# CUSS

Keywords: Tournament

CUSS (CUmulative Sum of Scores) is a possible tie breaker in McMahon Pairing or Swiss System tournaments and is calculated as the sum of the scores a player had after each round of the tournament.

In chess CUSS is also known as Sum of Progressive Scores or, simply Progress.

CUSS is approximating the expected SOS of a player, but can not be influenced by the performance of opponents like SOS can.

CUSS as described here is using winpoints of the player ( 1 point for a win no points for a loss, (Swiss CUSS) CUSS can also be done with the McMahon score of the player. I am not sure if this leads to a different result as the swiss CUSS. The version using the McMahonscore is the CUSS score is in use by the British Go association CUSP is roughly equivalent to the swiss CUSS score.

## Example

Suppose a tournament with the following top 4 results (lower ranking players made less wins)

```Name 	   R 1 	R 2  R 3  R 4  R 5  R 6  R 7  R 8  R 9 	R 10 Wins
Player 1  14+  10+   7+   5-  25+  11+   3+   6+   2+ 	 4-   8
Player 2  33+   8+   6+   3-  14+   4+   5+  15+   1- 	13+   8
Player 3  27+  11+   4+   2+ 	5-   9+   1-  13+  23+ 	 7+   8
Player 4  24+  23+   3-  17+  12+   2-  26+  11+  10+ 	 1+   8
```

The score then becomes (just count all values in a row together)

```Name 	   R 1 	R 2  R 3  R 4  R 5  R 6  R 7  R 8  R 9 	R 10  score
Player 1   1+   2+   3+   3-   4+   5+   6+   7+   8+   8-     47
Player 2   1+   2+   3+   3-   4+   5+   6+   7+   7-   8+     46
Player 3   1+   2+   3+   4+ 	4-   5+   5-   6+   7+ 	 8+     45
Player 4   1+   2+   2-   3+   4+   4-   5+   6+   7+ 	 8+     42
```

Or giving wins in rounds a value (Again just count all values together)

```Name 	   R 1 	R 2  R 3  R 4  R 5  R 6  R 7  R 8  R 9 	R 10  score
Player 1  10+   9+   8+   --   6+   5+   4+   3+   2+   --     47
Player 2  10+   9+   8+   --   6+   5+   4+   3+   --   1+     46
Player 3  10+   9+   8+   7+ 	--   5+   --   3+   2+ 	 1+     45
Player 4  10+   9+   --   7+   6+   --   4+   3+   2+ 	 1+     42
```

## Motivation for CUSS

The Idea behind CUSS is that players with wins in the earlier rounds will face stronger opposition than players winning the latter rounds, and therefore have more right on the prize.

## Advantages for CUSS

• Easily explained and calculated
• The CUSS score is only influenced by the players games. The results of their opponents against other players doesn't influence the outcome.
• Similarly, it can be exactly calculated at the end of the players game in the last round.

A prelimanary score can be calculated after each round.

## Drawbacks of CUSS

• The influence of the first round pairing is big. According to most tournament directors too big to be acceptable.
• Invites sandbagging starting against weaker players gives a easy early win. and a high CUSS Score, while the opponents rating doesn't influence the Cuss score (while it does in SOS)
• Should not be used in Round Robin or round robin like tournaments because the primary motivation behind Cuss (early wins lead to a stronger opposition) is not valid in these tournaments.

## Present use of CUSS

(February 2010) CUSS is not used in any tournaments any more. It's because it does not really reflect the average strength of the opponents. With CUSS playing a weak opponent in early rounds of the tournament means an easy win without the drawback of getting bad SOS. The influence of the draw is too big to be acceptable.

## Historical note

Several years ago CUSS was in use at EGF tournaments for a short period to eliminate the possibility of a player affecting the SOS of his opponents by intentional losing all is following games in order to reduce the chances of his opponents to finish at a good place. Why should he do so? Because he has a friend who has chances to finish at a good place too - and earn some prize money.

## Chess

MRFvR: In Chess tournaments, CUSS is called as Sum of Progressive Scores or simply Progress, and is commonly used. The above quoted drawback most disappears in the presence (which is usually the case for chess tournaments) of reliable rating for the vast majority of participants, since the initial draw would be rating guided. I'm not sure, however, if that would be still valid for a McMahon tournament.

Tapir: Maybe one should note the difference between Swiss (in Chess) and McMahon (in Go) tournaments here. With McMahon the theoretical previous rounds are scrapped already.

## Related system: SOL

An easier way that gives the same result is SOL (Sum of lost games round numbers)

Starting with the same results:

```Name 	   R 1 	R 2  R 3  R 4  R 5  R 6  R 7  R 8  R 9 	R 10 Wins
Player 1  14+  10+   7+   5-  25+  11+   3+   6+   2+ 	 4-   8
Player 2  33+   8+   6+   3-  14+   4+   5+  15+   1- 	13+   8
Player 3  27+  11+   4+   2+ 	5-   9+   1-  13+  23+ 	 7+   8
Player 4  24+  23+   3-  17+  12+   2-  26+  11+  10+ 	 1+   8
```

Only look at the lost games

```Name 	   R 1 	R 2  R 3  R 4  R 5  R 6  R 7  R 8  R 9 	R 10 Wins
Player 1  --   --   --    5-  --   --   --   --   -- 	 4-   8
Player 2  --   --   --    3-  --   --   --   --    1- 	--    8
Player 3  --   --   --   -- 	5-  --    1-  --   -- 	--    8
Player 4  --   --    3-  --   --    2-  --   --   -- 	--    8
```

The players score is the sum of the round numbers of the lost games

```Name 	    First loss     Second loss   Score:
Player 1    Round  4       Round 10      4 +10 = 14
Player 2    Round  4       Round  9      4 + 9 = 13
Player 3    Round  5       Round  7      5 + 7 = 12
Player 4    Round  3       Round  6      3 + 6 =  9
```

Math

• CUSS = SOL + (a*(a+1)/2 - b*(b+1)/2) with a = number of wins, b = number of losses. At least as tie breaker (with tied players having the same number of wins) it should be identical.
• Also ROS + SOL = n*(n+1)/2 with n = the number of rounds in the tournament.

CUSS last edited by willemien on May 20, 2010 - 17:15