I've seen some discussion.  A few examples are:

http://www.wargear.net/forum/showthread/1064p1/Tournament_tiebreaker

http://www.wargear.net/forum/showthread/1101

Here's my proposal:

Throw out the tournament "Score" (i.e number that starts at 10000).  Let's face it.  It really doesn't accomplish the task of fairly determining tiebreakers between players of equal score.  Instead, employ the following methods:

For R.R. tourneys: Use the SODOS (Sum of the Defeated Opponent Scores) for tiebreakers

For S.S. tourneys: Use the SOS (Sum of the Opponent Scores) as the primary tiebreaker and SOSOS (Sum of the Opponents' SOS) as the secondary tiebreaker.

(Reference Info: http://senseis.xmp.net/?TieBreaker).

Take a look.  I'm confident this is the solution.

They've already been proposed both (if I'm not wrong) (=

By the way, the actual score would work on swiss system assuming a slightly bigger number of turns. Right now Swiss System is set up to resemble an "elimination turnament", which is wrong, as it should be half the way between the RR and the Elimination systems.

Anyway, they're both good solution, as it is the head-to-head method.

(=

Do you have a link to the original proposal?

Is this one?

http://www.wargear.net/forum/showthread/1366/Swiss_System__Elimination_hybrid

Some here also:

http://www.wargear.net/forum/showthread/1064p1/Tournament_tiebreaker

http://www.wargear.net/forum/showthread/1070/More_rounds_for_swiss_tournaments

Some of the other solutions require dynamically allocating the rounds.  While interesting I don't think it's necessary and it also adds a lot of complexity.

My proposed solution is simple: Just extract already existing data from the scores to fairly determine tiebreakers.

For swiss tourneys, the first thing to do to make it more likely to have a clear winner is to setup the number of players properly.  Do this by having M^R teams (i.e. players in non-team tourney), where M = number of teams per game and R= number of rounds.   Regardless, the original post has a simple solution for swiss as well.

I want to re-iterate the benefits of the solution proposed in the original post:

• Simple, easy to implement
• Reasonably fair (if someone has an argument against this, let's hear it)
• Used in other gaming tournaments

Compared to the existing tie-breaker which is:

• Unfair
• Nonsensical

Conan wrote:

I want to re-iterate the benefits of the solution proposed in the original post:

• Simple, easy to implement
• Reasonably fair (if someone has an argument against this, let's hear it)
• Used in other gaming tournaments

I agree, this is a fine solution. However, we discovered that these systems can fail to break a tie. In this case, unless it is a "super important championship", the simplest thing to do is call it a tie. Ties are not well-liked, so we discussed some more complicated things (extending the tournament and things of that nature to break the tie).

Conan wrote:

Compared to the existing tie-breaker which is:

• Unfair
• Nonsensical

I strongly agree. However, opinion on this matter is divided. I don't know the right combination of words to convince people, but I have a feeling that asserting "unfair and nonsensical", while true, is not going to convince them.

It is not hard to produce concrete examples where the current system chooses a winner where it is hard to point to any good reason why that person was the winner. If you take the time to analyze these situations, you will see how weird the system is. 

Conan wrote:

For swiss tourneys, the first thing to do to make it more likely to have a clear winner is to setup the number of players properly.  Do this by having M^R teams (i.e. players in non-team tourney), where M = number of teams per game and R= number of rounds.   Regardless, the original post has a simple solution for swiss as well.

The purpose of the Swiss system is to be flexible with the number of players. I agree that we should use bracketed tournaments whenever possible. But... it is nice to have the option of not having exactly M^R players.

Here is a good example of our current system at work: three players, round robin two-player games. 

Player A beats Player B

Player C beats Player A

Player B beats Player C

This is the most tyingest tied tournament in all of tied tournament history. Each player has won a game and they played equally difficult opponents. 

Our system: Players A and C end with 9996 points, Player B has 10008 points and WINS!!!

So how would that example work under Conan's system? Or should it be declared an unresolvable tie and the tournament has no winner? If so, is that desirable outcome (i.e. noone won the tournamnet)?

I know we could have playoffs amongst the tied players but that has other problems (e.g. 3 tied players on a board which only supports 2 player games).

Sum of opponents score (SOS) for each player is 2. Sum of defeated opponent score (SODOS) for each player is 1. It is correct that it fails to break the tie. 

My claim is that we don't have great choices for the above tournament: We can arbitrarily declare a winner, we can call it a tie, or we can do a "playoff" consisting of replaying the tournament.

If you don't use a bracketed tournament, you open the door for these possibilities. 

So in other words we should just accept that some Swiss System tournaments will end in ties?

Any idea how likely this will be for WG tournament sizes?

Exactly. You could give the tournament host some tiebreaking options, but allowing ties should be the default.

The probability question is an interesting one. I'll get back to you on that.

Hugh's example, while showing that ties can exist even after the tiebreaker method (SODOS for RR), is not realistic because it's a smaller tournament than you can even create.  Though I don't have a lot of evidence, I've run through a few examples myself and seen the tiebreaker methods work well.

I think that in the (supposedly rare) case that a tie happens both players should be awarded the trophy.  When you hover over the trophy it could show the tourney name and, in parenthesis, the name of the co-winner.  It also seems reasonable (if the admin wants to implement it) to give the host an option for what to do in the case of a tie (i.e. no trophies or both trophies or replay??)

