Upper Bracket Advantage in Double Elimination

a difficult balance between reward and other factors


The recent ESEA Invite grand finals were historic in a way:

This actually spawned a discussion on the upper bracket advantage immediately following the game, in which the power of the upper bracket advantage was questioned as being too significant to overcome.

Fast forward a bit, and we get to Insomnia58. The eventual champions of Crowns eSports Club got into a heated discussion with the admins about what they perceived to be a lack of an advantage going into the best-of-five grand finals. After some wrangling, Full Tilt generously agreed to give up their map ban in exchange for being allowed to pick the first and third maps of the series.

As should be apparent, there’s a lot of controversy on what an upper bracket advantage should look like. I’ve given this a bunch of thought even before this has come up now as it’s a very difficult problem to solve.

By the Book

The straightforward view is that the upper bracket advantage must be a full set—as the bracket is double elimination, every competitor has to lose two sets in order to be eliminated from the tournament, so if the team coming from the upper bracket loses the first set of the grand finals, they have still only lost once and thus one of the two teams must lose again to be truly knocked out. ESEA has always applied this view, so it’s worth it to examine how the advantage has actually turned out over time. (To make things simpler for comparison, I’ll only consider best-of-three double elimination brackets.)

  • Season 5 on LAN: upper bracket wins on 1st set
  • Season 6 on LAN: lower bracket wins on 1st set*
  • Season 7 on LAN: upper bracket wins on 1st set
  • Season 8 on LAN: upper bracket wins on 1st set
  • Season 9 on LAN: upper bracket wins on 1st set
  • Season 10 on LAN: lower bracket wins on 2nd set
  • Season 11 on LAN: upper bracket wins on 1st set
  • Season 12 on LAN: upper bracket wins on 1st set
  • Season 13 on LAN: upper bracket wins on 1st set
  • Season 14 on LAN: upper bracket wins on 1st set
  • Season 15 on LAN: lower bracket wins on 2nd set
  • Season 16 on LAN: upper bracket wins on 1st set
  • Season 17 on LAN: upper bracket wins on 1st set
  • Season 18 on LAN: upper bracket wins on 1st set
  • Season 19 online: lower bracket wins on 2nd set
  • Season 20 online: upper bracket wins on 1st set
  • Season 21 online: lower bracket wins on 2nd set
  • Season 22 online: upper bracket wins on 2nd set

* This was an extremely weird situation where the admins were convinced to make the grand finals a single set due to time constraints despite the disadvantage it gave to the upper bracket team. I’m including it here for completeness, though I won’t consider it in further analysis.

Over 18 seasons, the upper bracket team took it within the first set 12 times, which is reasonable to expect since the team that wins the upper bracket is usually the best team. When it goes to a second set, the lower bracket team has won 4 times and the upper bracket team only once. While you could generally chalk the lower bracket wins to it being the better team, I do have to wonder whether it could also be based on momentum or other factors (after all, in three of those four wins, the second set was immediately played following the first set with no significant reset or delay). The final instance of the upper bracket team winning after the second set was an extremely unusual case, as discussed before.

Given all this, you can say with reasonable (though not extreme) confidence that the better team will usually prevail in the grand finals despite the presence of an upper bracket advantage.

Changing Approaches

Unfortunately, the set advantage approach does pose some difficulties. The most significant of these is the fact that the upper bracket winner can win enough games such that they would have won but still lose because the games were in two different sets. There’s also the matter of handling the two sets—the two sets should be handled as if they are completely separate, for fairness reasons, but usually are not (with restrictions like being played right after one another or not being allowed to pick the same maps or such between the two) which adds confounding factors into the mix.

The usual answer has been to condense the grand finals into a single larger set where the upper bracket team comes in with a score advantage; for example, in a tournament composed of best-of-threes, the grand finals tend to be a single best-of-five series with the upper bracket team coming in with a one-game advantage.

This approach has also fallen out of favor, given the many perceived advantages the upper bracket team comes in with (playing less sets, never facing elimination) and the perceived strength of a game advantage. As a result, certain tournaments (most notably the Dota 2 majors) now run the grand finals as a single straight series where the upper bracket winner only receives a pre-game advantage of some type.

A Matter of Perspective

In some senses, part of this debate hinges upon what perspective you take as far as the double elimination bracket. It you take it literally by its name, only one approach is fair: forcing the lower bracket winner to win two sets while allowing the upper bracket winner to win only one to clinch the championship.

However, “realists” look at the purist view and see several disadvantages that result, thus altering the format in some way to address those disadvantages. In a way, it takes a much different view of the purpose of a double elimination bracket as a tool to identify the two best teams. This makes sense when you look at when the lower bracket team dropped to the lower bracket in the Dota 2 major events:

  • The International 2011: upper round of 6
  • The International 2012: upper round of 6
  • The International 2013: upper final
  • The International 2014: upper round of 6
  • Dota 2 Asia Championships: upper final
  • The International 2015: upper final
  • The Frankfurt Major: group stage
  • The Shanghai Major: upper final
  • The Manila Major: upper round of 12
  • The International 2016: upper round of 12

In more cases than not, the lower bracket winner failed to reach the upper bracket final, and the lower bracket served as a second chance for them to prove their mettle as they reached the grand finals. If the grand finals serve to let the better team of the two best teams prove themselves in a direct series as a result, it makes no sense to significantly handicap the lower bracket team in the series.

There are generally two arguments against such an approach. The first weaker argument focuses on the weirdness that comes about in terms of games, such as if the lower bracket team loses the upper final 0-2 and goes on to win the grand finals 3-2 despite being 3-4 in overall games. Such problems are visible in almost every approach, however, including the pure approach, where an upper bracket winner can win the upper finals 2-1, lose the first set 0-2, and win the second set 2-1 to win the championship despite tying in overall games 4-4 and losing in grand finals games 2-3, or where a lower bracket winner can lose the upper finals 0-2, win the first set 2-1, and win the second set 2-1 to win the championship despite being tied in overall games 4-4. The realization must be that each set is its own atomic unit, and thus must be considered as a whole rather than divided up into separate games—particularly important as the same maps may be played in different sets, teams may adapt differently within a set as compared to between sets, and other similar factors may apply.

The other more weighty argument focuses on the advantage (or lack thereof) an upper bracket winner gets going into the grand finals. It’s a difficult argument to consider because of the different perspectives people may have on the issue: more realistic views will consider the lesser number of games played and the lack of worry about elimination as advantages in addition to whatever other advantages the structure of the tournament may grant (such as extra rest/preparation time and picking advantages), whereas more pure views will regard all of those as insignificant compared to the bracket and the results. The most direct counterargument that can be offered is that as the largest and most significant series of the tournament, the best team will prevail in the grand finals regardless, and thus no significant advantages should be given; the upper bracket should be able to win without them, and if it can’t win without them, it’s not truly the best team.

Overall, it’s a very complex issue and one in which there is no truly right or wrong answers due to the many different factors to consider. I have over time switched from the purist view to the realist view, and as a result have recommended a straight best-of-five series to conclude tournaments, but I recognize that not everyone will agree with me on this point for their own reasons.