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Cheat Sheet

Important numbers for each format, in one place! See the full guides to explore each format in a deeper fashion. I've also created a simplistic Google Sheet to calculate and compare certain values.

Single-Elimination

Strengths:

  • fastest format in the West
  • high-stakes every match

Potential Drawbacks:

  • half of your competitors are done after one match
  • if your seeding isn't great, then top competitors knock each other out VERY quickly
CategoryValue
(n is # of competitors)
Example / Notes
# of Matches Playedn - 116 competitors = 15 matches played
17 competitors = 16 matches played
# of Necessary Consecutive Roundslog₂(n) rounded up16 competitors = 4 rounds required
17 competitors = 5 rounds required
Distinct Placements1st & 2nd, 3rd* & 4th, 4x T-5th,
8x T-9th, 16x T-17th, etc.
Possible progressions1, 2, 3*, 4, 8, 16, etc.

*Only when a third place match is played.

Double-Elimination

Strengths:

  • competitors are guaranteed 100% more matches than in single-elimination! (two instead of one, don't get too excited)
  • stakes are still clear each match, and the "losers run" storylines now exist

Potential Drawbacks:

  • deceptively lengthy, and lower bracket can lag behind if you aren't careful
  • half of your competitors are done after two matches
  • if your seeding isn't great, then top competitors can still knock each other out VERY quickly
CategoryValue
(n is # of competitors)
Example / Notes
# of Matches Played*2n - 2 or 2n -116 competitors = 30 or 31 matches played
17 competitors = 32 or 33 matches played
# of Necessary Consecutive Rounds*Floor[log₂(n-1)] + Ceiling[log₂(2n/3)] + 1
[1] (or see below table!)
16 competitors = 8-9 required
17 competitors = 9-10 rounds required
Distinct Placements1st, 2nd, 3rd, 4th, 2x T-5th,
2x T-7th, 4x T-9th, 4x T-13th, etc.
Possible progressions1, 2, 3, 4, 6, 8, 12, 16, etc.

*Variance due to whether or not a 'bracket reset' occurs

# of CompetitorsTotal Rounds Required**
44-5
5-66-7*
7-86-7
9-127-8
13-168-9
17-249-10
25-3210-11
33-4811-12
49-6412-13
65-9613-14
97-12814-15

*just trust me on this one

**Total rounds assumes:

  • all matches are the same length
  • there are adequate setups to play all necessary matches simultaneously
  • all matches are played as soon as they are available (e.g. none held for broadcast, and start any Upper Round 1 and Upper Round 2 matches together if applicable)
  • perfect world, no delays

Round Robin

Strengths:

  • Most guaranteed matches possible
  • Great at acquiring seeding for a following stage

Potential Drawbacks:

  • Longest schedule required across all formats
  • Lacks an exciting punch on its own—needs a following stage
  • Can generate "throwaway" low-stakes match scenarios which can lead to sandbagging and/or collusion
CategoryValue
(n is # of competitors)
Example / Notes
# of Matches Playedn! / [2! × (n-2)!]
(# of combinations)
8 competitors = 28 matches played
17 competitors = 136 matches played
# of Necessary Consecutive Roundsn-1 (if n is even)
n (if n is odd)
8 competitors = 7 rounds required
17 competitors = 17 rounds required
Distinct PlacementsAll placements
(1st - nth)
Possible progressions1 to n

Swiss (Non-Eliminating Version)

Strengths:

  • Compromises between round-robin's guaranteed match count and elimination brackets' efficient runtime
  • Great for acquiring seeding for a following stage

Potential Drawbacks:

  • Lacks an exciting punch on its own—needs a following stage
  • Pairing, scoring, advancement, and tiebreak rules can confuse participants and viewers if not presented clearly in advance

As a reminder, the below values assume you are playing to completion (to determine a 1st place)!

CategoryValue
(n is # of competitors)
Example / Notes
# of Matches Played*ceiling[ log₂(n) ] × floor[ n / 2 ]16 competitors = 32 matches played
17 competitors = 40 matches played
# of Necessary Consecutive Rounds*log₂(n) rounded up16 competitors = 4 rounds required
17 competitors = 5 rounds required
Distinct PlacementsAll placements
(1st - nth)
Possible progressions1 to n

*The edge cases for non-square numbers of competitors are pretty messy and vary by community, so this is a very rough look at numbers

Citations

  1. Moore, J. (2021, February 25). The Math Behind SPR and UF.