Finals schemes

Various schemes are possible for the semifinals and finals of a sport with three teams per game, such as Zone. Here are several. Click for larger images.

Usually the top team going in to each game has first choice of colour, the second team has scond choice, and the third team gets what they get.

This is the old-style straight Ascension. Note my amusing habit of numbering games backwards.

Ascension requires one game per team (including the three game grand finals series). The average team will play three games.

Strategy: Don't come third.

Advanced Strategy: Choose which of the two teams you are playing now that you would prefer to play again in the next game. Play to make the remaining team come third.

Pros:

• Simple.
• Has a long history, having been used in many US Nationals, Australian Nationals from 2001 to 2004, and many leagues.

Cons:

• There is almost no difference between coming first and coming second. (It does determine whether you have second choice of colour, or no choice at all, in your next game.) This makes it different from the games you have been playing in the main part of the tournament, which is undesirable.
• The ability to easily carry the team you would like to meet again means that the final standings to some extent reflect who chose to carry who, rather than the actual relative skill of each team. This is particularly a problem for the team who go into the semifinals in second place: often their reputation is such that the third and fourth place teams choose to eliminate them. Additionally if two teams whose playing styles and strategies complement each other choose to carry each other, they can together proceed much further up the ladder than either of them could alone. (This happened in 2003, with Willetton and Northbridge A getting a long run together.)

Below is the Skip Ascension as used in 2005 and 2006. In this version, the #1 team gets a bye straight through to the grand finals. Additionally, the n-2th team (in this case, the 9th team) gets a bye through the first game.

Skip Ascension also requires one game per team (including the three game grand finals series), and the average team will play three games.

Below is a slightly different Skip Ascension: at the top, team 1 does not get a bye: they must play one game to get to finals. This means that team 2 plays only one game to get to finals instead of two. Additionally, the n-2th team does not get a bye: they are in the very first game. (Of course, you could draw two other similar grids, with a bye for team 1 but not for team n-2, or vice versa.)

(Also diagrams for Skip Ascension regular and Skip Ascension Irregular, which have the other two possible combinations of start and end.)

Strategy: Place as high as you can.

Advanced Strategy: If there is a team you would rather not see in a future game, play so as to make them come third. (But in doing this, you must be careful not to compromise your ability to come first.)

Pros:

• Skip Ascension has different outcomes for first, second and third, making it more like the games played in the main part of the tournament.

Cons:

• The diagram has crossing lines, meaning that a team may place above you in the final standings, without you having played them. For example, if a team lose their first game, the winner of the previous game will place ahead of them.
• Skip Ascension still suffers from the carrying problem in the game immediately before finals, which is of concern to the top-ranked team in that game (which might be team 1 or team 2, depending on which flavour of Skip you are using).

Below are two versions of Format D. The difference between the two is just how the games are arranged: in the first one, they are arranged to make it easy to understand how it conceptually works; in the second, they are arranged to avoid back-to-back games (except between the first and second games).

For n teams, Format D requires (n - 1) * 1.5 games, including finals. That's just under 1.5 games per team. The average team will play 4 or 5 games.

(Also diagrams for 5, 6, 7, 8, 9, 10, 18, 27 teams; Excel workbook.)

Format D can be seen as having three roads: high, middle and low. Your first game will be on the high road. As long as you continue to take firsts, you will remain on the high road. When you lose a game, you will drop to the middle road. There is no way up from the middle to the high road. When you lose a second game, you will be on the low road, from which there is again no way up. When you lose your third game, you are eliminated.

Strategy: Come first.

Advanced Strategy: In a high road or middle road game, you may voluntarily lose in order to hand first place to a team you would like to meet in a future game. This is risky, as every time you drop to a lower road, you are at more risk of being eliminated. However, some argue that this risk may be worth taking in the last high-road game before finals (game I on the above diagrams), because it pushes a team of your choice into the finals.

Pros:

• Format D is unusual in that most of the games are not back-to-back games: there is no team in this game that will also be playing in the very next game. This allows games to be scheduled closer together: generally one 12-minute game every 15 minutes, instead of one every 20 minutes. This means that even though Format D has many more games than Ascension or Skip, it requires only a little more time: Ascension or Skip get 20 minutes longer for each team added, whereas Format D gets 45 minutes longer for each two teams added, which is to say 22.5 minutes longer per team.
• Teams must lose three games to be eliminated (except the bottom two teams going in). This avoids issues with teams coming in cold, and issues with one-off aberrations, such as bad ref calls, bad packs, etc.

