# Fourteen Teams

## 14. Fourteen Teams

I have yet to find a solution to either the Fourteen or Fifteen team problem. The following solution was devised for the 1991 Central Plains Sectional.

### 14.1. The First Day Of Play

14.1.1. Overview:
In all of the formats described below, the first days' play is as follows:

Start off with three pools: two of five teams, the other pool has four teams. Round-robin within each pool. Eight teams qualify for the next day's elimination. Those eight teams are: two from each of the three pools, a wild-card, and the winner of the "eighth spot play-in." In this way, the top three teams from each pool each have a shot at making the next day's bracket.

The question, of course, is how to figure out which third place team is the wild-card, and which of the other two teams must play the "eighth spot play-in." The following scenario is one such possibility.

First, we recognize that the third place teams in Pools A and B each had to win two games (or, more precisely, finish ahead of two other teams) in order to finish in third place. This is one potential objective reason for letting one of those two teams be the wild card. The other team must play the "play-in" with the third place team from Pool C.

Point differentials are used to choose one third place team from the other. The two third place teams from Pool A and Pool B have four round-robin games, giving them four games' worth of point differentials. Exclude the high and the low, and combine the other two point differentials for a total point differential. (If the teams are still tied, use all four games). This exclusion is based on the fact that it is possible that a team who has to play the top seed (and/or the bottom seed) of the entire tournament may be at an unfair advantage (or disadvantage), and that the top and bottom seeds are in Pools A and B.

The team with the better point differential becomes the wild card, the other teams must "play-in" against the third place team from Pool C.

This solution, of course, leaves a lot to be desired. Chief among the problems are using point differentials with differing opponents. On the other hand, no one gets eliminated by a point differential. The worst that can happen is that a third place team must play against another third place team. At least the fate is in the teams' own hands.

14.1.2. Seeding:
The initial seeds should be as follows:
```                    Pool A          Pool B          Pool C
Seed #1         Seed #2         Seed #3
Seed #6         Seed #5         Seed #4
Seed #7         Seed #8         Seed #9
Seed #12        Seed #11        Seed #10
Seed #13        Seed #14
```
14.1.3. Schedule:
The following is a good schedule to use:

Assume that pool A has five teams, and pools B and C have four teams each.

```                    Fields:  1      2      3      4      5
9:00   B1-B3  B2-B4  C1-C4  A1-A3  A4-A5
10:45  B1-B2  C1-C3  C2-C4  A1-A5  A2-A4
12:30  B3-B4  C1-C2  C3-C4  A2-A5  A3-A4
2:15   B1-B4  B2-B3  C2-C3  A1-A4  A2-A3
4:45                 3B-3C* A1-A2  A3-A5

(* this game is the one between the third place finishers of pools B and C)
```
Note that the round-robin for the two pools of four (B and C) are played over four rounds on three fields. They could be played on three rounds on four fields, but there are two disadvantages of that method. First, it takes up an extra field. Second, most of the teams would be done after the third round while pool A still has two more rounds to go. The schedule above uses less fields and keeps more players around.

Last minute suggestions: take the top team from each pool. They are the top three, and they can play their own round-robin to determine first through third.

Next, determine the next eight teams: the three second and third place teams, the fourth place team from pool A, and one other team. I don't know how to get this other team. Perhaps the last place team with the smallest losing differential between themselves and the second-to-last place team. Or, how about the two teams with the smallest losing differentials play off? The best scenario, of course, is if during the course of the first day, one of the teams decides that they don't want to go on to the next tournament. Whatever is decided, however, make sure all the captains agree on it.

Then, these eight teams go into the double elimination, see Table 8.1.1. Of course, the teams will not be playing for 1st through 8th, like in the table. Take the top five teams from the bracket (1st through 5th in the table), and they are 4th through 8th in this format.

Good luck

### Table 14.1. Fourteen Team Round-Robin Grid

```           1  2  3  4  5  6  7  8  9 10 11 12 13
-  -  -  -  -  -  -  -  - -- -- -- --
1 - 13  2  5  8 11  3  6  9 12 14  4  7 10
2 - 12  1  4  7 10 13 14  5  8 11  3  6  9
3 - 11 14  6  9 12  1  4  7 10 13  2  5  8
4 - 10 13  2  5  8 11  3  6  9 12  1 14  7
5 -  9 12  1  4  7 10 13  2 14  8 11  3  6
6 -  8 11  3 14  9 12  1  4  7 10 13  2  5
7 - 14 10 13  2  5  8 11  3  6  9 12  1  4
8 -  6  9 12  1  4  7 10 13  2  5 14 11  3
9 -  5  8 11  3  6 14 12  1  4  7 10 13  2
10 -  4  7 14 13  2  5  8 11  3  6  9 12  1
11 -  3  6  9 12  1  4  7 10 13  2  5  8 14
12 -  2  5  8 11  3  6  9 14  1  4  7 10 13
13 -  1  4  7 10 14  2  5  8 11  3  6  9 12
14 -  7  3 10  6 13  9  2 12  5  1  8  4 11

1 v  2   3 v 14   4 v 13   5 v 12   6 v 11   7 v 10   8 v  9
1 v  5   2 v  4   3 v  6   7 v 13   8 v 12   9 v 11  10 v 14
1 v  8   2 v  7   3 v  9   4 v  5   6 v 14  10 v 13  11 v 12
1 v 11   2 v 10   3 v 12   4 v  8   5 v  7   6 v  9  13 v 14
1 v  3   2 v 13   4 v 11   5 v 10   6 v 12   7 v  8   9 v 14
1 v  6   2 v 14   3 v  4   5 v 13   7 v 11   8 v 10   9 v 12
1 v  9   2 v  5   3 v  7   4 v  6   8 v 13  10 v 11  12 v 14
1 v 12   2 v  8   3 v 10   4 v  9   5 v 14   6 v  7  11 v 13
1 v 14   2 v 11   3 v 13   4 v 12   5 v  8   6 v 10   7 v  9
1 v  4   2 v  3   5 v 11   6 v 13   7 v 12   8 v 14   9 v 10
1 v  7   2 v  6   3 v  5   4 v 14   8 v 11   9 v 13  10 v 12
1 v 10   2 v  9   3 v  8   4 v  7   5 v  6  11 v 14  12 v 13
1 v 13   2 v 12   3 v 11   4 v 10   5 v  9   6 v  8   7 v 14
```