Fairness of KOTH pairing.

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)