Double Elimination

Post by **BeligerAnt** » Mon Oct 23, 2006 9:40 pm

The double elimination scheme used at AWS21 seemed very popular. Some people want all AWS's to be run using double elimination. However, it does merit some discussion...

Double elimination works really well, but ONLY for 2^n (2, 4, 8, 16, 32, 64...) entrants. We were lucky this time. If we want to use double-elim, how do we ensure a field of 16/32/64 every time?

I DO LIKE double elim, but when the number of robots actually starting isn't usually known until about 11:00 on the day of the event, it is hard to plan an exact competition.

I don't really like byes much at all. Although technically fair, they do deprive people of first-round fights. This means they go in "cold" to a second-round fight, possibly against someone who has already won one fight. With double elim, byes always propagate to the second round, albeit in the losers bracket.

This needs some serious thought. Some workable solutions would possibly be extremely unpopular.

For instance, we could limit multiple entries so that everyone that enters is only guaranteed one entry. If we get 32 different teams entering, then that's it, everyone enters only one robot. If we get less than 32 teams (most likely) then we allocate the remaining places fairly between the teams. This would mean that people with 4 robots may not be able to enter all of them in the main AWS competition. Any robots refused entry could be "standbys" to replace the inevitable "no-shows" or "failed to starts".

Alternatively, we could use some kind of qualification criteria to end up with a field of the right size. We could allow the top robots from the previous AWS to be "seeds" that automatically qualify and then have a short qualifying competition to arrive at the correct total number. This could be a mathematical nightmare, trying to get from any number of entrants to the required number. Also it raises several questions like "Is it fair?" and "What if the previous winner doesn't enter this time?".

I'm sure ther are other schemes, pleae post you suggestions.

Discuss...

Rhys · Post by **Rhys** » Mon Oct 23, 2006 10:17 pm

The best thing about double elimination is that you get 2 attempts. Unfortunatly, the 2 methods you have suggested remove this advantage. I don't think the first idea will be too popular, as most of us have more than a couple of ants, and want them all to compete. Also, if we end up with 33 or 34 ants, it would be unfair to ask any one or two teams to drop one of their ants, when others can enter all of theirs. Some people may end up having zero bites of the cherry, as opposed to the 2 they should get with double elimination.

I like your second idea lot more, but it still has a few flaws. Firstly, we'd have to find a way to seed robots and agree on it. However, the seeding system will clearly disadvantage, and possibly discourage newcomers. They could go all the way to an event, just to lose their qualifying match and be out, therefore missing the point of double elimination. We could have double elimination qualifying, but the whole vicious cycle would start again.

I think if we had seedings for all current ants, and put the highest seeded 24 (or 12, depending on how many attend) straight into the competition, and leave 8 (or 4) spaces for the qualifying, this would work. All we'd have to do then is find a fair qualifying format.

Leagues could be used to quickly and fairly give us qualifiers. Depending on numbers, we could have 1, 2, 4 or 8 leagues, where the top 4, 2 or 1 ant could go through. This would be done fairly quickly, and would mean that everyone gets at least fights.

The major problem would be seeding people. nobody can really have the ultimate say as no-one is independant.

EDIT: Another problem with the seeding system is that people like Josh and Dave, who turn up to different events with different ants will be endlessly qualifying, whilst us consistent types would stay where we are.

Andrew_Hibberd · Post by **Andrew_Hibberd** » Tue Oct 24, 2006 11:21 am

We where very lucky with the numbers on saturday. Would it not be possible (and i didn't want to be the one to say it) have melees in the first round. This would make it more complicated, but have 3 robots in the first round, in which 1 goes to the winners brakcet and the 2 lossers go into the lossers side. As long as they had a 1 on 1 in the second round then it seems fair.

The only other thing i can think of is clashes. If a team has 4 entries then one entry should be in each quater of the first round. However this meant that pete w had to fight defiant and combat ant later. This can't really be avoided unfortunatly, any suggestions on this?

Seeding is a good idea, but i don't think that it is the best way to run it. The main reason i see is to avoid people being disapointed by not letting there robots compete.

Remote-Controlled Dave · Wed Oct 25, 2006 9:40 am

I think, if a team enters four robots, they should be prepared for the possibility that they would fight their own robot at some point along the line. Obviously, if it's avoidable, then it should be avoided, but if there's no other alternative...I was always prepared to.
I like the idea of seeds too. Could a rough list be worked out judged on a robot's form at the last event, then it could be ammended at the start of the next one, based on whether someone doesn't turn up. If people like me or josh are included in a seeding and then turn up with a different robot, the equivalant one could be seeded.
I see no reason to turn people away though. There's always room for more people and robots. The format of the event should come second to that in my opinion.

peterwaller · Post by **peterwaller** » Wed Oct 25, 2006 1:58 pm

I think I have worked out a way of running double elimination in steps of 4 robots. There are no byes as such but some groups being smaller have one less fight to get to the final. This system also keeps the groups just about in tact so splitting teams amounst the groups should mean no clashes until late on. There is always going to be the problem that people eventually may have to fight themselves the discussion was if the fact that someone was going to have to fight a robot he had already fought was reason enough not to swap. Here are examples for 24,28,32,36 and 40.
http://i109.photobucket.com/albums/n66/ ... 6/nw24.jpg
http://i109.photobucket.com/albums/n66/ ... /nw28b.jpg
http://i109.photobucket.com/albums/n66/ ... /nw32b.jpg
http://i109.photobucket.com/albums/n66/ ... 6/nw36.jpg
http://i109.photobucket.com/albums/n66/ ... 6/nw40.jpg
Green arrow is winner red is loser.
Comments please.

olivers · Post by **olivers** » Wed Oct 25, 2006 2:51 pm

I liked the double elimination as everyone did get at least 2 fights. As has been mentioned above though you need the right numbers and it is a pain to work it out (my head still hurts).

