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Tournament Mechanics: A Primer

Discussion in 'Tournament Discussion' started by AltF4, Nov 3, 2007.

  1. AltF4

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    With the ever nearing release date of brawl, the smash community will find itself at an important point in its future. We will as a community come to a consensus on many issues as to what should and should not be included in competitive play. In addition to this, however, brawl's release gives us the opportunity to reevaluate the basic tournament mechanics that we likely take for granted. There are many highly misunderstood aspects to tournaments today that are standard and others that are ignored for poor reasons. This article will explore those mechanics to better aid tournament directors in making decisions.

    To begin, let's define some terms that we will be using throughout this discussion.

    - Accuracy: The accuracy of a tournament is the quality that players should place according to their skill. (Skill being defined in a moment) But the gist is that the "best" player should place 1st, the 3rd "best" person should place 3rd, etc…

    - Fairness A tournament system that does not give advantages to any players rather than others is called Fair.

    We have all been to a tournament where a relatively unskilled player advances far through a bracket by way of not having to play tough opponents. Conversely, we have all seen highly skilled players knocked out of a tournament early by having to play other highly skilled players immediately. Both of these situations are "unfair".

    - Number of games played Self explanatory: The total number of matches played by all participants in a tournament.

    Playing is fun, and we would like to be able to squeeze in as many games as possible. Tournaments where you get to play a single match and then are eliminated are not fun. So this value would like to be maximized.

    - Total amount of tournament time.: Related to Number of Matches Played, this is the actual amount of time it takes to run the tournament.

    Tournaments cannot take a week to finish; they must be able to be completed in a reasonable amount of time. Thus this number should be minimized.

    - Skill: An underlying approximation to how "good" you are. This is a single numerical value which is used to represent how adept at the game as a whole someone is.

    - Performance: This is a positive or negative value depending on how well you are playing during a particular match. It is notw how "good" you are in general, but how well you are playing relative to your average today.

    If you SD twice at zero percent in a match, you would have a very low performance for that match. If you zero-to-death your opponent flawlessly several times in match, that would be an indication of you having a high performance value for that match.

    - Consistency: Performance values for a player are normally distributed across matches. The standard deviation of this set of values is called the player's consistency.

    - Seed: A pre-ranking of players in a tournament according to their expected placement. This should essentially be a ranking of players' believed skill values. Note that lower seeds indicate high skill. (IE: seed #1 goes to the highest skill, etc...)

    - Entertainment: (of a match) A match is called entertaining if it is between two players who have similar skill. (As defined above) Also, the higher the combined skills of the players, the higher the entertainment value. Entertainment of matches should be maximized.

    - Upset: An upset is defined as when a player of lower skill beats a player of higher skill, typically due to some combination of the higher skilled player having a poor performance and the lower skilled player having a high performance.

    A "perceived" upset occurs when a lower seed loses to a higher seed due to inaccuracy of the seeds. IE: If a "no name player" is actually highly skilled, he may receive a high seed and appear to upset lower seeded players.



    Seeding

    Seeding is a very important (and often ignored) aspect of running a successful tournament. All professional sports leagues (NFL, NBA, MLG, etc...) use seeding in their brackets, and there's no reason for you not to. Let's move on to the details of why.

    Accuracy: Accuracy is increased if seeding is used. Players of high skill will be seeded away from each other initially, so that when they eliminate each other, it will be at near the end of the tournament as opposed to the beginning. This will help to ensure that high skilled players place highly and lower skilled players place lowly.

    Fairness: Brackets seeded to ranking are often criticized for their unfairness. It is believed commonly that seeding favors higher ranked players by giving them "easier" opponents. This misconception is typically brought about by the fact that the first matchup the 1st seed plays is against the lowest seed. So players often complain that that person gets "an easier bracket".

    But here's the problem: I've been sort of lying to you up until now, Accuracy and Fairness are actually the same thing. In a tournament, if you have perfect Accuracy, everyone will place exactly according to their skill values if no upsets occur. (IE: If you're the best, you get 1st, 4th best, you get 4th place.) How can this possibly be called unfair? Indeed it is perfectly fair!

    A seeded bracket ensures the following: If you perform according to your seed (beating everyone worse than you, losing to everyone better than you), you will place as your seed indicates. This is of course optimally fair.

    Example: If you are the 7th best person in the tournament, no upsets occur, and you place 3rd in the tournament, then the bracket was unfair to you! You placed more highly than you should have. The only way someone should be able to place higher than what their seed indicates is by upsetting players of higher skill.


