TieBreaker

A good document to read on tiebreakers is available here. The choice of tiebreakers available in Ire is coloured by my study of the available tiebreaker methods.

• I implemented MOS because I believe it can be a useful alternative to, or refinement of, the SOS tiebreaker.
• I also implemented MDOS to try to fix some of the problems with SODOS. SODOS has a problem with being variant on origin. Therefore, if the number of wins are not equal, you can have a different ordering. Hence we have MDOS and a SODOS which first takes into account the number of wins, then reverts to pure SODOS.
• By way of experiment I made OPERA tiebreaker, which is ideologically akin to SOS but based around rating points.

Now that we've taken the time to explain all of that, let me tell you a secret. We set the default tiebreaker as SOS. Almost everyone knows what SOS is and it is a straightforwardly decent tiebreaker to use in a McMahon tournament. The settings file has space for 3 tiebreakers by default. Don't feel you have to use all 3. You can actually add a fourth if you're just plain nuts.

What do we do if somebody took a bye? Well first off, every player taking a bye gets a half point added to their MMS. Then we say that your imaginary opponent is the average of all your other opponents. Once we've constructed the imaginary opponent, then we make the tiebreak calculations.

How do handicaps enter into the equation? Well, assuming that you allowed them, they are subtracted or added to the MMS of the opponent when considering the values of SOS, MOS, MDOS, or SODOS.

Remember that Tiebreakers are used to refine the Draw according to the PairingTheory. So unless you are using Simple pairing, then the order that you choose is important because you are defining the draw according to those tiebreakers. Having said that, we can also define an additional tiebreaker to apply only after the tournament has finished. This is done by adding the word END after the tiebreaker. As an example:

• Tiebreaker 1: SOS
• Tiebreaker 2: MOS END
• Tiebreaker 3: MDOS END

This pairs the tournament according to SOS and MMS. At the end of the tournament we weigh in with 2 additional criteria (out of sheer desperation?) to try to remove any possible chance of a tie occurring. Now let me tell you another secret. You can also specify that a tiebreaker only applies to Pairings! An example

• Tiebreaker 1: SOS PAIR
• Tiebreaker 2: MOS END
• Tiebreaker 3: MDOS END

So here we used MMS and SOS to build pairings, but in the final ordering we only used MMS, then MOS, then MDOS. Funky eh? Well maybe it is not really especially funky, but don't let that stop you from knowing that this exists and can be used in the program. To sum up, by default a tiebreaker applies to both pairings and end ordering. You can type the keywords PAIR and END to make further distinctions.

Definitions

• MDOS: A tiebreaker. I might have invented this one. It is the mean value of your SODOS. It might be less confusing if this was named ADOS.
• MOS: A tiebreaker. This is the Most Of your SOS. The score from the highest and lowest opponent are dropped. In the case of byes, an average from actual opponents will be used. For a very short tournament, such as 3 rounds, this might be unhelpful. In chess it is called Median or Median-Buchholz. Note that in rounds 1 and 2 we set MOS to equal SOS.
• SODOS: A tiebreaker. This is the sum of your defeated opponents' MMS. In the case of byes, an average from actual opponents will be used. In chess it is called Sonneborn-Berger. NOTE in our implementation we break ties first by looking at the number of wins to solve the McMahon origin problem.
• SOS: A tiebreaker. This is the sum of your opponents' MMS. In the case of byes, an average from actual opponents will be used. In chess it is called Solkoff.
• SOSOS: A tiebreaker. This is the sum of your opponents' SOS. In the case of byes, an average from actual opponents will be used. Suprisingly I have not found a name for this in the Chess world!
• OPERA: An experimental tiebreaker. This is the average performance rating of your opposition.