11 March 2006
©2006 by John P. Pratt. All rights Reserved.
The Swiss system tournament, popular in chess, could be fun for sports also.
A tournament which has been very popular with chess players for the last century is called the Swiss style tournament.^{[1]} It has many features which make it attractive for a variety of team sports, such as basketball. Those features include:
Here's how the new tournament works. The entries all play the same number of matches, in "rounds." If there is an odd number of entries, then another imaginary entry named "Bye" is entered as the lowest ranked, which loses every game.^{[2]} Three rounds are needed for five or six entries, four rounds for up to 12, five for up to 24, with an additional round needed for each doubling of the number of entries.^{[3]}
All of the teams are ranked according to some sort of preliminary ranking, which does not have to be very accurate. If no such initial ranking is available, the tournament works well enough with random seeding, and always correctly determines the winner. The top half of the entries are paired with the bottom half, such that the top entry plays the highest in the bottom half, the second in the top plays the second in the bottom and so on. After the first round, each of the winners gets one point and the losers get zero. In the case of tied games, each team gets half a point.
Let's look at an example of ten teams, each named for an animal, with the first letter of the name representing how good the team really is. For example, the Apes are the best team (starting with "A") and the Jackals (starting with "J", the 10th letter) are the worst team. Suppose that the preliminary ranking was good enough to get all of the teams to with three places of where they really should be. For example, the Apes should be ranked first, but they were entered as fourth. Here is how the first round might look.
Team  Team Name  Round 1 vs. Wins 


1  Bears  6  1 
2  Dogs  7  1 
3  Foxes  8  1 
4  Apes  9  1 
5  Hares  10  1 
6  Colts  1  0 
7  Eels  2  0 
8  Jackals  3  0 
9  Gators  4  0 
10  Ibises  5  0 
The first round is supposed to be a sort of "warmup" round where all of the top half teams are expected to win. In this case, that happened, but just barely. The Bears had to play the Colts, the Dogs played the Eels, and the Hares played the Ibises, which are all really next to each other in ability. Thus, while the tournament tries to have widely separated teams play in the first round, it won't happen if they are not ranked well. If there is an upset, the tournament handles it well as we will see in the next rounds.
In the second round, the attempt is made to pair all of those with the same score in the same manner. That is, the top half of all the entries with one point are paired against the bottom half that have one point.^{[4]} If there is an odd number of teams, then the bottom team with 1 point plays the highest team with a half point (if any), or zero points. The process is repeated for the lower groups. The resultant pairings and scores are shown for the example for Round 2.
Team  Team Name  Round 1 vs. Wins 
Round 2 vs. Wins 


1  Bears  6  1  3  2 
2  Dogs  7  1  4  1 
3  Foxes  8  1  1  1 
4  Apes  9  1  2  2 
5  Hares  10  1  6  1 
6  Colts  1  0  5  1 
7  Eels  2  0  9  1 
8  Jackals  3  0  10  0 
9  Gators  4  0  7  0 
10  Ibises  5  0  8  1 
First look at the pairing. Teams 5 and 6 were paired first because there was an odd number with 1 win, so the lowest team with a win (the Hares) were paired with the highest team with no wins (the Colts). Then the top half of the teams with one win were paired against the bottom half with one win, and similarly for zero wins. The final column shows the total number of wins after Round 2 (remember that the names of the teams tell who will win). After repeating the process for Round 3, the score sheet looks like this:
Team  Team Name  Round 1 vs. Wins 
Round 2 vs. Wins 
Round 3 vs. Wins 


