Tournament Mechanics: A Primer

[nealdt]

I was working on a Swiss mode for tio but got stuck on matrix transposes. There comes a point when two players are matched up against each other for the second time using the normal matchmaking rules, and there are very specific ways to deal with that. I unfortunately wasn't able to figure out a way to code the procedure... maybe AltF4 can check it out and lemme know if he has any ideas.

 

[AltF4]

Is Tio open source? If not, I'll see what I can do if you send me the stuff. Matrix operations always get hairy!

I don't think they're identical, but very very similar. Single elimination brackets with consolation matches, and swiss, I mean. Both have log(n) rounds. (binary log) The winners are handled identically, the tournament ends when there is one player with no losses. The losers are a little different, though...

Swiss has log(n) games played by everyone. Single elim with consolation is more complicated... The first round losers will have played 1 round, plus their consolation matches. They will play another bracket within their fellow losers.... Actually the more I think about it... Single elim with consolation is an awefull lot like double elimination without a championship match! I'll think about it more...

EDIT: I made some changes to the "Tournament" article in the SmashWiki. It was fun!

 

[darkNES386]

Hey AltF4Warrior... so my understanding is that the seeded elimination bracket is smartest?

 

[AltF4]

Well, I wouldn't say the smartest. I think I'm going to do some renovations with my first post. I feel like I spent too much time on single elim brackets and not enough time on lesser known mechanics.

You're asking in reference to your online brawl tourney right? It's not so cut and dry as what is *best*. Each of the styles have benefits and drawbacks. But don't think you're stuck doing just one kind of tournament! You can mix and match.

Doing an elimination bracket until you have 8 final players, and then doing a round robin is a good idea, for example.

The idea is to use the different styles in a combination that works best for your situation. If it wasn't clear enough from the first post, then that's my fault. Hopefully I'll get a new version up soon.

 

[darkNES386]

I was just asking if a seeded elimination bracket is wiser over a randomly arranged one. I find all your information organized quite well. There wouldn't be any harm in experimenting with other structures such as the one you suggested. I am a fan of your debating skills and I respect any other light or information you can shed on me.

The elimination bracket is the portion of the series I'm focusing on right now. It is my understanding that not many competitions (in general) deal with seeded brackets larger than 16... if that's the case, they just put them in pairs or groups (college basketball). I can't find an actual 1-64 seeded bracket. I guess I could always make one... am I missing something else besides the magic number concept of (1 more than the total number of players). It wouldn't be that hard though to use 4, 16-man brackets and properly adjust the various seeds... right? Let me know if you're confused.

 

[AltF4]

Oh, I see what you're saying with the seeds. Yes... I listed the how the seeding goes for a 16 man bracket, but further than that... I'll describe the pattern better so that you can make a bracket of any size seeded.

In a nutshell though: Every first matchup should have seeds that sum to N+1. But where to put each matchup gets tricky.

Start out by putting #1 on the left side of the bracket, then put #2 on the right, #3 on the right, #4 on the left, etc... Left, Right, Right, Left, Left, Right, Right, etc... Alternating on which side of each half you put the players. Hmm... I don't like that description . I think it's confusing. I'll come up with something better soon.

But yes: A seeded bracket is superior to an unseeded bracket. Even if you only have a little info, something's better than nothing. Just do what you can with the information you have. If you do pools, use the pool information to seed. You can even use melee skill as a broad approximation. (Mew2King is likely to be better than some random scrub at brawl, even the first day)

 

[darkNES386]

I'll try to come up with something using that description... you can do the same and we'll figure it out from there. I appreciate the help.

 

[All_Usernames_Are_Taken]

The best tournament setup all-around? Modified-Swiss style, with the Top 8 players playing in a single-elimination.

Set an attendance limit based on space and time constraints. For best results, each swiss round should last about 30 to 50 minutes - plan your tournament structure around that.

Number of Swiss rounds based on attendance:
9 - 16 players: 4 rounds
17 - 32 players: 5 rounds
33 - 64 players: 6 rounds
65 - 128 players: 7 rounds
129 players+: Good luck on that.

* All players may participate in all Swiss rounds.
* The top 8 players after the final Swiss round will advance to the top 8 single-elimination finals.
* Pairings for further rounds are based on previous standings.
* Players may drop at any time, and it is recommended that players with 2 or more round losses drop to expedite the tournament.

Top 8
* Where necessary, the standings after the Swiss rounds will still be used to determine final order in the standings (Win ratio, then win ratio of opponents that player played).
* Top 8 matches will be best 2 of 3
* Top 8 matches will have no time limit

Using this setup, even the largest tournaments can cut to Top 8 in 6 hours. Small ones can be done in 1 - 2 hours. Most importantly, all tournaments are properly fair this way.

