Calling all format wizards

[Hanoi5]

5 teams RR, 1st team advances directly to the final and 2nd and 3rd play for the second spot on the final.

[JanM]

Our District usually has more teams and we use 2 weekends, so I don't have any experience with these numbers and constraints, but I asked Chip and his feeling was that either one session (26 boards) Round Robin to cut to 4 and then semi's and finals (I didn't ask, but I think equal length matches, although that's awkward with your time and other event constraints - are the two losing semi-finalists going to be unhappy that they can't play in the Swiss? Maybe the solution to that is to say if both teams in a semi-final match want to finish it Saturday night or Sunday morning they can) or a full day Round Robin to cut to 2. Of course 5 -> 2 is a steeper cut than you'd like, but if you're using VPs in the Round Robin, and given that there are a reasonable number of boards, I suspect it's not bad. And certainly a 52 board final is a big improvement on only 26.

 

I assume that to suggest adding a day is impossible? Start on Friday with a Round Robin to cut to 4, then decent-length semi's and finals.

[hrothgar]

My natural inclination is to try to establish some benchmarks

 

Gerben has some code that he developed a few years back to simulate the results of a bridge match. I would think that this could be modified for this problem as well

 

Start by running a 52 board head-to-head match between two teams. Try and determine how often the strongest team wins. This gives you a reference point.

 

1. You can't do any better than this

2. Formats that aren't too much worse can be judged to be "good"

 

Start explictly testing different formats and see how they compare to the Gold Standard.

 

The only (really) tricky part of this problem is coming up with a reasonable estimates for the variance in the strength of the various teams entering into the event... (I suspect that this can have a real impact on the format)

[Cascade]

I suspect that round robin to cut from four to two is better than knockout.

 

Most seem to think that round robin is better than Swiss and knockout is essentially a one round Swiss.

[JanM]

Having once played in a Round Robin to cut from 4 teams to 2, I don't like it. The problem is that by the last match (especially if you happen to be playing a double Round Robin, as we were) one team may be mathematically eliminated. It is uncomfortable for that team to be playing the last match when they have no chance to qualify but the team they are playing does. Of course, the mathematically eliminated team will have lost to both other teams by a substantial amount, but believe me, that won't keep the other teams from thinking the eliminated team was "dumping," or at least not playing their toughest, in the final match.

 

Similarly, although it didn't happen in the event in which I played, one team could be a lock to qualify and be able to influence whether its opponent qualified or not (carryover should make it unattractive for a team to want to lose to its final opponent, of course, but there's still some potential worry).

[mycroft]

I've liked the Page Playoff as an alternative to result-seed or winner-choose KOs, but it takes three rounds.

 

If you can do a 1-day RR to 4, then

1-2, 3-4 half-session (1 and 3 get seeding rights)

L(1-2)-W(3-4) half-session (L1-2 gets seed)

final full session (W1-2 gets seed)

 

it might work. What to do about carryover is up for discussion - I hate all of them so far. Worried about dumping on the last round? What about the alternative? If the last round has a team that has to blitz to qualify, and they swing for the fences, and it works, then they get an unusual carryover into their KO match (that they wouldn't get if this match were played the first round of the RR instead of the last).

[Cascade]

I did some simulations.

 

I assumed

 

A uniform spread of teams each 0.5 IMPs per board better than the next team.

 

A Standard Deviation per board of 7 IMPs

 

These are the results I obtained

 

Based on 108 boards (4 more than Justins constraint but it made some numbers easier)

 

27 board per match round robin

 

Best team won 66.45%

2nd best 24.48%

3rd best 7.19%

4th best 1.63%

5th best 0.25%

 

7 board per match round robin to reduce to 4 teams

8 board per match round robin to reduce to 2 teams

56 board final

 

Carryover from progressing teams matches

Best team 65.5%

2nd best 24.54%

3rd best 7.94%

4th best 1.71%

5th best 0.31%

 

Carryover from all previous matches

Best team 67.29%

2nd best 23.99%

3rd best 7.10%

4th best 1.40%

5th best 0.22%

 

9 board per match round robin to reduce to 4 teams

12 board per match round robin to reduce to 2 teams

36 board final

 

Carryover from progressing teams matches

Best team 64.72%

2nd best 24.61%

3rd best 8.36%

4th best 1.94%

5th best 0.37%

 

Carryover from all matches

Best Team 67.92%

2nd best 23.98%

3rd best 6.48%

4th best 1.41%

5th best 0.21%

 

Knockout for stages 2 and 3 with carryover from Head to Head matches

9 board round robin to reduce to 4 teams

36 board knockouts

 

Best team 62.92%

2nd best 25.88%

3rd best 8.80%

4th best 2.20%

5th best 0.43%

 

 

In theory I could tweak the numbers and rerun - its on a spreadsheet.

 

Comments:

 

The numbers were based on 10000 simulations for each scenario.

 

Discarding previous results was bad the best team won around 4-5% less often. Basically it seems you are throwing away information.

 

There wasn't that much difference with different numbers of boards at each stage.

 

Knockout was slightly worse than round robin to reduce from four to two.

 

In case you are wondering about 240 boards at each stage (720 boards in total) were needed to be about 95% sure that the best team would win.

 

I am sure there are many other things including inadequacies that I could comment on.

[TimG]

To me, the important factor is how often the best (and second best) team doesn't survive the round robin stage(s). And, how much a significantly weaker team's entry into a round robin increases the chances of the top team(s) not surviving.

 

I also wonder how the skill distribution affects matters. You had something like -1.0, -0.5, 0, -+0.5, +1.0. What if it was -0.9, 0, +0.1, +0.2, +0.6? Or, -0.6, 0, 0, +0.3, +0.3? How do these change the chances of the best teams not surviving the round robin?