Some of us at some point have wondered while looking at a bracket, “so there’s single-elim and double-elim, what about triple-elimination?” I had played around with the idea in my head and drew out some possible ideas for what it might look like but never fully fleshed it out. About 2 weeks ago, I saw a facebook status by Ankoku/aisight/Tony Cheng saying that anyone successfully running a triple elimination bracket would have his enduring admiration and respect. This was the motivation I needed. I had my triple-elim bracket design finished that night, posted that I wanted to try it at the next Norcal tournament, and got the OK from the community. We ran the triple-elim bracket on Apr 12 with 55 entrants and it was a fantastic success. We somehow finished it in under 6 hours, thanks to having 14 setups and the hard work of all the Norcal helpers *shoutouts to Mama Ko* So how does a triple-elim bracket work? What do you need to do to run one successfully? I’ll be describing how the whole thing works and referring to different rounds of different brackets, so you can look at what we did at the Norcal tournament as an example to follow along:
tio bracket (winners/losers only): http://i.imgur.com/M5OXLUq.png
2x-losers bracket, pre-finals: http://i.imgur.com/8J6RGDk.jpg
finals of each bracket: http://i.imgur.com/64SPk0N.jpg
A triple-elimination bracket can be run nearly identically to a double-elimination bracket with the addition that all the losers from losers bracket go into a third bracket (2x-losers, failures, the slums, the shadow realm, insert your favorite term here). You can run the winners and losers on tio just like you normally would, and write out the 2x-losers bracket by hand. But you have to have the right system for where to put the people that just lost in losers bracket. This is easier than it sounds (except for one complication and one ambiguity which I’ll talk about below); the one rule that you use to figure out how to structure your bracket is that the number of people who are coming down from the bracket above should always equal the number of people left in the bracket below (if you don’t, you have to have byes in the middle of the bracket which to me is nonsensical). Before we look at the triple-elim bracket, you can verify this is how it works with double-elimination brackets. Consider our 64-man bracket (byes count as players for the purposes of drawing a bracket): after round 1, we’ll have 32 in winners and 32 in losers. Round 2 of winners will send 16 down to losers, so we draw (or tio draws, really) our losers bracket such that we have 16 players left to meet them. We do this by pairing up the existing 32 in losers in R1 losers so we’ll have 16 left over afterwards. R3 of winners will send 8 to losers, so we have another round (R3) in losers to work the number of players in there down to 8 before they play those coming from R3 winners, and so on until it’s time for losers finals.
We can easily use this rule to draw out our 2x-losers bracket, but we run into a complication at the beginning. Using our 64 player bracket again, R1 of losers will send 16 players down to 2x-losers, but so will R2 of losers, because the 16 people that won in R1 losers will play the 16 coming down from R2 of winners – thus 16 sent to 2x-losers. The only way to resolve this without a weird asymmetric bracket is to have the people that lost in R1 losers play people that lost in R2 losers. This is a little unfair to the people that lost in R2 because their win did not get them further in the bracket, however, they do get to play a slightly easier (on average) opponent in 2x-losers compared to the people that have gone 0-2. In fact, a win and 3 losses in any order will result in the same placement. After this however, it’s very easy to draw up the rest of the bracket using our rule that the number of people in the bracket must equal the number of people coming down from the bracket above. R3 in losers will send down 8 players. So R1 of 2x-losers will cut 32 players down to 16, and then we’ll have the winners of those sets play one another in R2 to cut it down to 8. So R3 of 2x-losers will be people with 2 wins in 2x-losers versus people who just lost in R3 of losers.
So with that worked out, how does the rest of 2x-losers look? It’s very simple actually. So if you look at losers bracket, you see that it alternates between people in losers playing one another, and people in losers playing people just coming down from winners, where it looks like a branch gets added to the bracket. So if we look at how many people are in losers bracket in each round, it goes 32-32-16-16-8-8-4-…. In 2x-losers bracket, the effect is to simply add another round where people in 2x-losers are playing people coming down from losers, so we get something like 32-16-16-16-8-8-8-4-… instead; we have two rounds of branches getting added (people coming from losers) after each round of existing people in 2x-losers playing one another.
Okay, so now we’ve worked our way through the 2x-losers bracket and we’re getting close to finals (look at the example bracket). We’ve got a WB winner (winner of WFs, SFAT), LB winner (winner of LFs, Shroomed) and 2xLB winner (winner of 2xLFs, HMW). In our example, 2xLFs was Azusa vs HMW (it’s the loser of losers finals vs the remaining player in 2x-losers). We actually have another ambiguity here, in what order do these people play one another? Do Shroomed and SFAT play each other first (which is what is depicted in our bracket)? Or should Shroomed play HMW first? I could have easily drawn the bracket that way too. The first way is what I call ‘top-down,’ where WB winner and LB winner play one another until one of them has 2 set losses, in what I call ‘semi-grand finals’. So if Shroomed loses, that’s it, but if he wins a set, they play a 2nd set and the loser of that gets sent to 2x-losers (the winner would still have their 1 set loss and technically be in losers bracket), who then plays the 2xLB winner. The winner of semi-grand finals will await the winner of that match (call it ‘losers grand finals’ or something), and that will be grand finals, which is played out in any number of sets until one player has 3 total set losses. The other approach is ‘bottom-up’ where the LB winner and 2xLB winner play until one of them is eliminated, and then the winner plays the WB winner. I’m not 100% set on this, but I believe top-down to be the more favorable approach for two reasons. According to my math, resolving the top 3 in a top-down approach will on average take about 0.2 more sets, however, the first part of these sets (WB winner vs LB winner) can be played concurrently with anything that is going on in 2x-losers bracket, which is always going to be lagging behind winners/losers brackets. So ultimately I believe it may save time. The other reason is that in a bottom-up approach, the WB winner has a comparatively large advantage going into finals, and the 2x-losers bracket has a large disadvantage. If we assume all 3 players are of equal skill, in top-down, the WB winner has a 65.625% chance to win, LB winner has 25%, and 2xLB has 9.375%. In bottom-up, WB has about 78%, LB has about 19%, and 2xLB has about 3%. It is a matter of opinion as to how much advantage/disadvantage each player ‘deserves’ so this reasoning may not agree with everyone. I should also mention that ‘bottom-up’ is what I believe to be the most consistent mathematically with how we do double-elim (and in fact how you would do it for higher N-elim brackets), but practicality takes priority for me here.
