Buchholz score as a measure of fairness of the draw.
Average Ratings of Opponents, the Buchholz and Sonneborn-Berger System are some of the methods recommended by FIDE for breaking ties in Chess tournaments. While ties are the order of the day in chess tournaments, in the Scrabble world it is virtually unheard of. But what works for tie breaking in chess works well for evaluating Scrabble pairings. We will take a closer look at Buchholz in this post particularly since it's one recommended by John Chew, the creator of Tournament Shell for exactly this purpose.
The sum of opponent scores or Buchholz is “..the idea is that the same score is more valuable if achieved against players with better performances in a given tournament. Looks like an ideal tie-breaking method and has been used since the Swiss system was invented.” (Swissperfect, 2008)
In this context the score means the number of games won by each player. To avoid confusion with the number of points scored on the board, the term Bucholz score will be used when the discussion is about the total number of games won by a player's’ opponents. And this discussion is about evaluating the fairness of King Of The Hill pairings in Scrabble. This is fourth part in a series.
For example Hayati played against Erandi (3 wins), Thirandi ( 3 wins), Danusha ( 5 wins), Janidu (3 wins), Lalinka ( 3 wins), Navodya (5 wins) so her Buchholz score is 22. This is what is looks like for all the prize winners.
Table 2.4 Sum of opponents scores for each of the prize winners
Most of the prize winners have a Buchholz score greater than 20. For Akshai, it's only 17 but that's reasonably since he is placed only tenth overall isn't it? Let's see what the next table, it lists the players with the best Buchholz scores
|41||Lalinka De Silva||24|
|20||Janul De Silva||23|
Table 2.5 Players with the highest Buchholz scores.
There are 12 players with a Buchholz score of at least 23 and one of them Therunee ended up in 75th place. For comparison purposes the player at the 76th position had a score of 14. Among the prize winners only four players had a score of 24 or more. Let's also take a look at the table for top rated players.
|3||Janul De Silva||23|
|9||Thirandi De Silva||22|
Migara and Rehan suffered losses in the third and fourth rounds so their Buchholz scores are only 19 but Hasindu who suffered a loss in the second round and another loss in the third round still has a Buchholz score of 20 as shown in the table above.
Except for Vignesh most of the other rated players have Buchholz scores that compare favourably with the prize winners. Except that many of these players didn't actually win any prizes!
Though Janul lost the second game he obviously didn’t have an easy time of it from that point onwards, as can be seen by the fact that his opponents racked up 23 wins among themselves. In other words, Janul kept running into tough opponents who were all lurking in the second half of the field! Janul's Buchholz score is higher than that of five of the prize winners.
Thus in conclusion, the pairing system (King Of The Hill) has not treated all players equally as shown by the huge disparity in Buchholz scores. But I am not going to rest my case! There is a lot more evidence coming up!