Rapid Ranker Tournament

8 February 2006

The Rapid Ranker Tournament is more fun because all contestants play the same number of matches, all have a closely matched "final" contest, and all are ranked from first to last.

There is a need for a new sports tournament for groups of 5 to 12 contestants. Currently, the three most popular tournament formats are the single elimination, double elimination and round robin. The problem with the first two is that with one or two losses one is done playing, so it isn't fun for those who mostly just want to play and don't really expect to win. The problem with the round robin, where every contestant plays all of the others, is that when there are more than four entrants, it usually takes too many matches to be feasible. Is there a better alternative?

The Rapid Ranker tournament solves these problems by having far fewer matches than a round robin, and yet every contestant plays four matches, instead of only one or two. Moreover, it has all the elements of a fun tournament. There are separate matches for "Gold", "Silver" and "Bronze" medals, whereas the single elimination cannot even determine third place, and the double elimination doesn't always get it right. Moreover, at the end of the Rapid Ranker tournament, all the entrants are ranked from first to last. That can be important to those who would be very pleased just not to finish last. Another fun feature is that half of the entrants win their last match, whereas in a single or double elimination match, only the top player wins the last match. All of the rest feel like "losers."

Like all tournaments, this tournament works best if seeded well with an approximate initial ranking of all contestants. It is that preliminary ranking that helps make the small number of matches successfully rank everyone. If the initial ranking is perfect, then #1 will have beaten #2, who beat #3, who beat #4, and so on all the way to the bottom. Thus, everyone gets to play competitors of similar ability, and yet everyone also has a chance to win the gold in case the seeding was totally wrong.

How the Rapid Ranker Works

So how does this new miracle tournament work? Let us look at an example with ten entries. Let's suppose the tournament is for teams whose names alphabetically just happen to reflect how good they are. In other words, the Apes, Bears, Colts, Dogs, Eels, Foxes, Gators, Hares, Ibises and Jackals are both in alphabetical order and also their true ranking order.

First, list all the contestants in order of their preliminary ranking. Let's suppose that it is such that none is in exactly the right place, but that all are within three places of where they really should be. Figure 1 shows the teams listed in the preliminary ranking order in the Rapid Ranker form for the ten entries.

Round 1 vs Round 2 vs Round 3 vs Round 4 vs Final Rank

1. Bears 3 1. 9 1. 4 1. 2 1.

2. Dogs 4 2. 7 2. 3 2. 1 2.

3. Foxes 1 3. 6 3. 2 3. 4 3.

4. Apes 2 4. 5 4. 1 4. 3 4.

5. Hares 9 5. 4 5. 10 5. 6 5.

6. Colts 8 6. 3 6. 7 6. 5 6.

7. Eels 10 7. 2 7. 6 7. 8 7.

8. Jackals 6 8. 10 8. 9 8. 7 8.

9. Gators 5 9. 1 9. 8 9. 10 9.

10. Ibises 7 10. 8 10. 5 10. 9 10.

Figure 1. The Rapid Ranker with teams listed in the preliminary ranking order.

**Figure 1. The Rapid Ranker with teams listed in the preliminary ranking order.**
Round 1	vs	Round 2	vs	Round 3	vs	Round 4	vs	Final Rank
1. Bears	3	1.	9	1.	4	1.	2	1.
2. Dogs	4	2.	7	2.	3	2.	1	2.
3. Foxes	1	3.	6	3.	2	3.	4	3.
4. Apes	2	4.	5	4.	1	4.	3	4.
5. Hares	9	5.	4	5.	10	5.	6	5.
6. Colts	8	6.	3	6.	7	6.	5	6.
7. Eels	10	7.	2	7.	6	7.	8	7.
8. Jackals	6	8.	10	8.	9	8.	7	8.
9. Gators	5	9.	1	9.	8	9.	10	9.
10. Ibises	7	10.	8	10.	5	10.	9	10.

The number listed after the team name is the current rank of the opponent to be played. Thus, the top ranked Bears will first play team #3 which is the Foxes. Similarly, the Dogs will play the Apes in Round 1. After the teams play, if the lower team wins, then the two teams trade places on the chart. In this example, after the first round, the Apes beat the Dogs ("A" precedes "D" in the alphabet), so at the beginning of Round 2 they have swapped places.

Round 1 vs Round 2 vs Round 3 vs Round 4 vs Final Rank

1. Bears 3 1. Bears 9 1. 4 1. 2 1.

2. Dogs 4 2. Apes 7 2. 3 2. 1 2.

3. Foxes 1 3. Foxes 6 3. 2 3. 4 3.

4. Apes 2 4. Dogs 5 4. 1 4. 3 4.

5. Hares 9 5. Gators 4 5. 10 5. 6 5.

6. Colts 8 6. Colts 3 6. 7 6. 5 6.

7. Eels 10 7. Eels 2 7. 6 7. 8 7.

8. Jackals 6 8. Jackals 10 8. 9 8. 7 8.

9. Gators 5 9. Hares 1 9. 8 9. 10 9.

10. Ibises 7 10. Ibises 8 10. 5 10. 9 10.

Figure 2. The standings as Round 2 begins.