Use it.

 

[AltF4]

Bah! I thought I replied to to this a long time ago! Apparently the boards decided my post was unworthy. Here is a very shortened version of that post.

Swiss tournaments are backwards from brackets in the respect that they are more accurate at the bottom of placings and less accurate at the top. Where brackets are more accurate at the top of placings and less at the bottom.

Adding a round robin to the high end of the a Swiss tournament does the same job as adding pools to the bottom of a Bracket. In fact, they are essentially identical. Except Swiss with RR at the top suffers from tie issues.

Don't be so quick to say "best".

 

[All_Usernames_Are_Taken]

In fact, they are essentially identical. Except Swiss with RR at the top suffers from tie issues.

That's why you use win ratio, then opponents' win ratios for tiebreakers.

 

[AltF4]

Sure, you can come up with a tie breaker, but it's essentially an arbitrary decision about what to use. Anyone who loses money because of a tie breaker will feel very cheated. Plus it's not very exciting for a spectator. you want to see the "grand finals" with everything on the line.

Plus Round Robins can produce unbreakable ties. A three way tie cannot be broken by any tie breaking mechanism other than randomly choosing (which would be a horrible method).

Also, tie breaking mechanisms require you to keep track of that data for all matches, and that's more effort than most hosts are willing to put forth.

Lastly... what do you mean by "win ratios"? We're assuming two people (or more) have tied... which means they have the same win ratios. Perhaps you meant something else.

 

[darkNES386]

So if two people are tied in a pool.... is an additional match between them the best way to handle the tie breaker? Regardless of who won the match between the two of them?

 

[AltF4]

Well, see pools aren't usually an issue. Because in pools you typically have like the top half or more advancing.

Plus a tie between two people can always be broken. Just us the head-to-head results.

It's the three way ties (and more) that are sticky situations. Albeit this is a minor issue because it's fairly rare to have happen. But suffice it to say that when you have 3 people tied, there's no way to break it.

Because no matter what tie-breaker you come up with: A will beat B, B will beat C, and C will beat A. So who wins?

 

[darkNES386]

So you're saying that if player A and B are tied with points... if A beat B... then it is fair to say that A is ahead of B?

 

[All_Usernames_Are_Taken]

Use opponent's win ratio - the players who played to opponents who won more beat harder opponents, and thus did better.

 

[darkNES386]

^If two players won the same amount of matches = same amount of points... you're saying look at whoever else they each beat (who won more often)?

 

[AltF4]

He's saying that the person who played harder opponents should win the tie. You can measure this by calculating the combined win ratios of all opponents for a particular player.

Only one problem.

This doesn't work in Round Robin, everyone plays everyone. Thus if two people tie, they must have the same win ratio and their opponents win ratio must also be the same. (After all, they played the same people!)

And it doesn't work for brackets or swiss because ties are broken by doing consolation matches. So when would you use it anyway?

 

[darkNES386]

Consolation matches then is the answer to how I should go about this.

 

[AltF4]

Update! Changes:

- Colors changed around. I like this scheme better.
- Added more terminology in the beginning.
- Added better / more explanations for various things. (Like fairness of seeded brackets)
- Added some analysis of pools.
- Removed talk on single elim brackets. I didn't like how I was enumerating all the possibilities for different brackets, rather than discussing the various options as it is now.

I am trying to keep this oriented toward new tournament hosts, and perhaps old ones too. I would appreciate input both positive and negative on any aspect of the article. (Content, ordering, grammar, etc...)

Thanks a lot!

 

[dprim3]

I <3 over-analysis of competitive formats.

When I was a kid I used to make up "hockey leagues" with a format and teams and everything and decide the games by coin flip.

 

[KosukeKGA]

Hey, I do too. We should be buddies.

 

[AtticusFinch]

This thread is a major help to me, thanks to all who contributed. =]

The only thing that I believe needs to be added is how to make the most profit out of hosting a tournament in terms of; If blank amount of people show up, they should be charged blank emission fee, and the winning pot will be plank percent of all proceeds. Like fifteen percent or something like that. But that's just me lol

And thanks again.

Oh, P.S.

Is there any point in trying to seed your first tourney ever hosted by yourself? And is it smart to keep a record book of all who played, who they played, wins and loss' of all entrants to begin seeding?

 

[Greenstreet]

it sure wudnt hurt mate

 

[SothE700k]

I don't know if this has been asked yet, but what the heck, i'll shoot anyway.

Is there a proper procedure, test, qualifications kind of thing you can do to make accurate seeds? Because all the tournaments I've gone to (not just smash or games mind you), it seems like they went off a "first come, first seed" basis, which I know couldn't be anymore wrong from what you should do.

