Alpha, I think I'm confusing you on the subtext, which I should just omit. You seem to be following my main text though (Swiss is ideal in a scheduled tournament environment, which we should consider utilizing). 

Page 2 recap: Much agreement (Yertle included!) on Conan's system. Alpha and (especially) Hugh almost off topic. Questions about seeding arise. Tune in for Page 3.

Conan wrote:

Tom, can you explain how this is done currently?

Seeding is only done for Swiss system tournaments and is based on your board ranking. If you don't have a board ranking then you are given a default score of 1000. The players (or teams done by average ranking score) are sorted top to bottom then the list is split into halves. The top player from the top half plays the top player from the bottom half, then the second player from the top plays the second from the bottom half etc until all the games are filled.

tom wrote:

Conan wrote:

Tom, can you explain how this is done currently?

Seeding is only done for Swiss system tournaments and is based on your board ranking. If you don't have a board ranking then you are given a default score of 1000. The players (or teams done by average ranking score) are sorted top to bottom then the list is split into halves. The top player from the top half plays the top player from the bottom half, then the second player from the top plays the second from the bottom half etc until all the games are filled.

 

I am glad to hear that there is a seeding; I had no idea this was in place.

Is this be used for future rounds as well (only when there needs to be one person to fill a game with undefeated players) or is it done random?

The seeding only happens for the first round. After that it's random - I found that if you seed subsequent rounds you end up with players playing the same opponents again. Ideally it would seed while avoiding rematches but this hasn't been implemented.

Ok, it sounds like you have reached consensus, and far be it for me to come up against the phalanxes of theorists behind the systems being considered, but I decided to play around with my idea anyway.

I created a number of mock swiss tournaments with 2 players per game and 11 players total - I made sure there were three winners with 7-3 records that resulted in a tie using either SODOS or SOSOS (SOSOS always results in a tie if Player A beats B who beats C who beats A).

From there I decided to look at the records of their winning opponents (SOWOS = the scores of the opponents they lost to), with the premise that the the player losing to the best performing of this combination of players wins the tournament. 

So my method was (SOSOS/SODOS)/SOWOS

I was unable to come up with a scenario where this didn't work.

M57, it looks like that was round robin, not Swiss. In Swiss, we bracket in a way where the number of players is divisible by the game size.

For round robin, the proposal is SODOS (Sum of Defeated Opponents Score for those lost in the acronyms we've been using), and if SODOS fails, it is a tie. 

Keep in mind that the goal is not to just produce a formula to break ties. It is to break ties according to a reasonable criterion. Sum of opponents scores (SOS) measures the strength of schedule - the leader with the hardest schedule wins. Sum of defeated opponents scores (SODOS) measures the difficulty of the wins - the leader with the most difficult victories wins the tournament.

I have no idea what (SOSOS/SODOS)/SOWOS measures. Why is it reasonable to break ties with this?

That said, your previous suggestion of SOS/SOSOS/SOSOSOS/etc was completely consistent with the mindset of measuring strength of schedule. Yet, we have not produced a Swiss not broken by SOSOS (which isn't to say one can't be produced, so this may have merit, but we all suspect it is rare). If your 7-3 tournament isn't broken by SODOS, what about SODODOS? That would be consistent with the mindset of how we're proposing to break round robins.

hmm.. Any swiss that ends up with a single loss three way tie.. i.e., 10-1, 10-1, 10,1 (with intertwined/circular wins) kills all, doesn't it?  SOS SODOS SOWOS - doesn't matter.

M57 wrote:

hmm.. Any swiss that ends up with a single loss three way tie.. i.e., 10-1, 10-1, 10,1 (with intertwined/circular wins) kills all, doesn't it?  SOS SODOS SOWOS - doesn't matter.

Yes, this is a pure tie (you meant round robin, not Swiss).  This is a tie that should never be broken (except perhaps by a playoff) since the players performed equivalently in every way imaginable.