There’s actually one thing left to do to construct our bracket, which is to place the people coming down from losers bracket into 2x-losers in such a way as to prevent two players from having to play each other twice as much as possible. In double-elim, tio/challonge do this for us automatically: matches in winners are labeled by letters, and in losers bracket the incoming branches have a letter to show where the losers of those sets go. If you want to run a triple-elim bracket, you will have to come up with your own system for labeling the sets in losers bracket to keep track of who goes where in 2x-losers. My system was to label them in relation to the set coming down from winners. So if you look in our example bracket again, the loser of match F was violence, and he played 2jabjames in losers. In my hand-drawn bracket, I labeled this set ‘LF’ and you can see that since violence won, 2jabjames was placed at the branch labeled ‘LF.’ But there was a set in losers before this, where 2jabjames played Aja. I called this set ‘BF,’ and you can see that Aja was placed at that branch in 2x-losers. This is actually really difficult to optimize and I’m not entirely certain I have it worked out yet. It’s also difficult to describe concisely in an article like this, so let me just put it in one simple (imperfect) general rule: in each round of 2x-losers where you’re about to add new branches, look at the letter labels of every added branch before it (in my system, things like ‘BF’ and ‘LF’ count as ‘F’). You want to make sure that whatever letter branch you add is not one of those letters, nor is it any of the letters that appears before that letter in winners bracket. So for example, when I bring down ‘BV’ to double losers, I look in the tio bracket for V, and see that E and F were before V in losers, and K and L were before V in winners. This rule will not solve all your problems but it’s a start. If conflicts do come up, I believe it’s acceptable also to rearrange the players in the new branches by hand, like the option in tio (but NEVER switch around players in an existing branch!). Generally speaking, you can also take what you did with the ‘BX’ round and flip it around for the ‘LX’ round.
OK so now, what resources do you as a TO who wants to do one of these need? What factors should you consider during your execution of the tournament? The most important rule is, ALWAYS run as much of 2x-losers as possible, and ALWAYS be on the lookout for matches in losers/2x-losers that are behind the rest of the bracket. A good rule of thumb is to run 2 rounds of winners, then immediately run 2 rounds of losers, and immediately after that begin 2x-losers. This will eliminate the most people in the shortest amount of time, reducing the chance that you’ll have to deal with DQs or people not showing up to their set. After every match of the second round of 2x-losers has been started, you can begin to call other matches, again using the rule that if there are sets to be called in 2x-losers, start those. If not, call sets in losers, and if there’s nobody in losers waiting, call winners. This program also fits in well if you have a dedicated stream setup: after the 2 rounds of winners, you can continue to call 1 set of R3 winners (and beyond) on the stream setup which will slowly advance the sets you are able to call in losers and 2x-losers. How much time will this tournament take? Let me compare it to what you need for double-elim, since many people are familiar with what’s needed to run that. Take however much time you think it would take to run your double-elim bracket with the same number of setups and multiply it by about 1.5. This makes intuitive sense because you’ll have exactly 1.5 times the number of sets you’ll need to play. At our tourney, we had 55 people with 14 setups, which I would expect to take a little over 4 hours, and we ended up finishing in just under 6 (it also helped that nearly all our finals sets were 3-0; remember that finals may take a long time in this format!). A few other helpful tips: draw our your triple-elim bracket the night/morning before and run through a quick 32-player example to make sure you have your system right. You as a TO need to be able to focus only on calling matches and writing down the results. And of course, all advice for regular brackets applies: label your setups and call sets at specific stations, make sure you get players to report results, and get 2 or 3 people to help you out with calling matches, observing progress, and to fill in for you if you’ve also entered the bracket. I believe that once you understand how the system works, it’s actually quite easy to execute and lots of fun. Good luck!
I responded to this idea on a reddit thread for this article, before realising that there was an article… it covers why triple-elimination might not be a good idea from a mathematical perspective, pertaining to win conditions https://www.reddit.com/r/smashbros/comments/4k9fxw/singleelimination_doubleelimination_what_about/d3dj1mi
“In fact, a win and 3 losses in any order will result in the same placement.”
This is not quite accurate. If you first lose twice so you end up in 2x-losers round 1 and then win a game before losing the third time, you actually get further than if you first win and then lose 3 straight (or lose-win-lose-lose). In the latter scenarios you’re eliminated on 2x-losers round 1 while in the first one on round 2.