    How to seed? Ranked seeding should always be done in the following pattern: (given for 16 players)

    [​IMG]

    This pattern is chosen for a specific reason: it guarantees an even distribution of skill at all levels except the final. (Where it is impossible) You should notice that all first round matchups a have players adding seeds to 17. This means that each half of the bracket has total ranking points of 68. You can see that there is no "preferable" place to be on the bracket at any particular level, making the bracket perfectly fair. The skill values for every area sum to the same values. In round two, for example, every matchup sums to 9.

    Entertainment: Seeding by rank ensures that the higher skilled players will play each other, thus entertainment is increased. In general, the entertainment of matches in a bracket increase as the tournament progresses.


    Double Elimination Bracket

    Double elimination has several effects on a tournament, which can be summarized as such:


    Number of matches: Making a tournament double elimination doubles the number of matches that need to be played.

    Time To Complete: Adding double elimination to a tournament will more than double the total time to complete it. (Read the next section on Concurrency for an explanation as to why adding double elimination more than doubles the total tournament time.)

    Accuracy: Double elimination will increase the accuracy of a tournament by increasing the number of games a player must win in order to upset better players. IE: If the probability of an upset is 1/4, the probability of it happening twice consecutively is 1/16! Playing more games makes it more unlikely that an upset will occur.




    All Brackets



    Accuracy In the real world, (due to seeding inaccuracies) brackets tend to be increasingly accurate at the top of the placings, and less accurate at the bottom of the placings.

    Number of matches: This is really fairly simple. Think of it this way: each game played causes a player to get a loss. The tournament ends when all but on player has 2 losses. The number of games in the tournament must then be the number of losses each player can have times the number of people in the tournament:

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

    Time To Complete: (Concurrency) We have all been to a tournament where everything is moving quite smoothly during the entire process right up until the final few matches. The end of a tournament almost always tends to drag on long past everyone's expectations. (sometimes well into the morning hours) Why is this?

    It is because bracketed tournaments rely on Concurrency. That is: the fact that some matches cannot be played until certain other ones have finished. It seems obvious, yes? The finals cannot be played until the semi-finals have finished, after all. And this phenomenon has a profound delaying effect on bracketed tournaments.

    This makes the formula a bit more complex, but don't be scared off. Just use a calculator, and let it do the hard work.

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

    An important thing to note is that the second part does not have a TV variable in it. This is intentional, because it represents the second half of the rounds in a bracketed tournament. These matches must be played one after another, and having additional TV's doesn't help to speed it up.

    Also of note is that the second part of the formula runs on a higher order than the first, that means that for large tournaments: even though you finish 75% of the matches, you're still less than half of the way done in terms of time. This is why tournaments frequently run over time at the end. They think "well, we're almost done with the matches" when really you're only about half way done.

    Round Robin Tournaments

    Round robin is an alternate method of running a tournament instead of using a bracket. In a nutshell, Round Robin involves each participant to play every other participant. We will now explore the various pros and cons to this alternate tournament scheme.

    -Accuracy: In general, round robin tournaments are more accurate than brackets of any variety. The reason is obvious: every possible matchup is played. You have the maximum amount of data from which to declare a winner instead of just a subset of that data.

    -Fairness: Round Robins are also perfectly fair. Every player plays exactly the same people, so this is apparent. In comparison, seeded brackets are considered fair because they offer each player equivalent matchups. Round Robin goes one step further and offers identical matchups.

    -Entertainment: Since every matchup is played, every appealing match can be viewed. However, the average entertainment value of a Round Robin match is rather low. This is because the majority of the games being played are not between two closely and highly skilled players. In comparison, brackets tend to eliminate out the lower skilled players, quickly leaving the majority of matches played entertaining.

    -Number of Games Played: This is the very famous “Handshake Problem”. Long story short, the number of sets in a round robin are [n(n-1)/2]. Which is a lot compared to a double elimination bracket with only 2n games.(Where n = number of participants)

    -Time to Complete Tournament:

    This is where round robin fails. Simply put, they take too long to finish for any more than a dozen or so people.

    n(n-1)/2 sets
    5n(n-1)/4 matches (Averaging 2.5 matches / set)
    5n(n-1) minutes (Average of 4 minutes / match)
    5kn(n-1) minutes (Scaled to consider an efficiency coefficient, k)
    5kn(n-1)/TV minutes (Scaled to consider multiple TV setups)


    Total time to run a Round Robin tournament formula: 5kn(n-1)/TV
    Where:

    n = Number of participants
    k = efficiency coefficient that describes how efficiently you ran your tournament. (as little wasted time as possible)ost to tell me how long it took from start to finish, how many people you had
    TV = The number of total setups for the tournament. (TV’s + Cubes in the case of smash)

    Note that the formula gives you the total time in minutes! You have to convert to hours + minutes. (IE you might get 190, which means 3 hours, 10 minutes)

    I have found so far that 1 is not a bad starting point for k. But if you run a round robin, please post saying:
    1) How long it took from start to finish.
    2) How many total setups you had.
    3) How many people participated.

