Having discovered a useful alternative to the standard 16-team double-elimination bracket among those available at tournamentdesign.org, I spent some time looking at other brackets posted on Joe Czapski’s web page.
They’re a mixed bag. The 13DE bracket I considered (and essentially rejected) in the last post is not typical, in that it makes no use of “if necessary” matches (other than the recharge round). Most of the other double eliminations make extensive use of those rounds, and that makes them hard for me to evaluate – my simulator wasn’t built with them in mind.
But there is one other candidate I want to consider: Joe’s 8DE. Here is a version adapted to tourneygeek style: jc8. (Here, for contrast, is a standard 8DE: 8destd.)
Is this useful as a shifted 8DE?
Joe’s designs sometimes make it difficult to decide what matches belong to what round. This doesn’t trouble Joe because he doesn’t use my match-naming system – his matches are simply called “game 1”, “game 2”, and so forth. But I find it useful in many ways to think of the matches as forming rounds, and so try to impose my A1, A2, … , B1 etc. system when I redraw them for tourneygeek. It’s not always easy.
The critical structural feature is Joe’s 8DE is the cascade of matches at the bottom of the bracket, starting with the one I’ve labeled D3. It’s not clear that the match is really part of the D round – perhaps it should be E2 because it requires completion of both the A and B rounds, and so can’t be called when D1 and D2 are called. It would fit in nicely as an E if the contingent G1 match is not played. But, on paper at least, it looks like if belongs in the D round because when G1 is played it is the same distance, in rounds, from the ultimate result as the other D matches.
As G1 and I1 are never both played, Joe’s 8DE plays out in a maximum of six rounds, and it’s done in five if neither G1 nor I1 are played (something that happens about 40% of the time in my simulation). In contrast, the standard 8DE always takes six rounds, and if there’s a recharge it takes seven.
There’s a cost, however, for this possible round savings. In the event that G1 is played, the D3 cascade is pretty darned ugly from a fairness (B) perspective. The D3 drops not only have a harder match (against each other) than the other D matches, but then they get a tougher next opponent in the form of the C drop.
Here’s how the design plays out. With luck = 1, there’s a dead heat between Joe’s 8DE and the standard 8DE, with fairness (C) at 13.48 and 13.49 respectively. But where there’s more luck to mitigate the effect of the shenanigans in the D3 cascade, Joe’s 8DE is the winner, 57.94 to 59.13.
As with the 16, the recharge round is essential to Joe’s design, which underperforms without it. The fairness (C) numbers without the recharge are 17.21 and 62.20 for Joe’s 8DE, and 16.84 and 61.77 for the standard 8DE. So the “shifted 8DE” is not the way to go if you’re dispensing with the recharge round.
Any recommendation of Joe’s 8DE comes with the same flock of additional caveats as I mentioned with the 16DE – I won’t repeat them here. But it seems that Joe’s handiwork is worth strong consideration.
I don’t even have an 8DE on my printable brackets page – until now, I didn’t know there was any alternative to the standard design, which is widely available. But perhaps it’s time to put one there, and if I post the standard bracket, it will only be fair to post Joe’s design also.
2 thoughts on “A Shifted 8DE?”
There is, of course, another potential “shifted” 8 bracket (AB.C.|.X.R), but it doesn’t save a round and I believe it doesn’t improve any measure of fairness by much, if at all.
The similar structures for 16 (AB.C.|.|.D.X.R) and 32 (AB.C.|.D.E.|.X.R or AB.|.C.DE.|.|.X.R) are almost certainly inferior to the normal shift for those numbers, but it might be interesting to test them.
Good point. I tend to avoid designs that drop two rounds together unless I’m drafting a third bracket, when they’re sometimes all but unavoidable. But it wouldn’t hurt to test them. I’ll do that soon.
Right now, I’m finishing up comparative runs on Joe’s 8DE and the standard 8DE without recharge, and I’ll edit that information into the post.