A reader alerts me to an innovative format that can be used to determine the winners of a four-team pool. This is usually done with a round robin, in which each of the four teams plays each of the other teams once (or, sometimes, twice). The Dual Tournament format instead plays a bracket that’s essentially a single elimination with a consolation to determine second place. What are the advantages and disadvantages?
Here’s the bracket, which I’ve redrawn in tourney geek’s standard style from here.
Perhaps the main advantage is that it avoids violations of the maxim 3, which counsels the designer to avoid matches in which one player’s incentives are very different from the other’s. Assuming that two players qualify for advancement to the next stage of the competition, every match will affect qualification one way or another. And this will also add to the spectacle value of the competition, as there will be no “dead rubber” matches.
A second advantage is that its results are unambiguous. In a four-player round robin there’s always the chance that the results will be {2-1, 2-1, 2-1, 0-3} or {3-0, 1-2, 1-2, 1-2}, either of which will require some sort of tie break in order to choose the two players to advance. In the Dual Tournament format no tiebreaks are required, as the result will always be {2-0, 2-1, 1-2, 0-2}.
Another possible advantage is that it requires one fewer match – five rather than six. Of course, from a participation perspective, this is a disadvantage rather than an advantage. The number of rounds does not change.
There are some possible disadvantages also. The D1 match may well be a rematch between two teams that have already met. This is more than a mere possibility. From my simulator, it happens 44.8%/49.6% in (high skill/low skill) with a blind draw. If the teams are seeded in the ordinary way shown on the bracket, it happens even more often: 63.8%/53.3% (high skill/low skill). Whether this is a critical objection depends, I suppose, on how much you want to avoid rematches.
The unambiguous results also come with a cost. Some of those unambiguous results are not particularly satisfying. With only five matches being played, there will always be at least one, and frequently two, of the possible matches that aren’t played. Sometimes the missing match will be the one between the first and second place finishers. There are other possible results that many would find odd.
Finally, the round robin can be scheduled in advance, so that every team (and its fans) know exactly where and when they’ll be playing three matches, which is of considerable value to some tourneys.
I’d be inclined to favor the Dual Tournament approach for events in which there are no good ways to break ties. I’m not so sure I’d want to use the method if good tiebreaks were available.
tourneygeek.com 
This format has been in use in professional Starcraft tournaments for nearly 20 years. It can also be thought of as a double elimination bracket where the top two players get the same prize so there’s no need to play a grand final.
Some of the disadvantages are mitigated by the broader context of the event. In Starcraft, there are usually 32 players entering the event who are then split into eight groups of four. Each group plays through this format and the top two in each group advance to the round of 16. The players are then split into four groups of four and each group plays through this format again. The top 8 then face off in a single elimination bracket. So even if the two players who advance never played against each other in the group, they could potentially have to play against each other later in the event.
I think that the event organizers have stuck with this event because it offers the following benefits: 1) It is easy to explain who advances and why, 2) There are always five matches, which makes it easier to run each group in a single session, 3) As you mentioned, every match is important, 4) Rematches allow the commentators to craft a narrative and viewers get to see if a player can learn from how they lost earlier in the day and adapt their play style to counter their opponent.
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The AFL & NRL use something moderately similar for 8 teams, which gives them the advantage of avoiding rematches in that third-round slot.
I built an 8-team Page DE (2-0 teams get byes that count as losses) without any rematches until the final. It’s 5 rounds, and Round 4 has conditional matchups based on who the semifinalists are…sometimes the two 2-0 teams will have to play an elimination game against each other. Really good when time doesn’t play nice for your competition.
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