    I would very much like to get a good empirical value for k. Also, it might be fun to try and compare k values for tournament efficiency bragging rights!


    - Intangible: Round Robins have the flaw that it is always possible that you get a tie. In fact, it is possible that everyone in the tournament tie for first and last simultaneously! In comparison, brackets have the advantage of always being able to declare a clean cut winner.

    Pools

    Pools are a tournament mechanic used to form a hybrid of both round robins and brackets. What is done is all players are separated into groups called Pools. Each pool runs a round robin tournament within each other, and then the top X from each pool will move on to a regular bracket. (Or more rounds of pools, in some cases)

    Note that Pools are typically only run in a sufficiently large tournament, not smaller ones.

    Accuracy Pools drastically help to increase the accuracy of a large tournament. This is because the task of accurately seeding every player is not practical. With pools, one needs not seed every player, but rather only about 1 or two per pool, which is much more manageable.

    The other effect is: self-seeding. Pools are a good way of matching player up against one another to detect any obvious and egregious oversights in the seeding process. For example, if an unknown player is actually highly skilled, he will have the opportunity to give himself a high bracket seed by placing well in pools. The seed going into the pools does not matter as much.

    Time to Complete:

    Let:
    a = number of pools
    b = number of people per pool
    n = total number of people
    k = efficiency coefficient
    TV = number of TV's used

    5kn(n-1) /TV (Round Robin formula)
    5kb(b-1) /TV (Pool of b people)
    a * 5kb(b-1) /TV("a" pools of b people each)
    5kn(b-1) /TV (simplified)


    5kn(b-1)/ TV

    This is the formula to compute how long it will take to complete "a" number of pools, with total participants on n. As you would have guessed, it looks remarkably similar to the Round Robin formula.

    Other things to consider:

    Continuation Sets: A continuation set is a way of handling rematches in a double elimination bracket. Most smashers recognize it by the way MLG handles rematches. I’m not sure why, but the general opinion of this is overwhelmingly negative. The fact is that having a continuation set is a better method than having each set handled separately.

    The reason is that the winner is guaranteed to have won more games over his opponent. I’ll use an example here from an actual tournament that took place here in Arizona not long ago.

    -Player 1 wins the winners finals set 3-1
    -Player 2 comes back into the championship finals and wins the second set 3-2
    -Player 2 then wins another set 3-2.
    -Player 2 wins the tournament.

    But you can see that they both won 7 games! Player 2 is awarded the victory in the tournament because of the order in which he won the games, not how many games he won, which should be the case. A continuation set essentially says “You have to win more games over your opponent in order to beat them” which is perfectly reasonable.


    Thanks for reading! I would like to keep adding to this article, so please let me know if there is anything that needs adding, removing, or modifying. I’d love to hear what you have to say!

    Coming soon:
    -Analysis of pools.

    -AltF4
     
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  2. South_Paw

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    First post! <3 Dan!


    I agree with pretty much all of it, because it's true, so far their is no perfect bracketing system that covers everthing... as good as something gets for fairness, the worse it gets for entertainment until like the quarter finals usually.

    The exceptions for that, as I'm sure people will agree, are when two players that have never played before play and have a close match (from meeting randomly in a bracket), my example of this would be hugs vs light from AZOne. im pretty sure it wasn't very far into the bracket, but somebody had them sit down on the projected tv and play, and the second match was probably the most tense and epic of the tournament. So sometimes it is possible (but im not disagreeing with you, just pointing out an exception, that im sure you know about anyways =P )

    i think the first two rounds of winners and losers are generally the most boring matches of a tournament, it would be great if we could figure out a good way to help with that (without having to eliminate using pools)
     
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  3. Rapid_Assassin

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    What do you think of other, less commonly used bracket types? Like round robin, swiss format...
     
  4. AltF4

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    Thanks!

    I'm going to be adding other non-brackets soon. Round robin in particular.

