DrawMyFixture

13 team knockout fixture

13 teams: 3 byes, 10 teams play Round I, 12 matches over 4 rounds.

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Knockout fixture — 13 teams · 3 byes · 12 matches · 4 rounds

TournamentVenueDate

13 teams: 3 byes, 12 matches, 4 rounds.
Total byes
3
teams that do not play Round 1
Byes in each half
Upper 1Lower 2
Teams in each half
Upper 7Lower 6
Total matches
12
not including a third-place match
Total rounds
4
worked out from the textbook illustrations
Byes go to teams
1, 8, 13
in serial order; the order the byes are given is in the steps below

The bracket prints on one A4 page (portrait).

Add team names

Names fill serial numbers 1 to 13 in order. Without names, the bracket shows Team 1, Team 2…

The textbook places teams by lottery. Shuffle gives the names random serial numbers.

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Knockout fixture, 13 teams3 byes. 7 teams in the upper half, 6 in the lower half.Round IRound IISemi-finalFinalUPPER HALFLOWER HALFTeam 1BYETeam 2Team 3Team 4Team 5Team 6Team 7Team 8BYETeam 9Team 10Team 11Team 12Team 13BYETeam 1Team 8Team 13Winner123456789101112
BYE = no match in Round I. Numbers in circles are match numbers.
Match list (text)

Round I

  1. Team 1 gets a bye
  2. Match 1: Team 2 vs Team 3
  3. Match 2: Team 4 vs Team 5
  4. Match 3: Team 6 vs Team 7
  5. Team 8 gets a bye
  6. Match 4: Team 9 vs Team 10
  7. Match 5: Team 11 vs Team 12
  8. Team 13 gets a bye

Round II

  1. Match 6: Team 1 vs Winner of Match 1
  2. Match 7: Winner of Match 2 vs Winner of Match 3
  3. Match 8: Team 8 vs Winner of Match 4
  4. Match 9: Winner of Match 5 vs Team 13

Semi-final

  1. Match 10: Winner of Match 6 vs Winner of Match 7
  2. Match 11: Winner of Match 8 vs Winner of Match 9

Final

  1. Match 12: Winner of Match 10 vs Winner of Match 11

Match list

Knockout fixture — 13 teams
Match no.RoundMatchDateTimeVenue
1Round ITeam 2 vs Team 3
2Round ITeam 4 vs Team 5
3Round ITeam 6 vs Team 7
4Round ITeam 9 vs Team 10
5Round ITeam 11 vs Team 12
6Round IITeam 1 vs Winner of Match 1
7Round IIWinner of Match 2 vs Winner of Match 3
8Round IITeam 8 vs Winner of Match 4
9Round IIWinner of Match 5 vs Team 13
10Semi-finalWinner of Match 6 vs Winner of Match 7
11Semi-finalWinner of Match 8 vs Winner of Match 9
12FinalWinner of Match 10 vs Winner of Match 11

Byes (no match in Round I): Team 1, Team 8, Team 13. Total matches = 12.

How this was calculated

  1. Total Number of Matches = Number of teams − 1 (not including third place match)

    Total Number of Matches = 13 − 1

    = 12

  2. (Number of teams + 1) ÷ 2 = Teams in Upper Half

    (13 + 1) ÷ 2

    = 7

  3. (Number of teams − 1) ÷ 2 = Teams in Lower Half

    (13 − 1) ÷ 2

    = 6

  4. Byes = next power of 2 − number of teams participating

    Byes = 16 − 13

    = 3

  5. Upper Half = (Byes − 1) ÷ 2

    Upper Half = (3 − 1) ÷ 2

    = 1

  6. Lower Half = (Byes + 1) ÷ 2

    Lower Half = (3 + 1) ÷ 2

    = 2

  7. First bye to last team of Lower Half, second to first team of Upper Half, third to first team of Lower Half, fourth to last team of Upper Half; same pattern for remaining byes

    Byes in order go to teams 13, 1, 8

    = 13, 1, 8

  8. Rounds = number of times 2 is multiplied to get the next power of 2

    16 = 2 × 2 × 2 × 2

    = 4

    Note: Not a textbook formula — worked out from the textbook illustrations (4 teams → 2 rounds, 8 → 3, 11 → 4)

SourceCBSE Physical Education Class XII, Unit 1 (PDF)

How the 13 team fixture is drawn

Upper half and lower half

13 is odd, so the upper half gets (13 + 1) ÷ 2 = 7 teams (Teams 1–7) and the lower half gets (13 − 1) ÷ 2 = 6 teams (Teams 8–13).

Byes

Byes = next power of 2 − number of teams = 16 − 13 = 3. 3 is odd, so the upper half gets (3 − 1) ÷ 2 = 1 bye and the lower half gets (3 + 1) ÷ 2 = 2 byes.

Which teams get the byes, and why

The textbook places byes in this order: the 1st bye to the last team of the lower half, the 2nd to the first team of the upper half, the 3rd to the first team of the lower half and the 4th to the last team of the upper half. The remaining byes follow the same pattern, moving inward. For 13 teams:

  1. Team 13 — last team of the lower half
  2. Team 1 — first team of the upper half
  3. Team 8 — first team of the lower half

Teams with a bye do not play Round I. They go straight to Round II.

Round I and total matches

13 − 3 = 10 teams play Round I in 5 matches:

  • Match 1: Team 2 vs Team 3
  • Match 2: Team 4 vs Team 5
  • Match 3: Team 6 vs Team 7
  • Match 4: Team 9 vs Team 10
  • Match 5: Team 11 vs Team 12

Total number of matches = number of teams − 1 = 13 − 1 = 12 (not including a third-place match). There are 4 rounds, because 16 = 2 × 2 × 2 × 2 — worked out from the textbook illustrations, not a textbook formula.

Print or save as PDF

Tap “Print fixture (A4)” and choose “Save as PDF” as the printer to get a 13 team knockout fixture PDF. The bracket prints on one A4 page (portrait).

Questions

How many byes are there in a 13 team knockout fixture?

Byes = next power of 2 − number of teams = 16 − 13 = 3. 3 is odd, so the upper half gets (3 − 1) ÷ 2 = 1 bye and the lower half gets (3 + 1) ÷ 2 = 2 byes. The byes go, in order, to teams 13, 1 and 8. These teams do not play Round I and go straight to Round II.

How many matches and rounds are there for 13 teams?

Total number of matches = number of teams − 1 = 13 − 1 = 12, not including a third-place match. There are 4 rounds, because 16 = 2 × 2 × 2 × 2 (worked out from the textbook illustrations, not a textbook formula).

How are 13 teams divided into the upper and lower half?

13 is odd, so the upper half gets (13 + 1) ÷ 2 = 7 teams (Teams 1–7) and the lower half gets (13 − 1) ÷ 2 = 6 teams (Teams 8–13).

Can I print the 13 team knockout fixture or save it as a PDF?

Yes. Tap “Print fixture (A4)” and choose “Save as PDF” as the printer to get a 13 team knockout fixture PDF. The bracket prints on one A4 page (portrait).