# BASS tie breaker

BASS is a tie breaker for use in team tournaments?. It was developed in 2006 by Bass for use in the Finnish Team Go Championships (See Tournaments that use BASS below).

BASS is a backronym for "Board wins And SOS Summed".

## Calculating BASS

To calculate the BASS score of a team, you add the number of individual games the team members have won to the team's SOS score.

That is: BASS = Board wins + SOS (with the plus meaning mathematical addition)

## Using BASS

The BASS tie breaker can be used in any team tournament that uses the Swiss tournament system. It is intended to be used as a primary tie breaker.

### Recommendations, for and against

If you think a 4-0 win is better than a 3-1 win, AND if you think any result would be more impressive if gained against the tournament winner, then BASS is currently the best tie break method you can choose for your team tournament. -Bass, 2012-01-14

As always, only apply a tie breaker if you absolutely cannot accept ties. Even in that case, you should first try to choose a tournament format that does not produce ties in the first place. -Bass, who thinks this is the general consensus among the tournament organizers of the world

## Tournaments that use BASS

• Finnish Team Championships, Open division, since 2008 (when there are enough players for Swiss, eg. 2008, 2011 and 2012) (note: in 2008 the board of the FGA decided that the tournament system for the open division be reconsidered each year, aiming at the most sensible tournament format, given the purpose of the tournament and the number of preregistered teams.)

# History and analysis

## Development

The tie breaker was developed by having experienced go referees look at the results of a recent team tournament, and letting them judge the apparent performance of the tied teams. The results were considered to be the reference points for a "fair tie break". Several numerical methods were then tried, until one was found, that in no cases reversed the order of the teams. That method also happened to imitate some thought processes that one of the referees had used to come up with his reference tie break, and so, here we are.

The original research is available (in Finnish only) on the Finnish go wiki.

## Properties

### General Case

In the general case the BASS tie breaker awards higher points for playing well, and higher points for getting the same result against a stronger opponent.

The following results are equivalent in the eyes of BASS:

• A match with N-1 board wins, against a team with M+1 wins
• A match with N board wins, against a team with M wins
• A match with N+1 board wins, against a team with M-1 wins
• ..and so on, in both directions.

This happens to be very nearly the method an average human intuitively uses for judging the performance of a team: "you lost 0-4 against the tournament winners, but they were incredibly strong, what with their winning the tournament and all! If you had played the number two team, you would very likely have been able to win at least one of the games"

### Typical case

A typical format for a team tournament is a 5 round swiss tournament with four members per team.

In this case, the reasoning of the general case does not extend all the way (the opponents' points can range from 0 to 5, but there are only 5 possible match results), so pairing luck in the early rounds will still play a role. The luck factor is, however, much smaller than in other, popular tie breakers:

• When using only SOS as the primary tie breaker, an early pairing against a weak team is punished: very little SOS will be gained from that match.
• When using only the number of board wins as the primary tie breaker, an early pairing against a weak team is rewarded: an easy clean sweep will bring the maximum number of board wins with minimal effort

Similarly, when paired against an unreasonably strong opponent, SOS will lavish the player with undeserved tie breaker points, while Bw will just hand out a "zero".

In both cases, these two biases are, purely by a stroke of luck, in opposite directions. This means that when the two tie breaker scores are summed, the respective biases tend to cancel each other!

### Special case: if all wins are equal, BASS reduces to SOS.

The BASS tie breaker works a lot like SOS, but it also takes into account the additional information available about the nature of the wins. If all the wins happened to be similar (say, 4-0), then BASS reduces to SOS.

```
```
 BASS₁ <=> BASS₂ <=> denotes "comparison". Board wins₁ + SOS₁ <=> Board wins₂ + SOS₂ definition Bw₁(lost) + Bw₁(won) + SOS₁ <=> Bw₂(lost) + Bw₂(won) + SOS₂ separate board wins by their originating matches 0 + N * M₁ + SOS₁ <=> 0 + N * M₂ + SOS₂ No board wins in lost games; N = team size, M = number of won matches N * M₁ + SOS₁ <=> N * M₁ + SOS₂ The teams are tied, so M₁ equals M₂ SOS₁ <=> SOS₂ Subtracting N * M₁ from both sides does not affect the comparison

For the purpose of the exercise, one might consider a regular Swiss tournament "a team tournament with one player teams". In a Swiss tournament, SOS is a generally accepted tie breaker. Therefore, at least in some cases, BASS provides very desirable results.

### Special case 2: In a Round Robin tournament BASS reduces to Board Wins

In a Round Robin tournament, all the teams have faced each other. Therefore, any two tied teams will also have identical SOS. (Apart from each other, their opponents are the same.)

Therefore, the only part of BASS that will produce any difference is the Number of Board Wins.

The number of board wins has been a traditional way to break ties in a round robin team tournament, so BASS produces desirable results on the other axis too.

## Evaluation

• Rewards exactly what one wants to reward in a go tournament
• Compatible and consistent with the Swiss system
• Pairing artifacts have a smaller effect than in other popular tie breakers
• Even in a 3-0 or 0-3 situation, the final board result will still count for something
• Fairest known tie breaker (for the best available definition of "fair")