McMahon Tiebreakers - SODOS and Rating out, Head-to-head in


I’d just like to amend (title) tournament tiebreakers, because the current system is not entirely logical.

The title tournament results (including the decision of title match participants and trophy assignments) would use the following tie breaker (which has been implicitly applied for a while):

  1. Points (High > Low)
  2. Status (Normal > Disqualified > Resigned, disqualifications due to system hiccups would be treated as Normal)
  3. SOS (High > Low)
  4. SODOS (High > Low)
  5. Overall Rating
  1. Fair enough.

  2. Obviously no disqualified/resigned player should win, but if there is a reliable way to distinguish proper DQ from ‘server hiccup DQ’, I’m fine with 1>2.

  3. SOS. Alright, if you have the same number of wins as someone else, ‘having played ostensibly stronger opponents’ should be valued higher. Now the trouble with SOS is DQs/Resignations. Maybe A’s opponents were stronger than B’s, but more of them quit the tournament. In this case it becomes confounded with ‘having played fewer quitters’. I don’t have much of a problem yet with this one though, mainly because I haven’t looked at how bad this problem is. Perhaps we could change this to “Sum of Opponents’ Status”, 0 for DQ/res and 1 for active. Bonus: the abbreviation would stay the same. :smirk:

  4. SODOS. And here I clearly disagree. It should be head-to-head. Why? Well if you’re even on points and your opponents were ostensibly equally proficient, if A has a winning record against B, it’s hard to argue that the player with a losing record should outrank the other. Finally, to quote Christoph Gerlach (who wrote his dissertation on McMahon pairing):

Using SODOS as a tie breaker after SOS is also questionable. If SODOS will discriminate between two players, these two players have the same SOS. Let’s say Player 1 has a higher SODOS, this means that he has won to stronger opponents compared with Player 2. But he also lost to weaker opponents compared with Player 2 (we know this because both have the same SOS). Would anyone really think it is more significant to win against stronger opponents than losing to weaker opponents?

  1. Overall rating. What? This makes absolutely no sense and should be replaced by a Tie-breaker game. Yep. If you’re tied on score with someone and your opponents have fared equally well and you drew in the head-to-head, the only logical tiebreaker is one more game.

In summary:

  1. Points
  2. Status
  3. Sum of Opponents’ Scores
  4. Head-to-head
  5. Tiebreaker game


Oh, cool idea on the one more game tiebreaker


I’ve also seen SOSOS used before, and it might be worth consideration.


It would be more coherent than SODOS, but there is no problem SOSOS fixes that head-to-head doesn’t. SOSOS ‘does’ have the advantage of (probably) not requiring more games to be played, but the downside is that a) you’re essentially squaring all the noise in SOS by calculating that derivative and b) the tie could still remain.


I don’t agree with your hierarchy. I would say:

  1. Points (obviously the basis of a tournament)
  2. Status

but then:

  1. Head-to-head (in my view more important, and certainly easier to explain, than more obscure tiebreakers)
  2. Tiebreaker game (only if there is time)
  3. Kyu / dan rank at start of tournament (higher rank wins)


Much rather than your opinion I’d like to hear your arguments.

Now I’m not particularly attached to SOS (see previous remarks) but I wouldn’t throw out something I haven’t had the time to investigate thoroughly. SODOS and rating/rank are just clearly nonsensical tiebreakers that are of no discriminative value to the tournament. They’re irrelevant to everything (with the marginal exception of rank having some influence on grouping).


I have three arguments:

– Simplicity. If tiebreaks are easy to understand then it’s better for the tournament director, it’s better for the players, and it’s better for the spectators. There is no room for disputes over the tiebreaking, and people watching the progress of the tournament can make worthwhile predictions of how the tiebreaks will affect the results.

– Show. It’s more exciting for players and spectators if the results are decided by direct encounters rather than mathematics. Well, for me at least.

– Individual accountability. In my opinion, it is best for tiebreakers to take no account of how third party players fared in the tournament – that’s not under the control of the relevant individuals.


First, thanks for bringing up the discussion!

I made the current title tournament rule based on the following official/default/implicit tournament rule for OGS, i.e.:

  1. Status
  2. Points
  3. SOS
  4. SODOS
  5. Rating

Since in my opinion, the Disqualification Criteria, which disqualifies players with one single timeout, is way too harsh, I switched Status and Points in this hierarchy.

I agree that the remaining ones doesn’t make much sense (btw, on OGS, SOS is actually sum of opponents’ wins instead of sum of opponents’ scores) and they work like coin tossing in most cases, but the reason I didn’t change the other settings is simply because I’m doing the result reporting manually, and under current title tournament rule I only need to keep an eye on disqualified players when reporting players’ tournament ranking based on their system-decided ranking :wink:

I like the idea of head-to-head points, but one problem is when there are n players with the same score, you need to find out O(n^2) games played among them, which could be quite tricky when it’s done manually.

The tiebreaker game, however, can take quite a long time (as long as one extra round) for correspondence tournament, so it doesn’t seem feasible in this case.

Therefore, based on all the trade-offs, I’ll add the extra rule of head-to-head score as the third tiebreaker only for deciding the ranking of players with points that are not lower than the points of the third-place. In other words, I’ll manually calculate the head-to-head points to decide the top few (>=3) players. For the rest, the current rule will still be applied, at least before I had time to write a script to compute them automatically.

This new rule would be announced in the next tournament announcement and it’ll take effect for tournaments that start after the day of the announcement.


The maestro himself! With a pragmatic solution to an unfortunate lack of functionality I wasn’t aware of. :slight_smile:
I disagree on the DQ timeout thing though. If you can’t make it on time in a corr game, with vacation etc… you probably didn’t care enough. :3 Well, I suppose it makes sense for live games.

But yea, so SOS is even worse than I thought. What happens if people play each other more than once? Do you count the “opponent wins” twice/thrice? If not, people with a larger number of different opponents would be favored.

My next suggestion writes itself. Built-in tiebreaker selection & computation! @anoek When you’ve got the time. :heart_decoration: