arrival of a new set of drops. Here, in contrast, is the pattern for a shifted 64:

32 > 16
16, 16 > 16
16, 8 > 12
12, 4 > 8 > 4 > 2
2, 2 > 2 > 1

This is A.B.C.D.|.|.E.|, which shifts the C and D drops together, eliminating the two consolidation rounds before the shift, but adding one after. Alternatively, you could shift the D and E together:

32 > 16
16, 16 > 16 > 8
8, 8 > 8
8, 4 > 6
6, 2 > 4 > 2 > 1

This yields A.B.|.C.D.E.|.|, which is probably the preferred pattern for most applications.

As you see, with the conventional architecture always has each round with a number of lines that’s a power of two. But, as the alternatives show, you don’t need to always have a power of two as long as you can end up with one.

Now, if our 64 tourney was a double elimination, or a consolation in which only one player is paid in the main bracket, {32, 16, 8, 4, 2, 1}, there would be a double shift available:

32 > 16
16, 16 > 16
16, 8 > 12
12, 4 > 8 > 4
4, 2 > 3
3, 1 > 2 > 1

which gives A.B.C.D.|.E.F.|.|. This saves two rounds, but it needs the single F drop to make it come out right in the end.

In the next post, I’ll return to the problem of building a lower bracket for a 48.

 

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