    Really quick though: Round robin is ideal except for two problems:

    1) Time. There are [n(n-1) / 2] games in a round robin tournament. (Where n is # of ppl) That means the number of games played grows geometrically with extra people, as opposed to linearly like with a bracket.

    2) Ties. A round robin always has the possibility that there is no clear winner. It can have ties of any number of people. It's even possible for every player to tie for first and last simultaneously! But with a bracket, you're gauranteed a clear cut winner.
     
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  5. Coin Chaser

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    i must say i always enjoy when someone breaks down a process with a lot of words....idk call me weird

    but great work and i look forward to reading more!!

    im sure im just thinking about this too much or something but wouldnt a seed bracket be considered unfair to someone that isnt very ranked or new to the tourney scene.....maybe im just being a jerk and challenging the word "perfect" or "always".....but then again i probably jsut answered my own question when it comes to u didnt add the factor of upsets....go me.....

    i think when u add the "upsets" factor i will probably understand the system more.....idk if thats next for u....and im not rushing u to do this 1st if ur already working on something....but that would prob be most beneficial for me

    thanx and keep up the good work!
     
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  6. House M.D.

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    i haven't gone to a ton of tournaments, so perhaps i am not entirely qualified to have an opinion here, but it seems like pools followed by a double elimination bracket is a solid format for a number of reasons.

    fairness/accuracy: to make it fair you would implement seeding into placement into pools, and then only the result of pools would affect bracket placement. while this could lead to certain inequalities, the idealizations of ordinality (a player always beats worse player but loses to better players) and having enough tournament data to perfectly rank (especially given that skill changes over time) mean that this type of tournament is probably and fair/accurate as we can hope to get in the smash community anyway.

    entertainment: your comments regarding the bracket apply hear, but i would like to add that pools play could add a level of excitement for people on the bubble of getting in (they have a rooting interest which makes things so much more tense).

    time: if the pools are small enough and the tournament is well run, the time should not be significantly longer than simply doing a double elimination bracket.

    as a final note, this format is MUCH better for less experienced players than any of the listed formats because they get to play a good number of matches when they would normally be out after 1 or 2 matches. the pools round could help immensely in furthering the development of these players.

    and yes, continuation set is absolutely a good call.
     
  7. darkNES386

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  8. maXXXpower

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    Dan for President 2008. **** good 1000th post.
     
  9. AltF4

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    Coin Chaser: I'll add something more specific about this in the post. But here's how it goes briefly:

    Someone says "Doesn't seeding by rank make it easier for high ranked players and harder for low ranked players? Just look at the brackets, the #1 seed plays lower skilled opponents than, say, the 8th seed."

    This is a very common misconception. The problem with the reasoning is that you're not taking into account the 1st seeded player or the 8th seeded player themselves. Think about it. The top seeded player already has an inherent advantage because he's the best person there. Everyone he plays will be of a lower skill than him. The advantage you see isn't the tournament bracket giving him an advantage, it's just the fact that there's nobody better than him.

    Same with low ranked players. They appear to have to play harder opponents, only because in comparison to them everyone's a hard opponent. How could a tournament bracket possibly make it "easy" for the lowest seed? It's impossible. So instead everything is made exactly even, so that any advantages / disadvantages are only your own.

    I'll have a better explanation I think up soon. Along with an actual picture of a bracket instead of a *insert photo here*.

    House MD: Yea, I'll be adding pools real soon too. And you're pretty much right about everything with pools. They help to seed for you, and they let low skilled players play a bunch of games.

    Maxx: Naw, go and vote for Colbert instead. :)

    DarkNES: Decide for yourself. That's the point of the whole thing. To inform tournament organizers about the various tournament mechanics so that they can make good decisions about this sort of thing.
     
  10. Jam Stunna

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    While I agree with this, how am I supposed to seed Joe Smasher at a small local tournament? Those are the types I usually run, and seeding doesn't seem to be very practical.
     
  11. AltF4

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    Yes. That is a problem. Essentially you do your best to seed as much as you can. Seed the players you know to be skilled, using power rankings or past tournaments or whatever. Past that, you can use pools for a good method to let players seed themselves.

    The system is written with the assumption that you can seed every player with perfect accuracy. But of course you'll never be able to do that completely. Just remember that even a rough estimate is better than resorting to random placement.
     