How about a tie breaker after SODOS/SOWOS or whatever is chosen based more or less what we have now? (..the scoring system where everyone comes in at 10,000)  Combine the somewhat arbitrary old with whatever new we come up with for a compromise solution?

--> New system / Old System.

Probably the only instance it will be used is in the circular win case, and it's likely as good as anything else we can come up with; AND there are a couple of plusses I can think of.  It's already coded ..and understood by the community in that it's essentially the system we use for global and board rankings. Tom has it ready and waiting.  It could be hidden from view during the tournaments and only posted/announced if/when it is used.

M57 wrote:

How about a tie breaker after SODOS/SOWOS or whatever is chosen based more or less what we have now? (..the scoring system where everyone comes in at 10,000)  Combine the bad old with the new good for a compromise?

--> New system / Old System.

Probably the only instance it will be used is in the circular win case, and it's likely as good as anything else we can come up with; and there is one plus I can think of.  It's already coded and documented.  Tom has it ready and waiting.  It could be hidden from view during the tournaments and only posted/announced if/when it is used.

Compromise?? Where was there disagreement? Why are you breaking a circular tie? The fairest way to break a circular tie is randomly. We had agreed that in the rare case of a circular tie, we would call it a tie. There is no reason in a circular tie why one of the tied players should be declared the winner over the others. (but if you must, if you really really must, seriously, chance beats all other options.)

Hugh wrote:

There is no reason in a circular tie why one of the tied players should be declared the winner over the others. (but if you must, if you really really must, seriously, chance beats all other options.)

                     ..not even nice game of Rock-Paper-Scissors?

M57 wrote:

                     ..not even nice game of Rock-Paper-Scissors?

                                                    

Yes, yes...Or a playoff of some sort like rock-paper-scissors (so it doesn't _feel_ like its chance!)

M57 wrote:

From there I decided to look at the records of their winning opponents (SOWOS = the scores of the opponents they lost to), with the premise that the the player losing to the best performing of this combination of players wins the tournament. 

So my method was (SOSOS/SODOS)/SOWOS

I just realized I did not understand what your slashes meant. I thought they meant division!

Now I understand: you mean to first use SOSOS or SODOS (depending on whether it is a Swiss or a round robin), and then if that fails, use SOWOS. Ambiguity's a killer.

For round robin, this won't work because every player has the same Sum of Opponent scores (SOS) and because Sum of Opponent scores = sum of defeated opponents score + sum of lost to opponents score. That is, SOS = SODOS + SOWOS. Thus, if SODOS is tied in a round robin, so too will the SOWOS be tied.

For Swiss, you are essentially saying to use SOS, use SOSOS, and if that fails, use SODOS (or equivalently, use SOWOS, since SOS is tied). This is a new proposal.

Hugh wrote:

For round robin, this won't work because every player has the same Sum of Opponent scores (SOS) and because Sum of Opponent scores = sum of defeated opponents score + sum of lost to opponents score. That is, SOS = SODOS + SOWOS. Thus, if SODOS is tied in a round robin, so too will the SOWOS be tied.

Hmm.. I am definitely doing a poor job of describing my proposal..

Consider the following RR.  I made it such that A, B, and C lose 1 game to each other, and the rest to some combination of I, J, and K, with the result being an SOS or SODOS tie.

What I meant to say is the Sum of the Winning Opponent's Defeated Opponent's Scores (SOWODOS).

You could also take the Sum of the Defeated Opponent's Defeated Opponent's Scores (SODODOS), which would give you an inverted solution per your comment regarding the sum of Defeated and Winner's Scores.

I guess you could argue which is more appropriate, I think it's SOWODOS, but either way it should work with Round Robins.  I'm tempted to say that I could produce a tie using this method. I'd probably start with the triad at the top going 8-2, each with a loss to each other and also the same player (that'd do it) or possibly three players with the same SODOS, but this has got to be quite rare..?

