Scorekeeping for a Triple-Elimination Contest

by Howard Rush
Previously published in the MACA Newsletter

Elements of a triple-elimination contest

The triple-elimination system we use is an extension of the double-elimination system in FAI rules. We have quite successfully used this system at the Bladder Grabber for a dozen years or so, and most of the other big contests now use it.

In each round, all contestants who have not yet lost three matches are matched together in pairs. If one person is left over after a given round n, that person will fly his round-n match against an opponent flying in round n+1. That cross-round match is flown after round n is over and before round n+1 starts. If the number of people in round n+1 (not including the guy left over from round n) is odd, then the same guy will fly his round n+1 match against an opponent flying in round n+2. He continues to be a round behind until the first of the following happens:

He suffers his third loss,
He is the last person remaining with fewer than three losses, or
The number of people in a round is even.

If the number of people in a round is even, he flies a match in the round in addition to the cross-round match. He then catches up in the number of matches flown.

The contest progresses until only one person has fewer than three losses. He is the winner. Placing of others is determined by the number of wins minus the number of losses. In the event of a tie for place, the tied contestants fly off using the above procedure, except that only one loss each is allowed during a flyoff (note that several fliers might be tied for a place). Ties occurring during a flyoff are resolved by the above procedure, but again only one loss each is allowed.

Some interesting properties of a triple-elimination tournament

The total number of matches is three times the number of contestants, plus or minus about two matches. This is because everybody loses three times except the winner. Every match results in one loss. A smoothly running AMA contest takes about 6 minutes per match, not counting breaks. Therefore, it takes 3 hours of contest for each 10 contestants.

Half the matches in a contest happen in the first three rounds.

Everybody participates in the first three rounds. It is possible (and preferable) to run the contest continuously for the first three rounds. The second round can be posted before the first round is finished. Indeed, the first three rounds can be posted before the contest begins. In the method shown below, the second round is posted as the first round is getting underway; the third round is posted in the early part of the second round.

Running the first four rounds or so lickety split imposes little burden on the contestants if matches for a given round are posted at least half an hour before the end of the previous round. Because few contestants have been eliminated, each contestant has a pretty long time between his matches. He has plenty of time to prepare for his next match. And, when the next round is posted early, he can see when he needs to be ready for his match.

Judges who are accustomed to contests where they always know at least one of the contestants will inadvertently switch results on score cards in big contests when two strangers are flying each other. Check that contestant names correspond to the expected streamer colors.

Some recommendations on matching policy

As specified by FAI rules, we refrain from matching two guys against each other more than once when it is possible to arrange matches otherwise. Repeat matches may be unavoidable at the end of the contest. Traditionally, we also avoid matching together two guys from the same place (or from whatever other affinity group they choose), although we do give priority to avoiding repeated matches. It seems silly for a guy from Houston to drive a thousand miles from Houston to fly against other Houston guys.

We know of no tidy mathematical method to do this double seeding automatically. The matrix method used at the F2D Team Trials, for example, is random and fair, but does not separate people from the same affinity group, nor does it avoid repeat matches after the first three rounds. The following method facilitates double seeding and gives flexibility in scheduling the sequence of matches. I don't know how to write a computer program to do this, but a person can do it by fiddling with the matches a little.

Carrying out the procedure outline herein requires a somewhat mathematically minded person who has studied the procedure before the contest. An unprepared person will typically impose constraints on the procedure until he can cope with it. The result is a substandard contest.

The mechanics of operating the scoreboard

Get a big board into which pins can be stuck. A 4' x 8' sheet of plywood works, but Celotex or cork is better. Matches are posted by pinning pairs of 3" x 5" cards (or better yet, 4" x 6" cards) to the board in columns denoting the sequence of matches.

If you are alternating between two flying circles, put an even number of pair of cards in each column (except, of course, the last column if the total number of matches in the round is odd).

Make room on the board to have two rounds posted simultaneously. Initially the first round will be on the left half of the board and the second round will be on the right. When the first round is finished, you will replace it on the left side of the board by the third round.

Assign one 3" x 5" card to each contestant. Put the contestants name in the upper left corner of the card. Colored cards are a handy way to sort people by affinity group, e.g., green for the Northwest, brown for Southern California. If there are more groups than there are card colors, you can write group names on the backs of cards.