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  12. the_suicide_fox

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    In a single elim, ranked bracket wouldn't it make more sense to have 1st play 9th, 8th play 16th, etc, so the difference in skill is evenly distributed? You would want to limit the difference in skill as much as possible not have huge gaps. In your formula, the 8th/9th players will inherently have the hardest first matchup b/c their skill difference is so small compared to 1st/16th player matchups. If 1st place gets an advantage no matter what then their skill should be balanced by having them play a reasonably skilled team. Having 1st play 16th is like basically giving the win to 1st, whereas having 16th play 8th would more than likely result in 8th place winning, but at least 16th place has a shot at advancing if they have improved/changed strategies since the rankings were made. It would also be more accurate, since players will still lose to teams ranked higher than them, but the chances of the middle rankings (6-11) getting all mixed up in the results will diminish significantly.

    EDIT: Also I'd like to mention I use single elim random seeding. However, for my type of tournament it isn't that inaccurate, since we only do a 1st place prize and it's amateur style. I'd prefer to do double elim random or double elim pools if possible but I just don't have that much time. IMO swiss format is the best format all around in every one of your sections except time. It takes a long time to run a swiss tournament format even if you do eliminations (e.g. after round 3, top 50% of players advance to the next round)
     
  13. South_Paw

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    I think I know what you're wanting to say...

    The way I explain it to someone who's seeded low and has to play a top player is... say we do a 8 man... 1st plays 8th first round right? sounds unfair, but then you realize that 2nd will play 7th, and so on, and you see that in the losers bracket, 8th is more likely to play 7th and 5th to play 6th... if 1 played 2 or 3 first round, then 2 would dominate the losers bracket (and maybe even beat out 3 or 4 early) and it turn out to be less fair.

    Hope it helps
     
  14. AltF4

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    Okay, I went and added an image for a 16 man bracket.

    You see, the pattern that you see in the bracket (in the first post) is chosen specifically because it maximizes fairness and accuracy. It is of course possible to come up with other patterns, but you will necessarily sacrifice fairness. If you change that pattern, there will be some area of the bracket with a higher average skill and some portion with a lower average skill. That is why it is called fairness.

    Important concept: Fair means that the bracket doesn't give any advantages to players. It does not mean that it should offset any advantages that players already have. The #1 seed comes into the tournament with an inherent advantage, that he's the best one playing. The tournament bracket should not try to penalize him for being better, that would be unfair.
     
  15. South_Paw

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    I know this is your thread Dan, but I'm REALLY bored, so I thought I'd help.

    Double Elimination:

    1st: 1
    2nd: 2
    3rd: 3
    4: 4
    5: 6
    5: 5
    7: 7
    7: 8
    9: 10
    9: 11
    9: 9
    9: 12
    13: 15
    13: 14
    13: 16
    13: 13


    I did this straight from TIO... I arranged them in order from best to worst (1 being best and 16 worst), and this is what came out. Perfectly accurate to 4th place, then you have some ties, starting at 5th, where 5th and 6th tie, but still pretty close (you could even go MLG and have those players play it out for the placing)

    And now for a single


    Single Elimination:

    1st: 1
    2st: 2
    3rd: 4
    3rd: 3
    5: 8
    5: 5
    5: 7
    5: 6
    9: 16
    9: 9
    9: 13
    9: 12
    9: 15
    9: 10
    9: 14
    9: 11

    Still accurate for the first two or three places, but after that it gets really sketchy.


    Now double elimination by Skill level (Tio). 1-5 will be Advanced, 6-11 Intermediate, and 12-16 Beginner


    1: 1
    2: 2
    3: 3
    4: 4
    5: 7
    5: 5
    7: 8
    7: 6
    9: 10
    9: 11
    9: 9
    9: 12
    13: 13
    13: 15
    13: 14
    13: 16

    Still really good, it made for some really close skill level matches in losers and the second half of winners.
     
  16. pntchandler

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    AltF4,

    Interesting article. A little off-topic. I'm planning to run another Melee tourney at the store next Sunday, 11/11/07. This will be a singles tourney. I order to save time we're planning to use TIO but that would probably save us perhaps 1 hour at most. You remember the last one went for nearly 7 hrs. I was thinking 4-man free for all FFA. Double elimination, so 2 advance and the other two go to losing bracket. In all fairness, how do I prevent people from doubling up or others running away. Is this format used in compatitive Smash? If so, what are the rules? You recall the issue with Wobbling. I'm trying to avoid new issues.
     
