velobici: interesting URL Herman. (2008-02-25 00:19) [#4384]

The tie break report from the first link that Herman Hiddema provides is quite interesting. In it we see that the winner of the tournament Xuefen Lin faced a more difficult field than the second place finisher Takahiro Kitagawa according to SOS value (270 vs 220), but a weaker field according the average rating of opponents (7.6 vs 7.7). This is even more noticeable when comparing Xuefen Lin to Yongfei Ge, the third place finisher (SOS: 270 vs 210 and 7.6 vs 8).

If we believe the rating system works, then Yongfei Ge faced the most difficult field of opponents; more difficult than anyone else in the 2005 US Open.

Xuefen Lin was fortunate, at least as far as SOS goes, in playing players with results in the top decade only. This ensured that each of her opponents had a relatively high McMahon Score (MMS) and so provided her with a high SOS. Both Takahiro Kitagawa and Yongfei Ge were paired by the tournament director (or his software) with players in the second or even third decade of players. These pairings disadvantaged both Takahiro Kitagawa and Yongfei Ge with regard to the SOS that they could accumulate irrespective of their win/loss results. Unfortunately, we do not have the time series data...which of the six games did each player lose. Losing one's first game is much more disadvantagous for SOS than losing the last game.

Each of these three players lost only one game. They fell one game short of having the best records possible based upon their own achievement. In the end, the value used to distinguish among the top four players, all 5 wins and one loss, was influenced by the pairings assigned to each player. Would either Takahiro Kitagawa and Yongfei Ge have own 5 games given the SOS favorable pairings received by Xuefen Lin? Don't know. But each one having received multiple pairings in the second and third decades had diminished chances to win the tournament due to the tie breaker selected.

Note: Since each player played all rounds and there wer no draws, I would have expected that SOS would equal the sum over the set of opponents of each opponents initial McMahon Scores and number of wins (SOS = sum(MSS initial + wins)). Rearranging terms the sum of the initial McMahon Scores of the set of opponents plus the sum of the wins of set of opponents (SOS = sum(MSS initial) + sum(wins)). That does not seem to be case. The top four players played against people in the top band only. All the people in the top band had the same initial McMahon Score and therefore the term summing the initial McMahon Scores is identical for all four players and only the second term (sum(wins)) distinguishes one of these four players SOS from another. Doing the math:

Player             op. wins      SOS   list SOS
Xuefen Lin:        4 4 5 4 5 5 = 27    270
Takahiro Kitagawa: 3 2 4 4 4 5 = 22    220
Yongfei Ge:        3 3 3 4 5 3 = 22    220
Haifeng Liu:       2 3 3 4 3 5 = 20    200

velobici: Lin lost in the last round ? How do you know ? (2008-02-25 00:24) [#4387]

Herman which link are you referring to? The link to the results on the page provided by your first link is broken. Are you referring to the link that I provided ( http://www.usgo.org/congress/2005/USopen%20results-05.htm)? If so, that list shows wins and losses without time ordering information. This is clear from the results of Kitagawa and Liu. They could not have both lost to Lin in the last round. Furthermore Ge is shown vs Phipps in the last column whereas Lin is shown vs Ge. The results are listed with all wins first, then all loses. Its a shame.