1  Bears  6  1  3  2  4  2 
2  Dogs  7  1  4  1  6  1 
3  Foxes  8  1  1  1  10  2 
4  Apes  9  1  2  2  1  3 
5  Hares  10  1  6  1  7  1 
6  Colts  1  0  5  1  2  2 
7  Eels  2  0  9  1  5  2 
8  Jackals  3  0  10  0  9  0 
9  Gators  4  0  7  0  8  1 
10  Ibises  5  0  8  1  3  1 
Again, look at the pairing, which now becomes more tricky. We have to repeat the process and also make sure that no two teams have played each other before. We begin at the top and work down. There are only two teams with two points, so they are paired (the Bears and the Apes, the top two teams). There are six teams with one point, and ideally the top three are to be paired against the bottom three. That works for the first pair, namely the Dogs and the Colts. At first it looks like it will work for the second pair (the Foxes and Eels), but that would leave the third pair to be the Hares and the Ibises who already played each other in the first round. Thus, the Foxes are instead paired with the next team down, being the Ibises. That leaves the Hares to be paired with the Eels. Finally the two teams with no wins are paired. If this all sounds complicated then you see why computer programs often do the matching.
Now look at the scores after Round 3. The Apes are already the only team with 3 wins and the Jackals the only team with 0 wins, so the top and bottom teams are pretty much known already. The fourth round will help confirm those positions, as well as help to break the fourway tie for second place. Here's how it looks after Round 4.
Team  Team Name  Round 1 vs. Wins 
Round 2 vs. Wins 
Round 3 vs. Wins 
Round 4 vs. Wins 


1  Bears  6  1  3  2  4  2  7  3 
2  Dogs  7  1  4  1  6  1  10  2 
3  Foxes  8  1  1  1  10  2  4  2 
4  Apes  9  1  2  2  1  3  3  4 
5  Hares  10  1  6  1  7  1  8  2 
6  Colts  1  0  5  1  2  2  9  3 
7  Eels  2  0  9  1  5  2  1  2 
8  Jackals  3  0  10  0  9  0  5  0 
9  Gators  4  0  7  0  8  1  6  1 
10  Ibises  5  0  8  1  3  1  2  1 
Again look at the pairings. Begin with the Apes, only team with 3 points. They cannot be paired with the highest team with 2 points (the Bears) because they've already played, so they are paired with the next team with 2, the Foxes. Then the Bears cannot be paired with the next team with 2 points (the Colts) because they played in the first round, so the Bears are paired with the only other team with 2 points (the Eels). Then the remaining team with 2 points (the Colts) are paired with the highest team possible with 1 point, being the Gators (they've already played both the higher teams, the Dogs and the Hares). There are three teams left with one point. Before pairing them, we note that the Jackals, with 0 have already played two of them (the Gators and the Ibises). Thus, the Jackals must play the Hares, which leaves the Dogs to play the Ibises. If those last two had already played, we'd have to go back to the top and work down again through a different route, such as the Apes playing the next team down, the Colts.
Team  Team Name  Round 1 vs. Wins 
Round 2 vs. Wins 
Round 3 vs. Wins 
Round 4 vs. Wins 
Opp. Wins 
Rank  

1  Bears  6  1  3  2  4  2  7  3  11  2 
2  Dogs  7  1  4  1  6  1  10  2  10  4 
3  Foxes  8  1  1  1  10  2  4  2  8  5 
4  Apes  9  1  2  2  1  3  3  4    1 
5  Hares  10  1  6  1  7  1  8  2  6  7 
6  Colts  1  0  5  1  2  2  9  3  8  3 
7  Eels  2  0  9  1  5  2  1  2  8  6 
8  Jackals  3  0  10  0  9  0  5  0    10 
9  Gators  4  0  7  0  8  1  6  1  9  8 
10  Ibises  5  0  8  1  3  1  2  1  6  9 
Another problem I see with this tournament, is that it doesn't really save all the close games for the last round, as was hoped. For example, the top two seeded teams played numbers 7 and 10 in the last round, and indeed none of the teams played any close competitors, except the Apes and the Foxes, who were seeded third and fourth. But in reality, even the Apes and Foxes were not close in ability.
To me the real problem with this tournament is that the entire basis is not correct, namely that the teams should be ranked by the number of wins, ignoring who was played (except as an afterthought in the case of a tie). So I have proposed another tournament, called the Rapid Ranker which has all of the features of the Swiss system, but has nearly every match in the final two rounds be between competitors who are ranked next to each other. It is described in detail in another article.^{[6]} When this same example is played in the Rapid Ranker, only two teams are out of order by one place (Foxes and Gators). While I believe the Rapid Ranker usually ranks teams better than the Swiss system, it will probably take a detailed statistical study to prove that.