 

[nealdt]

You have to know the local community, Soth, or know someone who does. The best way to seed is according to skill and you obviously can't judge skill by looking at someone. A good host will know the local Smash community well and be able to rank the best players for seeding, OR know and trust someone enough to do that for them.

 

[SothE700k]

You have to know the local community, Soth, or know someone who does. The best way to seed is according to skill and you obviously can't judge skill by looking at someone. A good host will know the local Smash community well and be able to rank the best players for seeding, OR know and trust someone enough to do that for them.

Aww...dang it
I don't even know about the community here, if there is one. Just friends who play it is all I know.

*sigh* Thanks though.

 

[nealdt]

Well, that's the "best" way to seed an elimination bracket. You also have the option of seeding by location, which will at least break people up depending on where they're from. That's better than random/first-come seeding by far.

 

[-!-]

this is gonna be really helpful

 

[Corpsecreate]

Love this thread. Though I have looked into the maths behind this just recently and couldnt help but find differences in my formulas to what is written here. The first one I found was this:

Single Elim= n sets to be played
Double Elim = 2n sets to be played

This is definetely wrong. Consider a 32 man bracket single elimination tournament. The number of sets that are to be played from left to right are:

16, 8, 4, 2, 1
16+8+4+2+1 = 31, 31 is not n it is n-1.

For double elimination with 32 people:

1, 1, 2, 2, 4, 4, 8, 8, 16, 8, 4, 2, 1, 2 (Grand Finals which can end in either 1 set or 2 sets, assume 2 sets)
1+1+2+2+4+4+8+8+16+8+4+2+1+2 = 63, 63 is not 2n it is 2n-1.

The next one I see different is the time to complete for brackets. This is easily the most difficult and complex formula out of them all.

[ 15kn/TV ] + 10log2(n)

I've seen [formula] used to indicate that an integer of this value is to be taken though I'm not sure if that is what you intended. Even so, while I believe this formula is incorrect, it should be pretty obvious that having more than n/2 tvs has no effect on the time. Since the largest number of sets playable at one time will always be before anyone has been knocked out, which will also always be n/2. My formula is as follows:

Double Elimination: ceiling( 2n/TV + log(TV^2)/log2 -1)*t
Single Elimination: ceiling( n/TV + log(TV)/log2 -1)*t

n = number of people
TV = number of TVs
t = time per game

Note: These formulas are valid only for 0 < TV <= N/2

I have tweaked it a little to include Best of X sets and to take into consideration winners/losers/grand finals as Best of Y sets but this is the bare formula I got.

For the Round Robin, while I agree it is correct, it has limits as well.

5kn(n-1)/TV minutes

As before, this is accurate for as long as 0 < TVs <= N/2. Also, this will only be accurate if optimised 'networking' between players is achieved. If theres 50 players and player 1 finishes all his matches early then later down the track there will be wasted TVs because theres two less players (one being the person who has finished and two being the person that COULD have been playing player 1) to be using a TV.

As for pools, I havent looked too deeply into it myself yet but it does seem similar to what I'm getting. Factoring in the number of TV's is proving to be the difficult part.

 

[nealdt]

Corpse: in the elimination formulas, "n" is the number of players in the tournament. In your example, if 16 sets are played in the first round, then there are 32 players involved, which is effectively "n". Unless you made a typo, because you already stated 32 people and then said a single elim is 2n-1. And unless you're just being picky about the -1... I'm pretty sure AltF4 is a programmer and we don't really care about a simple constant like minus one .

 

[Corpsecreate]

Yes it was a typo And of course you need the -1 constant. If you were to make any estimate on time using a formula without the -1 then the estimate would be 1 set worth of time off.

 

[nealdt]

Yes, but computer science people don't care about 1 set's worth of time. The N has a much bigger impact and is much more important to consider when evaluating timing constraints.

T.O. says: "ok, with 64 people there are about 64 matches, which means I can do this and that and... ok, I think we'll be fine. OH WAIT THERE'S ACTUALLY 63 MATCHES OH NOOOOOOOOoooooooo."

 

[pockyD]

it does actually matter a little bit time-wise, since that potential last match doesn't happen in parallel (this is assuming the non-existent 'last match' is something played by the winner of the tournament) (also it's often 2n - 2 matches)

i find total # of matches to be an irrelevant stat though; the most important is the maximum number of matches that could happen in parallel at once (pretty much how many 1st round pairings, although varies a bit with byes), combined with the number of rounds

 

[Corpsecreate]

The way I derived my formula for the 'parallel' matches or rounds or whatever u want to call it, the hard one to find, was like this.

