Fairness of KOTH pairing.

2016 July 4 at 07:15 » Tagged as :scrabble, koth, pairing, yui,

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
1 Aabid Ismail 16.67 1
4 Hansi Weerasooriya 22.67 3
41 Lalinka De Silva 24.50 3
18 Nikesh Moorthy 27.17 2
75 Therunee Karunaratne 27.67 2
20 Janul De Silva 28.00 2
5 Radinka Dissanayake 28.17 2
25 Qays Sangani 29.00 1
7 Danusha Muhandiramge 31.50 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
1 1134 Aabid Ismail 16.67 1
20 1054 Janul De Silva 28.00 2
5 897 Radinka Dissanayake 28.17 2
37 847 Thirandi De Silva 32.17 1
3 924 Hayati Rassool 32.50 2
38 964 Janidu Karunarathne 35.33 2
21 938 Thavalakshman Yoganathan 37.00 2
2 1148 Migara Jayasinghe 42.83 0
13 1053 Hasindu Arumapperuma 44.83 0
15 840 Vignesh Pirapaharan 49.17 0

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 under8 champions and a two time under3 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)