This is part three, in a series of posts on King Of The Hill pairings a widely used pairing system at Scrabble tournaments. The analysis is carried out using the results of the Age Group Scrabble Championship 2015.. The tables on this post can be recreated by web scraping the contents of the above link.
The fairness of the draw can be calculated based on three different criteria as described on the official website of tsh, the most widely used pairing software in Scrabble and the one used for this tournament
Average Opponent Rank
The rank of a player is the position he occupied at the end of the tournament. Therefore Average Opponent Rank is the sum of the rank of each opponent faced by a given player divided by the number of rounds.
As an example Qays played against Lochana, Zahra, Rizvi, Ashvin, Duilini and Radinka their ranks were 34, 42, 11, 58, 24 and 5 which add to 174 and averages to 29. Players with lower Average Opponent Rank (AOR) have faced stiffer competition.
The table below outlines the average opponent rank sorted by AOR in ascending order. Lower AOR means the player's opponents secured better placings.
|Position||Name||Average Opponent Rank||Number of prize winning opponents|
|41||Lalinka De Silva||24.50||3|
|20||Janul De Silva||28.00||2|
|37||Thirandi De Silva||32.17||1|
Table 1: Best Average Opponent Ranks
Only four of the prize winners figure in this list but the champion has the best AOR of all players. 75th placed Therunee and 41st placed Lalinka have better AORs than eight of the prize winners. Lalinka and Hansi were the only players to meet three prize winners. Lalinka managed to win two of those games (vs Migara and Yenuli) yet her own position is 41st.
Compare the above with the next table which examines the AOR figures for top rated players.
|Position||Rating||Name||AOR||Prize Winning opponents|
|20||1054||Janul De Silva||28.00||2|
|37||847||Thirandi De Silva||32.17||1|
Though top rated players are the most likely contenders for the title as well as the remaining nine prizes, and the stated objective of KOTH is to pair contenders, three of the top rated players haven’t been paired against prize winners at all. These three happen to be two former under 18 champions and a two time under 13 champion!!
Thus the Average Opponent Rank shows that there is considerable disparity in the manner in which rated players were paired and KOTH has failed to fulfil its objectives. Based on Average Opponent Rank, King of the Hill has been anything but fair
(Note: Average opponent rank table for Prize winners is presented in section 2.3)
- Buchholz score as a measure of fairness of the draw. »
- « Analysis of Pairing Systems : Definition of Terms.