  17. South_Paw

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    FFA is never used in major tournaments

    And the main problem with the previous tournaments was simply because there would often be open tv's not being used... with TIO, just use the tvs feature... put in how many tv's you have, and whenever you call a match, you set it to a certain tv, and when you mark the match as finished, it opens the tv for another match, and this saves a HUGE amount of time on brackets.
     
  18. nealdt

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    Good thread, AltF4. I'd just like to throw in SmashWiki's Tournament article, which also has a lot of information about bracket formats and might be useful to people. You should also consider adding some of your information to the article.
     
  19. the_suicide_fox

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    What you're describing is bracket balancing, not fairness. To be "fair" each player should be paired with one of a similar difference in skill compared to the others. Having the 1st and 9th place (out of 16) play is "fair" but it doesn't balance the brackets as you said. However, your whole concept of a balanced bracket contradicts fairness. Either the bracket is balanced or it is fair, not both. But you also added the skill difference instead of subtracting it, which I think is the problem in the logic. The brackets are balanced and fair if you take the difference in skill not the sum.
     
  20. PaperDream

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    Thanks for posting this, that explained a lot, and also thanks to South_Paw for your post as well. They were very helpful to me.
     
  21. AltF4

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    SoutPaw: If you take into consideration consolation matches, any tournament bracket with raked seeding will have results that perfectly mirror the seedings.

    PnT: Yea... FFA's are bad. They're essentially random. One of the biggest problems is that FFA's discourage actual fighting. It's in your best interest to run and hide while everyone else fights, but that makes for a boring game when everyone does it. Of course you don't have to listen to my advice, but I would recommend against an FFA tourney.

    Neal: Hey, thanks for the kind words. You're quite well known in the tournament organizing circle, it means a lot to me. I'd love to contribute to the Wiki.

    Suicide Fox: Well, then we're just arguing about semantics. I've defined fairness to be the quality that a bracket does not give advantages to certain players. If it treats everyone evenly, I would call it fair. If you would prefer to call it something else, then that's fine. But I like my terminology so far. :)

    Oh, also: If you sum the skills of the players and then divide by two, you get the average skill of the players in the match. But there's no point to dividing by two since there is always 2 people per match. Hence summing the skills does give you a quantity that is essentially the same as the average skill, just scaled up by a factor of two.

    Subtracting the skills gives you the entertainment value of the match. A large skill gap is likely to be a blowout. A smaller skill gap is likely to be an entertaining match.

    Do not confuse Entertainment Value with Fairness. This is a really important concept. Perhaps I haven't been explaining it well enough.

    Someone asks the question: "Who has an easier bracket? The top seed or the bottom seed?" At a glance it looks like the top seed is given an easier bracket, but he's not. The top seed and the bottom seed are in exactly the same place. They play each other in the first round. They have the exact same path through the bracket, thus neither of them has an advantage over the other except the inherent advantage that the top seed is better.

    This advantage is not caused by the bracket, but by the fact that the top seed is better. It is not the responsibility of the bracket to make up for the fact that the bottom seed is not as good. To do so would be UNfair to everyone else.

    As it turns out, the pattern shown is the only one where every matchup has the same average skill. Thus, every position in the bracket is equal and fair.
     
  22. the_suicide_fox

    the_suicide_fox
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    But your suggestion does give an advantage to the top seeded players and is reduced as you go down the line. Your not understanding what I'm saying about difference of rank. In your system, the 1st seeded team has the advantage during the first round, and that's b/c the 8th and 9th seeded teams play first round. The difference in rank for these match ups means that 1st seed has a very easy set whereas 8th seeded has a significantly harder set. If you have 1st play 9th, 8th would play 16th meaning the brackets are being equally fair to all players, not giving any one player a huge rank difference over/under another player. The main reason MLG has 16th play 1st in the championship bracket is b/c people would tire of seeing the same 2 players duke it out at the start of every tournament. They have 16th seeded play 1st seeded first because the top 8 seeded are ALREADY in the championship brackets. 9th-16th place are from the playoff bracket the day before, which means those teams will usually be different. In reality though, a truely "fair" method is to make the rank difference equal among the matchups. MLG does it differently to pump up the "entertainment" value.

    EDIT: Another reason MLG does the seeding this way is b/c since they have a tournament to get into the championship, a team could essentially lose on purpose to get a 12th seed and have an easier bracket than get 9th and play 1st seed in round 1. However, if you do pools or some other kind of ranking for all players then my suggestion makes more sense.

    You say fairness and entertainment values are different, when they are actually the same number. Only thing is the smaller the difference the higher the entertainment value. However, just because a bracket has an euql average skill doesn't mean any specific match is fair.
     