Now we shall draw and post the first round. Shuffle the cards. Select at random pairs of cards of different colors. This ensures that matches will be between contestants from different groups. Each pair is a match. Write the name of each contestant's first-round opponent on the left edge of the contestant's card.

Post the pairs of cards on the board. Avoid having two consecutive matches involving guys who are helping each other. It's logistically difficult for them. When you finish posting the first round, announce of the PA that you have done so and that folks should check the matches for conflicts. Typically, some situations occur where you have put people helping each other in adjacent matches, or where you have paired up people from the same affinity group. Move matches around until everybody is happy or until the round begins, whichever occurs first. Then announce over the PA that the board is in the final configuration for the round. Do not alter the sequence after that. You could cause a guy to miss his appointment in the circle and strife will result. People will complain if you move their cards, even if you just tidy the cards up without changing their sequence.

There are two other pieces of paperwork to produce after posting the matches:

Prepare a score sheet with contestant names for each match, and
Make a list of names together with streamer color by each name.

The former goes to the circle marshal. The latter goes to the pull-test posse, which issues a streamer as a pull-test receipt.

When the first round has stabilized, it's time to draw the second round. For this, you use an auxiliary set of cards. This set has on each card only the contestant's name. Draw second-round matches from this auxiliary set of cards. When you draw a pair of cards, check to see if the pair duplicates a first-round match. If so, swap a card with a card from another pair to avoid having the same guys fly against each other a second time. Remember that avoiding repeat matches has precedence over avoiding matching guys from the same town.

Post the second round. Note that if the last match in the first round is in the left circle, the second round should start in the right circle, as shown below.

Announce that the round has been posted, as you did for the first round. You will need to announce it more than once to get everybody to notice; the first round will be in progress and some people will be involved in flights. Again you may need to make some adjustments and to announce the final configuration. You should have the second-round matching finalized at least half an hour before the end of the first round. Now write the name of each contestant's second-round opponent under the name of his first-round opponent on the left side of the contestant's primary 3" x 5" card. The primary cards, remember, are now pinned on the left side of the board in the first-round posting. Prepare score sheets and pull-test list as for the first round.

As completed match sheets come in, put a W to the right of the winner's name and an L next to the loser's name on the winner's card. Put an L to the right of the loser's name and a W next to the opponent's name on the loser's card. As the contest progresses, a row of W's and/or L's will appear at the top of each contestant's card next to his name. A column of the contestant's opponents and how each fared against him will be listed below his name. The figure below shows an example card.

There are different methods for listing winners and losers, and ambiguity is inevitable. Unless you fancy being asked the same question 10^5 times, I suggest you post the example card on the board.

When the first round is finished, take down the primary cards from the board and use them to draw the third round. You can suspend updating the primary cards with second-round results while you are drawing the third round. You can catch up later. Post the third round on the left side of the board where the first round was posted. Announce as before and finalize the matching sequence at least half an hour before the third round begins.

The number of participants may diminish starting with the fourth round, as people become thrice defeated. When a contestant has lost three matches, set his card aside; he's gone.

One typically waits for the final results of the third or later round before drawing the following round from among the survivors. This causes an interruption, which is acceptable if there is plenty of time to finish the contest. For really big contests or contests with a time constraint, you may wish to avoid inter-round interruptions by using the optional trick described below.

Continue for subsequent rounds, continuing to avoid repeat matches and matches between members of the same group. Take breaks between rounds as required. Solicit comments on matching as before and freeze the matching sequence when the first flight of the round begins.

Mr. Robert Burch suggests a poster listing contestant names and their win-loss record. This is a nice touch, but it is an additional effort.

An optional trick

When you draw the matches for the third round, rather than posting the pairs in a random sequence, put the matches containing all the people with two losses in the first part of the round. (This does not affect who flies against whom - only when they do it.) After those people have all flown, you know who are eliminated in the third round and hence the participants in the fourth round. You can then immediately draw and post the fourth round using the auxiliary cards. This process can continue for subsequent rounds until the number of matches without a two-time loser becomes too few to give you time to draw the next round.

If you don't use this trick, you can discard the auxiliary set of cards after the second round.