Here's an example of a 3 round Swiss that ended with 6 players with 2 wins and 1 loss each.  I ended up winning due to my score, but if you employed SOS, then SOSOS, CastratedHorse would have won:

Name                       SOS         SOSOS         Score

CastratedHorse       12            91               12500

Conan                      12            88               12680

AttilaTheHun            12            83               12410

bearcatj01                 8            79               12500

Garfield                      8            77               12410

AdamN                       3            59               12318 

Notice that with just 3 rounds there was enough data that the 6 out of the 32 players, each with the same 2-1 record, could distinctly be ranked 1 through 6 using the SOS/SOSOS.  That seems pretty good.  If someone could point me to another tournament with several tied records, I can try running this tiebreaker system on it and print the results.

Conan wrote:

Hugh's example, while showing that ties can exist even after the tiebreaker method (SODOS for RR), is not realistic because it's a smaller tournament than you can even create.  Though I don't have a lot of evidence, I've run through a few examples myself and seen the tiebreaker methods work well.

I believe you are right that such instances are rare, but over time they will probably happen and it is important to have a plan for dealing with pure ties. Unrealistic isn't quite right, though:

Any round robin with 3 leaders who beat each other in the way of my example and beat all other opponents will end with a tied SODOS.  When two tied leaders have lost two or more games in a round robin, there are ways it can end tied. So, unrealistic isn't the right word because it can happen in any tournament in a variety of ways. It's rare, especially with larger tournaments, but a system does need to address the rare for it to be systematic. I want to say that SOS/SOSOS ties will be quite rare in Swiss, but it seems like the Swisses end in larger ties on average, so... hard to say.

Conan wrote:

I think that in the (supposedly rare) case that a tie happens both players should be awarded the trophy.  When you hover over the trophy it could show the tourney name and, in parenthesis, the name of the co-winner.  It also seems reasonable (if the admin wants to implement it) to give the host an option for what to do in the case of a tie (i.e. no trophies or both trophies or replay??)

I agree. Options here are good. Replay can be tricky, depending on the player size of the game, but if it is possible, I like the option.

Conan wrote:

If someone could point me to another tournament with several tied records, I can try running this tiebreaker system on it and print the results.

We began here: http://www.wargear.net/tournaments/view/133

I'm curious who won: http://www.wargear.net/tournaments/view/80

http://www.wargear.net/tournaments/view/124

http://www.wargear.net/tournaments/view/146

Also curious: http://www.wargear.net/tournaments/view/68

http://www.wargear.net/tournaments/view/48

I have some comments that I'll post at a later time based on my experiences in another gaming community, but on the whole this suggestion beats the current system. (And I think it is important to plan for pure ties and allow them.)

Any round robin with 3 leaders who beat each other in the way of my example and beat all other opponents will end with a tied SODOS.  When two tied leaders have lost two or more games in a round robin, there are ways it can end tied. So, unrealistic isn't the right word because it can happen in any tournament in a variety of ways.

You are right on this point.  It seems the most likely tie would be in RR w/ 1v1 games and 3 leaders, each of whom beat one of the other 3, as you keenly pointed out.

In a RR with 3 player games, I can imagine a scenario where there are two with the highest score.  If A had beat B in their game together then A will probably win the tiebreaker; If neither won the game in which they played together, the tiebreaker system would still likely produce a winner.

You're probably right that ties will be harder in Swiss.  I'll need some time to look at your example tourneys!

I'll update this post as I get the results in.

Listed first is the winner w/ proposed tiebreaker, in RED is the one awarded the trophy with the current system.

The RR tourneys: The score listed is the SODOS

We began here: http://www.wargear.net/tournaments/view/133

• Viper = 19 / CiscoKid = 16

I'm curious who won: http://www.wargear.net/tournaments/view/80

• Viper = 140 / Likes It = 131 / CiscoKid = 127

http://www.wargear.net/tournaments/view/124

• rubbermonkey = 22 / RiskeyBack = 21

http://www.wargear.net/tournaments/view/146

• CiscoKid = 15 / Oatworm = 14

The Swiss System tourneys (these will take longer to look at):  The two scores listed are SOS, SOSOS.

Also curious: http://www.wargear.net/tournaments/view/68

http://www.wargear.net/tournaments/view/48

The Swiss System tourneys:  The two scores listed are SOS, SOSOS.

Also curious: http://www.wargear.net/tournaments/view/68

• Tesctassa II = 10, 83 / Hugh = 9, 81 / Gimli = 9, 81 / asm = 7, 73 / Alpha = 6, 70 / Vataro = 5, 62

http://www.wargear.net/tournaments/view/48

• Mad Bomber = 12, 75 / Seige07 = 9, 78 / Mongrel = 8, 71 / Master Bratac = 7, 72 / j-bomb = 6, 76

regardless of whatever math you folks are arguing about (tended to tune out when the math came out); i thought the tourneys had been been changed to be head-to-head and if still tied after that, then Score....at least until you convince Tom of something else to replace it....

Okay okay. Non math summary so far: Conan suggests a tiebreak method (well known, used from other gaming communities) over score. The goal is to at least convince Tom, but it would be nice for rest the community to see the value in this, and the harm of the current system.

Hugh says it doesn't always break a tie, and that it is insanity to break "pure ties". Conan says such ties are rare. Hugh agrees, but wants ties to be dealt with systematically. Conan agrees. Throughout the thread, examples of tournaments are given where score produced a questionable winner. We can expound on why they are questionable if need be, but Conan's data on tournaments we've run is quite damning for the current system.

I believe there is more to say, more to discuss, and that most of it won't come down to math. (Score is mathematical in nature, it's design and intentions, mathematical, so the reasons for its inadequacy in this context, will have to be discussed using at least some mathematics.)