Maximum likelihood
Maximum Likelihood
ML tie breaker methods use statistics to work out a tournament rank for players on equal scores to decide who has had the best performance. A simple example is to use your favourite rating program (eg from a server, or European ratings) with everyone starting on the same rating.
basic technique We can use GoR to calculate tournament performance rating. Several programs alread yexist implementing the formula to calculate change of rating, deltaR, after a tournament. All that needs to be done is to find the entry rating for which deltaR=0. Relatively trivial to program. It would be nice to see this incorporated in some Draw programs.
I think this is a good idea actually. For example, consider this event. One player finished in 3rd as his first round opponent was unable to play in the last 2 days, costing him SOS. However discounting the first round he would have jointly won with Silt. Using Tournament Performance GoR would have produced a different result. Something to consider for draw program makers.
pwaldron: From the table, the third place player still ends up losing on SOS tiebreaks even if the first and second rounds are discounted, although the gap becomes very small. The ML method has some advantages, although I would not want to be the tournament director trying to explain the statistics of the system to someone on the short end of the system.
After looking at the tournament grid, though, I have two questions:
- Was there some kind of seeding in the tournament? The eventual winner played only opponents who finished in the top eleven of the tournament. Naturally this helped his SOS score compared to the second- and third-place players, who got paired much lower down in the field.
It was a European McMahon, with the bar was set at 2dan I think. Although they seem to claim it was 3d (Cornel - Jantunen says otherwise)
- It seems that the SOS tiebreak of the third-place finisher was not adjusted for the fact that his first opponent skipped the final two rounds. Shouldn't the SOS score of Ben He (the third-place finisher) be credited with 0.5 points per missed round? This doesn't affect anything this time, but it seems unfair to penalize a player because one of his opponents didn't play all the games.
GoDraw? adds the initial McMahon score for each round missed, which here was 0 I think.