Cons:

• There is little difference between second and third place, which is not as bad as Ascension (with little difference between first and second), but is still undesirable.
• It takes slightly longer to run than Ascension or Skip.
• There are games in which two teams are eliminated. This is undesirable because if a team misses first place in such a game by just a few points, they will feel that they were robbed by a bad ref call, a bad pack, etc.
• The advanced strategy of deliberately throwing a game to advance another team, to the extent that it is real, is a bad thing.

For n teams, Two Track requires n + 1 games, including finals. The average team will play 3 games.

Two Track can be seen as being like Format D with the bottom road removed. If you keep taking firsts, you stay on the high road. Once you take a second or third, you drop to the low road. There is no way back up from the low road to the high road. Once you lose a second game, you are eliminated.

Strategy: Come first. In games A and I, come first or second.

Pros:

• Like Format D, most of the games are not back-to-back games: there is no team in this game that will also be playing in the very next game. This allows games to be scheduled closer together: generally one 12-minute game every 15 minutes, instead of one every 20 minutes. This means that for odd numbers of teams or for large numbers of teams, it requires slightly less time than Ascension or Skip.
• Teams must lose two games to be eliminated (except the bottom one or three teams going in). This decreases issues with teams coming in cold, and issues with one-off aberrations, such as bad ref calls, bad packs, etc.

Cons:

• There is little difference between second and third place, which is not as bad as Ascension (with little difference between first and second), but is still undesirable.
• There are games in which two teams are eliminated. This is undesirable because if a team misses first place in such a game by just a few points, they will feel that they were robbed by a bad ref call, a bad pack, etc.


System S

By shade. System S requires nearly two games per team. The average team will play 6 games.



System S can be seen as having a high road and a low road. Note the double game just before finals: just as finals is a three-game series, this semifinal game is a two game series. Colours are chosen such that no team plays the same colour twice. Scores are summed over the two games. This feature can be added to any semifinals scheme.

Strategy: On the high road, come first. On the low road, place as well as you can.

Advanced Strategy: On the high road, deliberately lose in order to hand first place to a team you would like to meet in a future game. This is risky, and has a fairly low return on investment: you might have wound up facing that team anyway. On the low road, decide which team you would not like to face again, and make them come third, while being careful not to compromise your ability to come first. In the two-game series before finals, decide which team you do not wish to advance, and make them come third.

Pros:

• There's a second chance: nobody washes out after one game.
• Some games have different outcomes for first, second and third, making them more like the games played in the main part of the tournament.

Cons:

• It takes approximately twice as long to run as Ascension or Skip.
• The high-road games have a different shaped arrow coming out of them to the low-road games. This makes the scheme more complicated, and requires different strategy in different games.
• There is a game where two teams are eliminated.
• The various advanced strategies, to the extent that they are real, are undesirable.


Many other semifinals schemes are possible. I allege that the following properties are good:

• Should be simple to understand.
• Should be as regular as possible.
• Should have a smooth increase in difficulty over the whole ladder.
• As much as possible all the arrows on the diagram should be the same shape (as with Ascension, Skip and D, but not with S, for example).
• Should have different outcomes for each of first, second and third.
• Should make carrying difficult because it requires games the carrying team does not play in to come out a particular way.
• Should make carrying dangerous because a team has to run a substantially more risky game plan to effect the carry.
• Should not feature games in which two teams get eliminated.
• Should not feature crossing arrows on the diagram, as this allows a team to place ahead of another team without beating them.
• Should produce a result which accurately reflects the relative skills of the teams: better teams should be ranked higher.
• Should not allow any team (barring the bottom few) to get eliminated in a single game.
• Should play in a practicably short amount of time.
Many of these goals contradict each other: all schemes, therefore, are compromises.

Colour Choice

As mentioned above, in all these systems, the top team going in to each game has first choice of colour, the second team has scond choice, and the third team gets what they get.

In arenas where all three colours are approximately even, this makes little difference. But in arenas where colour matters a lot -- for example, a particular colour almost always wins, or a particular colour almost always loses, it makes a major difference, and upsets become rarer. For an example of this, see the semifinals of the New Zealand Invitational 2008, in which blue lost every game but one, and every team came out of the semifinals with the same rank they went in (though WA and VIC swapped places in the grand final).

If this is regarded as undesirable, the arena itself can be modified to be more even. Another approach would be to apply a handicap: if a particular colour always wins, multiply that colour's score by 0.9; if a particular colour always loses, multiply its score by 1.1. Keep increasing these multipliers until all colours win approximately evenly, or until teams make less consistent choices of colour in semifinals games. But such tuning should be done before semifinals day, and any multipliers should apply through the whole tournament, not just in semifinals games, in order that teams are continuing to play games that are as similar as possible to the games they've been practising through the main part of the tournament.


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