  23. AlphaZealot

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    MLG does runs a 32 team championship bracket for Halo 2 (and for SSBM back when it was used). 1st seed plays the 32nd seed. 16th seed plays the 17th seed.

    Every sport follows a similar bracket philosophy as well. In the NBA, the 8th seeded team plays the 1st seeded team, while the 4th/5th play each other. In NFL you have a similar system, but you have 4 play in games (two from each conference), the play in games are for "wild card" teams, meaning they essentially get the worst seeds when they enter the bracket.

    There really isn't any way to make an entire bracket fair. If the 16th plays the 1st seed, there is a huge gap in skill, way bigger than the 8th playing the 9th. Meanwhile, if you try the 1 plays 8, 2 plays 9, 3 plays 10 method then you'll end up having zero upsets and less accurate results as no team will recieve any sort of test until the later rounds of the tournament. Essentially, by seeding like most professional sports organizations, you have at least a quarter of the opening round match ups being close, usually much more. From that point the gaps between teams only narrows as well.
     
  24. the_suicide_fox

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    True

    But as I said before, Swiss format is the best all around in terms of fairness, accuracy, and entertainment. The only thing it lacks in is time, b/c it takes a looong time to run swiss.
     
  25. AltF4

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    The pattern shown isn't my pattern. Nor is it MLG's nor the NFL's, nor the NBA's. It is the only pattern used by any established competitive organization. And there is a reason for that, it's not just by chance,

    Suicide Fox: Maybe you're having a hard time because you're only looking at the very first round. Which is exactly what makes a lot of people think that the top seed is given an advantage. I'll post up a description that encompasses the entire run through the tournament.

    EDIT: Hmmm... it turns out that the calculations necessary to do the full thing is rather complicated and long. I don't have the time right now. I think I will by tomorrow evening though.

    Essentially you've got calculate the percentage chance of a player winning a particular match, and then calculate those odds for each match along the tournament bracket. The result will be a list of each player's "Odds of Winning".

    And you'll notice that the numbers will be skewed in favor of higher ranked players, ie: they will have a higher odds of winning the tournament. But this is both expected and welcomed. The higher ranked players are better, and SHOULD have a higher chance of winning. If everyone's chances were even, that would mean that the tournament is doing something to help out the bad players and hurt the good. Which would be unfair.

    Doing a pattern of 1-8, 2-9, 3-10, 4-11, etc... will aggregately even the "Odds of Winning" for each player. Virtually every player will have the same or very similar odds of winning the tournament. This is obviously unfair to the higher skilled players who ,despite being significantly better than everyone else, is just as likely to win.
     
  26. TedBoosley

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    Gigabits (Main Smash venue in Florida) does it this way:

    7-8 man pools seeded by lifetime seeding points at Gigabits (a flawed seeding system to start, but this is just how they do it)

    Top 3-4 (usually eliminate down to 24 or 32) from each pool move on to brackets, with first round byes going to the winners of each pool.

    Brackets are double-elim, 2/3... 3/5 in Semis/Finals


    Always been pretty fair, and the top players are always always Top 24 or 32.
     
  27. AltF4

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    Added:

    Round Robin analysis.

    There is a nifty formula for computing the total time a RR tournament will take. Give it a shot. The whole thing is near the bottom of the post if you're just looking for the new stuff.

    Thanks!
     
  28. B-Will

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    I will add to this post once I get the time to read through all of this...

    Very well done!
     
  29. AlphaZealot

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    I checked...I may have missed it, but you may want to add something about switching losers to the opposite side of a double elimination bracket to prevent double jeopardy.

    Also, add some color/formatting to the first post (it already looks pretty good) and I'll sticky this amazing work. Actually...maybe you could show a pic of a RR pool and a Double elim bracket (with where losers go). Or links to tio? Idk...just ideas.
     
  30. g-regulate

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    i still dont understand the point of this post. why do anything but seeded double elim? anything else simply isnt fair.
     
  31. AlphaZealot

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    I think the time formula is very useful. Also, it could cover the Swiss format, which I think actually IS the most fair/balanced (you always play someone who has a similar record as you). Pools to double elim is awesome too.
     
