Having considered the process of adding a third bracket in a few simpler contexts, we now return to the Big Peculiar Bracket (BPB) to look particularly at the third bracket that worked with the upper two, which together constituted a double elimination.
In the first part of this analysis, we identified some questionable structural elements. But the apparent flaws in the upper two brackets pale in comparison to those of the third bracket.
Still to come in this series are the results of simulations, comparing the BPB to alternate formats for the same number of entries.
In the previous post, we saw that the presence of even a single set of drops that wasn’t a power of two tended to upset the balance of the third bracket, often necessitating some overlapping of the drops. For the BPB, where everything in the top two brackets happens in multiples of three, there are bound to be challenges. There are seven drops sets from the second bracket of the BPB, with these sizes: 24, 24, 18, 12, 6, 3, 3.
Here, again, is the third bracket for the BPB: MichLower.
The drops were allocated in this pattern: E.EFG.HJ.K.L.|.|.|. The E drops are split between the first two rounds, with 20 going to the first round, and four to the second. By dropping some of the E’s together with the F’s and G’s together, and also yoking the H’s and J’s, the format is compressed into a mere eight rounds.
But this format sends three different sets of drops, E, F, and G, to the same round. That means that some players with a 0-2 loss record and others with a 2-2 record come to the same round. A one-win difference is unavoidable, but a two-win difference is another matter. So I’d have been inclined, faced with the 24, 24, 18, 12, 6, 3, 3 drop groups of the BPB to organize them E.EF.G.H.|.J.K.L.|.|. This arrangement would take nine rounds rather than eight to play, but this tourney had time enough to play an extra round, and the gain in fairness is considerable – one round with an overlap, as opposed to two overlapping rounds, including the awful EFG round.
I had designed a bracket for the BPB tourney, but with a different set of drops to accommodate. Recall that the BPB format, which is ostensibly a 6 x 16 format, is really a 3 x 32 format in disguise. If the second bracket were drawn explicitly as 3 x 32 it would allow the superior A.B.|.C.D.E.| shift to be used in place of the A.B.C.D.|.|.[E] shift that the BPB ended up with. Using the other shift changes the drop groups to 24, 24, 18, 12, 9, 6, 3. This set can be arranged FG.GH.JK.L.M.|.|.|, which has three rounds with overlaps, but no triple overlaps, and still plays in eight rounds. That is the format I use for the one of the alternative BPB formats in the simulation testing to be reported in the final post for this BPB postmortem series.
There are a couple of other things to note about the way the BPB last chance was constructed. In the problematical EFG round, at least the three kinds of drops are interlaced, to some extent, so that the imbalances can be reduced for the next round. But in all of the other drop rounds, there is no interlacing at all. Not only do the H’s and J’s drop into the same round, but they drop in blocks, playing each other. It’s not enough that the poor J’s, who have four wins, drop into a round where other players will have only two wins (or, if the tourney has 11 or more byes, even just one win). They also have to play other J’s. H’s, with their three wins, are treated a little more kindly, but they also have to play out the next rounds against other H’s.
The effect is analogous to the “walled garden” effect that happens when byes are grouped. This effect is explored in some depth in the series of Bad Byes posts, and we’ll have a chance to see it in operation again in the last of this BPB postmortem series, where I report simulator results. In the bad byes scenario, one can at least argue that the advantage of being able to start parts of the second round early compensates, to some extent, for the unfairness caused by grouping the byes. But in this context, there’s no excuse. The tourney doesn’t flow any differently, it just introduces a gratuitous (and lingering) source of unfairness.
A last observation is that the third bracket of the BPB seems to have made no effort to distribute the drops so as to avoid repeat pairings. And as actually played in the Open division, this caused a particularly unfortunate repeat to occur. One player, who was defeated in the first round of the top bracket was defeated again by the same player in the first round of the third bracket. This unfortunate soul (who is, as it happens, an excellent player who has won major championships in the recent past), not only has to endure an 0-3 record, but got to play only two different opponents.
Now, it’s not possible to delay possible repeat pairing in a third-level bracket for as long as they can be avoided in a second-level bracket. But with a little care it is possible to entirely avoid repeats for the first couple of rounds. At least one player has good reason to complain that no such care was taken.