Of course, even with this method you still have the 10-1 intertwined scenario that needs an tiebreaker.

Just my quick thoughts ignoring most of the above.

Why not let a pure tie happen after whatever is agreed upon?  There cannot reasonably be more than three people tied at the end of a tournament so give each of them the trophy if there is an irresolvable tie (i.e. tied record and tied SO...whatever).

After thought, these could even count as a 1/2 or 1/3 tournament win for the player overall total tournament win count.

M57, I really like your example. SOWODOS vs SODODOS: If you are using SODOS, then you already rejected that we should care about the sum of the scores of opponents that beat you. In SODOS-land, you have decided to place more emphasis on the scores of opponents you beat (very similar to head-to-head logic). So, with that emphasis, by the same preference that got you SODOS, you should use SODODOS (Sum of the Opponents you defeated's SODOS scores...)

I agree with Alpha's suggestion on pure ties: split the total tournament win count.

(Sorry M57, the 10-1 3-way round robin tie can't be broken fairly with the existing tournament information. Playoffs, chance, or some form of outside information is required. It is simplest just to call such events ties.)

So is there a consensus here? If so what is it exactly 

Hugh wrote:

(Sorry M57, the 10-1 3-way round robin tie can't be broken fairly with the existing tournament information. Playoffs, chance, or some form of outside information is required. It is simplest just to call such events ties.)

Absolutely; Ties will happen.  But with the addition of SODODOS the pure intertwined type of tie could possibly be the only time this happens, and even slight variations of it will produce a winner with very few exceptions. If this is agreed, then the options become:

1. [Wins-->SODOS-->SODODOS]  Ignore special H-2-H consideration.  Ties still possible (do whatever we're going to do with ties).
2. [Wins-->SODOS-->SODODOS-->H-2-H]  Use H-2-H results as final tiebreaker.  You could still have a tie if both lost in their H-2-H (3 player game, for example).
3. [Wins-->H-2-H-->SODOS-->SODODOS]  Apply H-2-H results before SODOS-->SODODOS consideration.  Ties still possible.

I know your preference is 3.  I'm starting to like 2.

Consider that with #2, and with a 3rd player win in a 3-player tie-breaker game, the third player (if he's close enough in the standings) could win the tournament by evening up the Wins column to a three-way tie AND coming out ahead in the SODOS-->SODODOS department (in fact, my guess is it would be likely given that he's going to get a major boost in the SODOS column from taking out the top of the leaderboard).  What's wrong with that?  I rather like it.

Of course there is the possibility that the two-way tie remains if the 3rd player wins and it's still not enough to tie the leaders.  Solution..  Play again.  If the third player wins again, recalculate; if he keeps winning, play until he overtakes the leaders in the standings.  This is very fair, and it provides a mechanism for the 3rd player to be in the hunt no matter how far back he is in the standings.

Hmm.. I just realized.. Regarding #2:  Where it comes to choosing the 3rd player for a playoff,  consider the possibility that more than one player may eligible to be in the game.  I.e. you could still have a 2 way tie for second place even after applying SODOS..  Solution.. You Could have play-offs for the number 2 slot to determine who goes to the show.  Apply down the line if a third player is needed.  Complicated, but it can be done.

Also, what is proposed for a playoff for a 2-player game with a 3-way tie?

tom wrote:

So is there a consensus here? If so what is it exactly 

As far as I can tell not much has changed. We like Conan's system:

Swiss: Wins, then Sum of Opponents Scores (SOS), then Sum of Opponents SOS (SOSOS).

Round Robin: Wins, then head-to-head, then Sum of Defeated Opponents Scores (SODOS).

In the event that these fail to break the tie, it is called a tie.

Though it took some posts to understand each other, it was brought up that there are round robin tournaments that SODOS doesn't break that a further iteration (using the same logic) would break. There is no consensus on usage yet (it is a recent proposal after all).