  32. AltF4

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    Hey, thanks for the support, AZ. If you're willing to give it the stick, then I'll do some work to spruce it up. :)

    I was in the middle of doing a time calculator for a bracket, just like for RR. But it actually is really complicated. Initially I just said:

    -2n sets (ignoring the -1 or -2 because it's negligible for a large enough n. Technically there are 2n -1 or 2n-2 sets)
    -5n matches (2.5 matches / set on average)
    20n minutes (4 minutes per match on average)
    20kn (scaled for efficiency coefficient that accounts for downtime)
    20kn / TV (Scaled for each TV you have)

    You can use this if you want... but it isn't right. The problem is that it treats every match equally. In a bracket, however, you have a problem with concurrency. That is, you can't play the finals before having finished the semifinals. So even if you have a 1000 TV's, the end of a bracket tournament will still take time. The last bunch of matches have to be played one after the other.

    To take that into account will involve binary logs and will look really ugly... I wonder if it'll be of any use if it is that complex.

    Round Robins don't have that problem because as long as you set up the order of the matches right, you don't have a concurrency problem.

    I agree, AZ, swiss is a really good format. I used to play Warhammer 40k, and it's predominately used there too. I'll do a writeup about that.

    EDIT: Btw, I'm an engineer, and not very artistically inclined. If you have any suggestions on precisely what to change to make it prettier... I'm all ears. In the mean time I'll do my best.. and ask my girlfriend, lol!

    G-Reg:

    People don't always do double elimination because they don't understand what it accomplishes, or because they think that it will take too long. People don't use seeds often because they think it gives higher skilled players advantages. (Which I've tried at length to dispel)

    Sometimes they're right. Often a tournament doesn't have time to do both 2/3 matches AND double elim. So which should he choose? Hopefully I can help to provide an educated answer. Which reminds me, I want to add a 2/3 sets section...

    Also, because using these mechanics add a level of complication to a tournament. Things are easier on you as an organizer without them. But the way I see it, if you're running a tournament, you are obligated to offer the best experience for your players that you can. This article hopes to inform those organizers so that they can offer the best experience possible.

    Oh, also, there are alternatives to brackets completely that people usually don't know about. (Like swiss) Smashers are just so used to either RR or Brackets, they assume there isn't anything else.
     
  33. AlphaZealot

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    check out the canadian tournament that is stickied, it has a nice, sexy opening post. You don't need like a logo or anything, but different colors and stuff help a lot so you don't get that "wall of text" feeling.
     
  34. AltF4

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    Update:

    -Changed thread title. I wound up deviating from just bracket stuff too much to call it bracket theory anymore.

    -Made pretty. Still more beautification to go, likely.

    -Added small section on Pools, and some more tournament time estimates.

    You know what would be awesome? If those formulas were included in Tio. You know, it could give an estimate on how much time the whole thing will take after you enter your info in. Doesn't Neal have a way to submit ideas for Tio?
     
  35. nealdt

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    Sure, you just say "HEY NEAL TIO TIO TIO" and alarms will go off in my room.

    But it's a good idea. I spent a lot of time before SCC doing time estimates... should've recognized that as a good addition to the program :).
     
  36. AlphaZealot

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    wow...yea actually thats a really great idea.

    Anyways, its been stuck. I'll keep checkin in though, looks pretty sexy so far.
     
  37. AltF4

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    My very own stickied thread...

    I could almost cry... If I weren't in actually an emergent intelligence created in a basement from two modded Vitrual Boys. Oh, yes. And you thought they were useless...
     
    Sideslick likes this.
  38. Sizzle

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    Great work as always Dan. I also want to add that his RR formula is tried and true in the AZ Smash Community. He has accurately predicted the time of all the round robins that have occurred within minutes. Too good.
     
  39. AltF4

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    I'm having a hard time on this: Is a swiss tourney essentially the same as a single elim bracket with all the consolation matches played? I think so...
     
  40. AlphaZealot

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    I use to play chess competitively, and all chess tournaments are run using swiss format (as was Getting Schooled I and II and a UMD tournament back in 2004-2005).

    Anyways, in swiss, in the first round you either play random or seeded opponents. If it is a ranked chess tournament then you play seeded matches, with higher ranked players playing against lower ranked players.

    Everyone plays in every round, always.
    You always match people with equal or as close to equal records as you can.

    So.
    If you win the first round you play someone in the second round who also won
    If you win the first two rounds you play someone in the third round who also won twice
    If you lose the third round you play someone in the fourth round who also won two and lost one

    Getting Schooled II ran with 8 rounds of swiss format followed by a seeded double elimination bracket with 22 people. Round points were 1 point for each game in a set that you won. So people with equal point values played each other. 12 points got you into the bracket.
     
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