Once thing I did notice was that with more fights like the weekend more robots took damage or had issues compared to AWS20. Seems like added reliability/more parts would be required.

I like PeteW's charts, again however you need the right numbers.

Has anyone been watching the snooker this week? They have little leagues where each player plays everyone in his division, sort of like the World Cup Something like this may work with AWS and may help with the numbers issues. It is easily varied for the number of ants in total and would quickly get it down to 8 or so leading to the quarter finals.

At the weekend we had 32 ants (62 fights), this would mean 8 groups of 4 ants. 6 fights per group (32 fights) then 16 (top 2 from each group) leading to 8 (quarters) then eventually the final so in total 48 fights. We could use seeds too from the previous AWS by putting 1 in each group (seeding is easy to do by looking at previous results).

Also by doing this everyone would get at least 4 fights, if you had a spinner in your group you could run away and lose but still possibly go through.

Thinking outside of the box.

Post by **BeligerAnt** » Thu Oct 26, 2006 9:11 pm

PeterW there is a bug in the 28-way and 32-way charts:
The loser of round 4 in the winners bracket should go into the losers bracket since that is the first fight they have lost.

Double Elimination

The problem I have with double elimination for difficult numbers is that the random chance of where you are drawn on the "starting grid" affects how many fights it will take you to get to the final. Also, if you lose one fight, the round that you lose in, coupled with your starting position, affects how many fights you then have to win to reach the final.

It is perfectly reasonable (to me) that if you lose a fight on the way to the final it will take you more fights to get there than if you win every fight straight off. That is how the maths has to work because there are more robots in the losers bracket (as time goes on).

For 16, 32, 64 robots it works out that the earlier you lose, the more fights it takes for you to win.
For example (for 16 robots):
If you win every fight, you need 5 wins to claim the title.
If you lose in the first or second round, you need 7 wins.
If you lose in the third round, you need 6 wins.
If you lose in the fourth round, you need 5 wins.

This seems fair to me.

What doesn't seem so fair is the way the maths goes when trying to cope with non-powers-of-2. Losers in the later rounds have to be fed in at odd points in the losers bracket, with extra rounds generated to end up with one finalist from each bracket.

For example, from Peter's chart for 36 entries:
The 24 entries at the bottom of the chart are "well-behaved", requiring 6 wins to go straight through, or 9, 9, 8, 7, or 6 wins if they lose in the 1st to 5th rounds respectively.
However, the 12 entries at the top of the chart are not so fortunate. The top 8 must win 7 fights to go straight through, or 9, 9, 9, 8, 9 or 7 wins if they lose in the 1st to 6th rounds respectively.
The remaining 4 entries require 6 wins to go straight through, or 9, 9, 7, 8 or 6 wins if they lose in the 1st to 5th rounds respectively.
It seems unfair that losing in a later round results in a harder route than losing in an earlier round.

Losing in the 5th round results in a 6-win route if you are lucky, or a 9-win route if you are one of the first 8 on the chart.

I'm not sure it's mathematically possible to get around these problems.

Thanks to Peter for at least having a go and moving the debate forward. 8)

Mini Leagues
Mini leagues sound attractive, but I'm not sure how well they would work for us. The problem is that we don't have points or goal difference. With a 4-way league it is very possible to end up with 3 robots with 2 wins each, especially as we don't realistically have much chance of "draws" occuring.

I think that's enough for now...

Simon Windisch · Post by **Simon Windisch** » Thu Oct 26, 2006 9:40 pm

My brain hurts... I use mini leagues for RRC, and if there's a tie then we just have a melee, but that's just for fun. The AWS is more important, but perhaps if we timed each victory then the fastest robot to win would score higher in the league then the slowest?

Simon

Rhys · Post by **Rhys** » Thu Oct 26, 2006 9:44 pm

Maybe time as a rudimentary gol difference? You'd get more exciting fights, and a bit more stratergy involved. Maybe not....

Nobody has mentioned the obvious about Double elimination yet though. The losers bracket will in theory be easier. Could we possibly see people throwing fights just to get an easier path to the final? It's a possibility. I don't think that's too much of an issue at the moment, as we have "different" robots, rather than good and bad ones. Certain robots have certain strengths against others, so it would be to much of a risk at the moment.

Edit: Damn Simon beat me to it. Need to type quicker

In all seriosuness though, I don't think an of the ideas mentioned here are radically unfair. As long as I get to turn up and compete in similar circumstances to others im happy.

Marco Roberts · Post by **Marco Roberts** » Fri Oct 27, 2006 12:14 am

I have alwase loved double elimination. With your theory off loosing on purpous to get to the esier side, the point is a second chance. What I mean is that you fight too your full potenshal till you are nocked out and then you have a second chance.
The main and only problem that I can see with double elim is spinners. If I personaly was fighting a spinner that was paticlally devestating then I would frow the match to not sustain much damage. This could mean tons of spinners just easily progressing rather then facing a real challenge.