In a tournament with R rounds, a player's ROS (ROunds Score) is the sum of his round points over all rounds in that he wins. Round points in round r are R - r + 1. Winning each round in a 5-round tournament, for instance, earns him an ROS of 5 + 4 + 3 + 2 + 1 = 15.
Round points decrease linearly, and in each round winning gives better round points than losing, for which a player gets 0, obviously.
In a tournament using strict folding to determine the pairings in one group (players with the same McMahon Score) it is expected that the possible opponents of a player will perform pretty much the same and will give a player the same SOS whatsoever. Why not make the tie breaker independent from the actual performance of the opponent?
Robert Jasiek: I do not recommend to use any tie breaker but if some is used, then at least it should be honest. I think that ROS is more honest than SOS in a Swiss or McMahon tournament with a typical pairing strategy.
Of course, one can also define an increasing (inverse) rounds score IROS if one thinks that more exhausted players get more important competition in later rounds. One can define about everything as a tiebreaker. In particular, since one can define ROS and IROS, it is absolutely unclear why one should use any tie breaker at all!
Christoph Gerlach: At best this shows that ROS/IROS are no good tie breaker (same league as SODOS) but this point cannot be used to declare all tie breaker as useless or bad. Also ROS is similar to CUSS which is accepted being a bad tie breaker. The argument against CUSS and ROS: why should an approximation be any better than using actual data if it's allready there (SOS)? Another drawback specific to ROS (and not to CUSS): having more wins gives you most likely more ROS even if you played much weaker opponents. Except at the very top of the tournament ROS is likely to mix up the final ranking with having (obviously) weaker player ranked in front of stronger players if used as first tie breaker.
RobertJasiek: "expected average strength of the opponents with extra bonus for winning more games" as a description of ROS is somewhat of an overinterpretation. When inventing ROS, I meant it to be "winning in earlier rounds is more important". From this my comment "more honest than SOS" is derived because SOS can be said to follow two intentions:
- "winning in earlier rounds is more important",
- "average post-tournament-view strength of the opponents".
Tapir: If anyone cares... ROS + SOL = n*(n+1)/2 (n = Number of rounds), is identical to CUSS for use as a tie breaker (in Swiss tournaments and the top group). Freaks, who are really interested, should refer to CUSS and the discussion at TheoryBehindSOS/discussion.