How to calculate SOS

This page is about the tie breaker called SOS, and the specifics on how to calculate SOS in various tournament systems.

Table of contents Swiss tournaments McMahon tournaments Hahn System Tournaments Players missing rounds Mathematical Relations

Swiss tournaments

In a Swiss tournament, to determine the SOS of player X use the following procedure:

1. List the players against whom player X played in this tournament.
2. Sum the scores achieved by each player in the list.
3. Adjust for missed rounds (see below).
4. The sum is the Swiss tournament SOS for player X.

McMahon tournaments

In a McMahon tournament, to determine the SOS of player X use the following procedure:

1. List the players against whom player X played in this tournament.
2. Sum the current MacMahonScores of all players in the list.
3. Adjust for missed rounds (see below).
4. The sum is the McMahon tournament SOS for player X.

Note: The program PyTD uses the term SOMS, in place of SOS, in MacMahon tournaments.

In practice there are two approaches to the inclusion of handicap games in the calculation of SOS.

• One says that the sum of the handicap you give during the tournament should be added to the final sum of your opponent's scores.
• The second is to ignore the handicap in calculation of SOS.

Hahn System Tournaments

In a Hahn System tournament, to determine the SOS of player X use the following procedure:

1. List the players against whom player X played in this tournament.
2. Sum the Hahn System scores of each player in the list.
3. Adjust for missed rounds (see below).
4. The sum is the Hahn System tournamnt SOS for player X.

Players missing rounds

If a player does not play on a round of the tournament, he will on average miss "half a win". This will adversely affect the SOS of his opponents. In Swiss and MacMahon tournaments, the common ways to compensate for this are to either award 0.5 points per missed game or to award 1 point for every two missed games, at least for the purpose of SOS calculation.

Question: what value is added for missed rounds in a McMahon tournament ?

If you intend to use SOSOS as a secondary tie breaker, it is important that you award some SOS to the players who missed the round too. A good way to do that is to treat the missed games as if the player had played against himself each time, winning every even numbered game.

Mathematical Relations

Score == player's initial score at the beginning of the tournament
       + adjustment due to each game won
       + adjustment for missed rounds.

Using variables:

S = Score
I = Initial score at the beginning of the tournament
W = adjustment due to each game the player Won
M = adjustment for each round the player Missed.

SOS == I + M + Sum of S
       I + M + Sum of (I + W + M)

In a Swiss tournament:

• I == zero for all players.
• W = one for each game won.
• M = one-half * number of rounds missed

In a McMahon tournament:

• I == McMahon score assigned to each player that start of the tournament.
• W = one for each game won.
• M = one-half * number of rounds missed

In a Hahn tournment:

• I = what does I equal ?
• W = a value between 0 and 100. (see Hahn System).
• M = how does Hahn handle missed rounds ?