Single Elimination, N = 64
32, 16, 8, 4, 2, 1

TV = 1, parallel rounds = 63 or N-1

if TV = 2;
16, 8, 4, 2, 1, 1
parallel rounds = 32 or N/2

if TV = 4;
8, 4, 2, 1, 1, 1
parallel rounds = 17 or N/4 + 1

if TV = 8;
4, 2, 1, 1, 1, 1
parallel rounds = 10 or N/8 + 2

And we see a pattern occur.
N/1 - 1
N/2 + 0
N/4 + 1
N/8 + 2

So.... N/TV + log2(TV) - 1

I checked to see if this formula worked for N when its not a power of 2 and when tvs were an odd number and it seems to work so long as you always round the number you get up to the nearest integer and the bracket is run optimally (Round 0, L, W, L, L, W, L, L, W...).

 

[Rappster]

Love this thread. Though I have looked into the maths behind this just recently and couldnt help but find differences in my formulas to what is written here. The first one I found was this:

Single Elim= n sets to be played
Double Elim = 2n sets to be played

This is definetely wrong. Consider a 32 man bracket single elimination tournament. The number of sets that are to be played from left to right are:

16, 8, 4, 2, 1
16+8+4+2+1 = 31, 31 is not n it is n-1.

For double elimination with 32 people:

1, 1, 2, 2, 4, 4, 8, 8, 16, 8, 4, 2, 1, 2 (Grand Finals which can end in either 1 set or 2 sets, assume 2 sets)
1+1+2+2+4+4+8+8+16+8+4+2+1+2 = 63, 63 is not 2n it is 2n-1.

The next one I see different is the time to complete for brackets. This is easily the most difficult and complex formula out of them all.

[ 15kn/TV ] + 10log2(n)

I've seen [formula] used to indicate that an integer of this value is to be taken though I'm not sure if that is what you intended. Even so, while I believe this formula is incorrect, it should be pretty obvious that having more than n/2 tvs has no effect on the time. Since the largest number of sets playable at one time will always be before anyone has been knocked out, which will also always be n/2. My formula is as follows:

Double Elimination: ceiling( 2n/TV + log(TV^2)/log2 -1)*t
Single Elimination: ceiling( n/TV + log(TV)/log2 -1)*t

n = number of people
TV = number of TVs
t = time per game

Note: These formulas are valid only for 0 < TV <= N/2

I have tweaked it a little to include Best of X sets and to take into consideration winners/losers/grand finals as Best of Y sets but this is the bare formula I got.

For the Round Robin, while I agree it is correct, it has limits as well.

5kn(n-1)/TV minutes

As before, this is accurate for as long as 0 < TVs <= N/2. Also, this will only be accurate if optimised 'networking' between players is achieved. If theres 50 players and player 1 finishes all his matches early then later down the track there will be wasted TVs because theres two less players (one being the person who has finished and two being the person that COULD have been playing player 1) to be using a TV.

As for pools, I havent looked too deeply into it myself yet but it does seem similar to what I'm getting. Factoring in the number of TV's is proving to be the difficult part.

this is really useful. may i quote this at my school's video game club?

 

[Corpsecreate]

Sure I guess.

 

[ranmaru]

How much time does a one day tournament usually take?

(With at least 5 tv's or more)

I want to have a tournament, and it might have around 30 people. I wanted to do pools, but I might need to do brackets if time doesn't allow pools. I want to know what I can work with.

Thanks for the help. : ]

I thought 8 hours would be good, but is that enough?

 

[HelpR]

Ok so, gonna need to pick some brains here: let's assume we have a 128 man tournament, and you had access to let's say... 15 tvs. At this point, which is more efficient? Pools? or double elimination bracket. I'm trying to do the math myself, but i dont have access to a decent calculator atm.

I guess my main question is, at which point does pools become more efficient then double elimination brackets (from a time point of view)? If at any point, that is

 

[Happy Pit]

what do you guys think about this?

http://www.smashboards.com/showthread.php?p=14784626#post14784626

 

[PlanFive]

Small question about the concurrency formulas in the opening post, but i was wondering if there was an upper limit in how big the TV variable can go? I'm assuming that (TV =< n/2, where n is the number of participants) has to be true because any other TV setups will go unused.

For those who are wondering, i'm trying to calculate how much time a swiss tournament with additional rounds and a cut to top 8 would take, assuming I have an infinite amount of setups. The additional rounds are there to ensure that the better players make the top cut (assuming they win of course) and to decrease the effect on subjective tiebreakers on the standings, similar to how professional Magic: the Gathering tournaments work. The problem that my playgroup has is that brackets tend to favor better players due to the fact that they stay in the tournament longer and therefore play more games with stakes on the line. My playgroup all play M:tG so they are familliar with that tournament structure, and we are trying to incorporate it with our smash tournaments as well