I have a group of kids in a competition in which we plan to award first, second and third place prizes. The nature of the competition is head-to-head contests with no way of determining seeding. What form of tournament is the more fair to determine 1st, 2nd, and 3rd – double elimination or round robin?
I believe either format will determine 1st and 2nd place correctly, but somehow intuitively I feel that round robin (every kid plays every other kid) is a bit more fair than double elimination. I also can’t figure out how to get a 3rd place winner out of a double elimination format. The tournament director is intransigent about using double elimination because “we’ve always done it that way.”
So, how do I determine 3rd place from double elimination? And does anybody have a strong argument or, better yet, a reference that shows the superiority of one format over the other?
Pros of double elimination:
-Fast way
-Certanity of winner
Cons:
-Mismatched players usually means that good people may be unfairly own3d at the start of the rounds and not get to their “true” round. Though this can be solved with an initial tournament to see where people are.
-There can only be a third place with a round robin round just before the final winner is determined. Even then it can put itself into an infinite loop.
Pros of round robin:
-Opportunity to play everyone, thus your have a truer measure of how you stand up versus others
-Can have as many “places” as you want
Cons:
-It’s rather slow, espcially if there are many people. People take performance hits after every game they play (because they play hard), and it’s not right if they wear themselves down while another player with a different state of mind is really on a roll and rolls them over.
-Slow determination of winner that’s not all that different from double elimination
Personally I’d go with double elimination. There’s a greater sense of competition because everyone must play their best on a single, focused round in which only one gets out alive. And the honor of winning a double elimination tournament is good-that means you haven’t lost once, or didn’t lose more than the 2 others you played during the roundrobin determination of third place round
To determine 3rd place in a double elim, the losers of the semi-finals compete. The winner of this round takes third, loser takes fourth. This competition usually takes place between the semi-final round and the final round, which has the benefit of allowing both finalists to rest before “the big one”.
You should avoid double-elimination unless the number of participants is a power of 2(4,8,16, etc) and you have plenty of time. A possibly better format is consolation, where the first round losers and 2nd round losers who got a first round bye are feed into the consolation bracket.
Round robin tournaments may have a problem if some of the kids loose the first 3,4,5 times. They will quit before completing the round, fouling every up.
If the number is a multiple of 8, then you can have various divisions, red, blue etc and combine some form of round robin(two groups of 4), then have the kids play their counterpart in the other group. The process allows many kids to be the best, second best etc without having a single overall winner or loser.
In a double elimination tournament, the third place winner is the guy who loses to the winner of the losers’ bracket. Sounds complicated, but in a D.E. you will have a winner of the winners’ bracket, who then waits to play the winner out of the people who have lost a game already. The last game of the losers’ bracket will determine who gets to go on and play the winners’ bracket winner, and the loser of that game is third place. Fourth place is the guy who loses the next-to-last game in the losers’ bracket. Draw it out on a diagram, it’ll be obvious.
A round robin is fairer, but will take more games, and you have to decide how a winner is determined. You don’t have the problem in a D.E. that it matters how the players are arranged on the diagram initially. That’s what seeding takes care of in some tournaments, but it’s not practical for kids.
If there are points in your contest, or times, then you could cluster the kids in “divisions” of four, and play three rounds in round-robin style as they do at Hogwarts. The player in each division with the best record at the end of three rounds (or in case of a tie, the player with the highest total score or shortest total time) progresses to the second phase. This could be interesting for kids, if the games played are fun for spectators–kids who have been eliminated will want to cheer for (or possibly against!) the winner of “their” division.
If you don’t have enough kids to form groups of four (let’s say that you had 20 kids playing: that’s five divisions, but that means five champs), then you can have the five winners, and the next three highest scores. You could arrange these in a seed structure, or just continue with three more rounds to determine which two players will compete for first, and which two will compete for third.
So, if we have twenty kids (name them Alfred through Ted for simplicity), then your tournament field might look like this to start:
ABCD
EFGH
IJKL
MNOP
QRST
B, G, J, P, and Q each win their bracket, but C,M, and T had very high scores as well (you might make it a prerequisite that any player who has beaten his division winner is considered for a wild-card slot in the second round before the general field is considered for those slots). So your post-season/second round looks like this:
BCMP
GJQT
(this maximizes the number of “grudge matches” – but I don’t think you can ever eliminate them)
And when Bob and Ted win their post-seasons (“the pennant”) then they go on to play for first and second. Before their match, Paul and Quentin, who each placed second in the playoffs, play for third.
Erg. I neglected to solve the problem of populating the first round. If the number of kids is 4n, proceed as above. 4n + 1, find a younger or older kid (someone’s brother who’s along for the tourney?) and mix him or her into one of the big groups with the understanding that he is “ballast” for that group. You now have 4n+2. 4n + 2, have the spare play a “best of three” while everyone else plays their three. 4n+3, have the spare three play round-robin (AvB, BvC, CvA) and solve as above.
Well, here’s an entirely different method, called Swiss. Set up a number of rounds, say, 5. In each round, competitors are paired based on their records so far. First round, everyone is randomly paired. Second round, pair up the 1-0 kids with 1-0 kids, and 0-1 with 0-1, and so on. The idea here is that you will play against someone with a similar skill level each round.
After five rounds of this, you can take the 8 or 16 players (depending on overall numbers) with the best records, and then do single elimination playoffs, generally seeding the competitors according to their records.
This method is very fair across the board, and doesn’t take as much time as round robin. You can also account for people dropping out between rounds very easily.
The thing about round robin is that it can get out of hand quickly. Having everyone play everyone else is fine when you have 4 or 6 players. But, if you have 20 players, it will take all day for everyone to play all 19 opponents. And, by the 10th or so match, everyone knows who’s gonna finish in the top 5 and who isn’t going to have any wins at all. And, of course, match #17, which pairs the kid with the 14-2 record against the kid with the 1-15 record, is going to be a major blowout and someone might actually get hurt. At minimum, both players will have a “who cares?” attitude.
The Swiss format, described above, fixes a lot of tournament problems.
