In principle, it’s possible to add another bracket to any knock-out tourney to make it a double-elimination format, and to turn a double elimination into a triple elimination by adding another bracket. In practice, however, there are a number of difficulties that need to be overcome.
Tourneygeek has spent a good many words on the way that these practical challenges may be met in the context of the double elimination, and I will presently offer some advice for those who want to run triple eliminations. First, however, I’d like to give some attention to the question of whether double- and triple-elimination tourneys make sense in the first place. As in other contexts, I’ll use the FEPS framework.
Fairness
One of the chief reasons to add a bracket is to make the tourney more fair. To the extent that there’s any chance element in the outcome of a particular contest, a single elimination, or knock out, is an unforgiving format. But we should note that the fairness gain is in the form of fairness (C), the ability of the format to reward the best players. Fairness (B) is at best a wash – there’s nothing in adding a bracket that makes the format any fairer in the sense that every competitor should have an equal chance. And, as we’ve seen in the past, and will encounter particularly when we consider adding a third bracket, there are often fairness (B) concerns.
Efficiency
Whether adding a bracket is efficient or not depends on what resources are most limited. Here’s I’ll limit the discussion to one common circumstance, where the chief limitation is the number of rounds that can be played.
Adding brackets is not particularly efficient in this respect. For example, a 32-tean knock-out tourney can be played in five rounds, but a standard double elimination takes ten, or possibly eleven if you allow for a recharge round.
Much of the discussion of double eliminations has concerned various ways to reduce the number of rounds. You can eliminate the possible eleventh round simply by not playing a recharge. You can save another round with a bracket shift. You can save another by omitting the reconciliation of the two brackets, turning the lower bracket into a consolation event. And you can save yet another by paying the loser of the upper bracket final for second place rather than dropping them into the lower bracket. Applying all of these expedients together, one possible 32-team consolation format from the printable brackets page shrinks from a possible eleven rounds to seven.
A 32-team triple elimination (triple elimination lines), with all possible recharges, can take as many as 17 rounds. As we’ll see in a future post, there are similar ways to trim the number of rounds needed when adding a third bracket.
Participation
The ruthless efficiency of a knock-out tournament makes it probably the worst possible format for participation. Half the field gets to play only a single match. Adding a bracket roughly doubles the number of matches played, ensuring that everyone gets at least two. If the knock out is the alternative, then participation is greatly enhanced.
But if participation is a chief concern there are other formats that should be considered. The Swiss system, which in its pure form is basically an elimination tourney in which no one ever gets eliminated, is well suited to competitions with enough rounds to run a double elimination (or even one or two fewer) does an admirable job of selecting a champion while keeping nearly everyone else playing. The round robin, perhaps as part of a pool system if there are too many competitors for a complete all-play-all approach, also gives people more play.
In my own small local backgammon club, participation is the highest value. So, unlike other clubs that run a small tournament each week, we simply play. We roll for opponents at the start of the evening, and then play as many matches as time allows, playing whoever’s available when one match ends. The results are reported, and once a year or so our leader tallies up the results of all of these matches and tells us who did best. If we played a formal tournament of any kind, it would probably be too much, or too little, for most of the players.
Enhancing participation valued by adding another bracket is, at best, a compromise measure, which lets people play more, but still observes the basic outline of the knockout.
Spectacle
Double and triple elimination tournaments are rare in professional sports. Where the highest value is spectacle, the format is drawn in two different ways. If the need is to sell tickets and broadcast rights to a lot of games, some kind of round robin is indicated. If the need it so extract the maximum value from in individual match, a knock-out is called for. In many professional sports, including all of the major ones in the United States, both are used – a long round robin regular season followed by a knock-out playoff.
The few double-elimination tourneys that have enough of a spectator following to be broadcast tend to be events that started as a more purely amateur matter. Some NCAA sports, and such things as the Little League World Series still have some element of double elimination to them.
tourneygeek.com 
I understand that the plain reason double- and triple-elimination tournaments are so rare compared to single-elimination tournaments is that the much lower level of excitement makes broadcast rights much less valuable.
However, with the virtually certain disappearance of spectators from sports due to COVID for many years to come – and in my opinion quite possibly for good even if the COVID pandemic does end – I have thought of the possibility that round robin tournaments will become unviable with no ticket sales and possibly even stadiums built or remodelled for permanent behind closed doors sport. I have also thought that lower level sport leagues with less TV revenue and less ability to keep crowds out will have to disband and join higher levels in the behind-closed-doors future of sport.
Both these changes would favour a move towards pure knock-out play in professional sport. However, even for television broadcasters who thrive on the unrivalled excitement of knock-out tournaments, they have a disadvantage unless all individual matches can attract maximum value.
With many more teams due to the inability to play at lower levels with gate revenue gone permanently, I have thought that double- or triple-elimination tournaments would prevent some teams playing only one game a season in sports that do not play knock-outs as a best-of series, and make for more reasonable numbers even in sports that do. A Swiss system might be another alternative if more teams must be accommodated, but in most sports that would be hard to schedule.
In this context, it has occurred to me to ask why best-of knock-out tournaments, which are less exciting and make individual games less important than a single-game knock-out, are so much more common than double-elimination or triple-elimination tournaments? It is also worthwhile to ask how many more games would a round-robin produce than a double- or triple-elimination tournament?
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