**Figure 2. The standings as Round 2 begins.**
Round 1	vs	Round 2	vs	Round 3	vs	Round 4	vs	Final Rank
1. Bears	3	1. Bears	9	1.	4	1.	2	1.
2. Dogs	4	2. Apes	7	2.	3	2.	1	2.
3. Foxes	1	3. Foxes	6	3.	2	3.	4	3.
4. Apes	2	4. Dogs	5	4.	1	4.	3	4.
5. Hares	9	5. Gators	4	5.	10	5.	6	5.
6. Colts	8	6. Colts	3	6.	7	6.	5	6.
7. Eels	10	7. Eels	2	7.	6	7.	8	7.
8. Jackals	6	8. Jackals	10	8.	9	8.	7	8.
9. Gators	5	9. Hares	1	9.	8	9.	10	9.
10. Ibises	7	10. Ibises	8	10.	5	10.	9	10.

If it seems unusual to have the top four teams play each other in the first round, the reason is to prepare for the big second round which determines the "final four." To give lower teams a chance to make the finals, they should play against the lower teams of the top four. In this case, in Round 2 the #5 Gators get to play the #4 Dogs and the #6 Colts get to play the #3 Foxes to get into the Final Four. So the first Round is preparation for the second. Any of the top five teams can lose the first round and still go on to win the tournament. Notice also that the pairings are all listed in advance, so a team can see who they will be playing in the future, and just who they have to beat to win.

Another feature is that the top four of Round 3 comprise the "Final Four." That is the "Silver Medal" round, in that both of the winners of those matches are guaranteed at least Second Place. Then the top match in Round 4 is the "Gold Medal" match, and the second match is the "Bronze" for third place.

Figure 3 shows how the tournament ends, with all teams having been correctly ranked, except for the Foxes and Gators being swapped. Often the final ranking is perfect, but sometimes the ranking will have one or two off by one place. Overall, it appears to rank about the best possible for so few matches. Occasionally, two contestants will have to play each other twice, but not nearly as often as in a double elimination format. Another similar tournament in which the competitors never play twice but are not ranked so well is the Swiss Tournament.

Round 1 vs Round 2 vs Round 3 vs Round 4 vs Final Rank

1. Bears 3 1. Bears 9 1. Bears 4 1. Bears 2 1. Apes

2. Dogs 4 2. Apes 7 2. Apes 3 2. Apes 1 2. Bears

3. Foxes 1 3. Foxes 6 3. Colts 2 3. Colts 4 3. Colts

4. Apes 2 4. Dogs 5 4. Dogs 1 4. Dogs 3 4. Dogs

5. Hares 9 5. Gators 4 5. Gators 10 5. Gators 6 5. Eels

6. Colts 8 6. Colts 3 6. Foxes 7 6. Eels 5 6. Gators

7. Eels 10 7. Eels 2 7. Eels 6 7. Foxes 8 7. Foxes

8. Jackals 6 8. Jackals 10 8. Ibises 9 8. Hares 7 8. Hares

9. Gators 5 9. Hares 1 9. Hares 8 9. Ibises 10 9. Ibises

10. Ibises 7 10. Ibises 8 10. Jackals 5 10. Jackals 9 10. Jackals

Figure 3. The Rapid Ranker often correctly ranks all entries.

**Figure 3. The Rapid Ranker often correctly ranks all entries.**
Round 1	vs	Round 2	vs	Round 3	vs	Round 4	vs	Final Rank
1. Bears	3	1. Bears	9	1. Bears	4	1. Bears	2	1. Apes
2. Dogs	4	2. Apes	7	2. Apes	3	2. Apes	1	2. Bears
3. Foxes	1	3. Foxes	6	3. Colts	2	3. Colts	4	3. Colts
4. Apes	2	4. Dogs	5	4. Dogs	1	4. Dogs	3	4. Dogs
5. Hares	9	5. Gators	4	5. Gators	10	5. Gators	6	5. Eels
6. Colts	8	6. Colts	3	6. Foxes	7	6. Eels	5	6. Gators
7. Eels	10	7. Eels	2	7. Eels	6	7. Foxes	8	7. Foxes
8. Jackals	6	8. Jackals	10	8. Ibises	9	8. Hares	7	8. Hares
9. Gators	5	9. Hares	1	9. Hares	8	9. Ibises	10	9. Ibises
10. Ibises	7	10. Ibises	8	10. Jackals	5	10. Jackals	9	10. Jackals

How to Divide up the Contestants

The ideal number of entrants for the Rapid Ranker is eight, and the maximum is twelve. There are separate tournament pairing forms for six, eight, ten and twelve contestants. If there are five, seven, nine, or eleven contestants, then use the form with one more entry, with the lowest ranked player being a "bye." Larger groups should be broken into "divisions" of nearly equal numbers, with at most one division having an odd number of entrants. Thus, twenty contestants should be broken into two groups of ten. If a grand champion of the divisions is wanted, then the top two from each division could have a play-off. Avoid having five or six in a group if possible; the tournament works better if 18 are divided into 10 and 8 rather than three groups of 6, and the play offs between divisions are also simplified.

Conclusion

The Rapid Ranker Tournament appears to be an excellent choice for 5-12 contestants because it ranks them well and they all play the same number of matches. For a more detailed comparison of this tournament to others and more about the pairings for each number of entrants, see my article, "The Rapid Ranker Tournament is Fun."