Is Total Prestige the most fair way to rank players after N rounds of Swiss?
Would a SoS Weighted Prestige make a little more sense as a ranking metric for Swiss tournaments, to take into account the quality of the wins attained?
Under current Swiss scoring systems, players in a tournament are ranked by:
- Total Prestige (2 points for a win/bye, 1 for a draw/timed win, 0 for a loss/timed loss)
- Tiebreakers on SoS = Sum(opponents prestige)/(#rounds^2)
- Additional tiebreakers on xSoS = sum(opponents opponents prestige)/#rounds^2
Pairings are determined in a pyramid way whereby players are ranked with those around them in terms of current prestige after each round i.e. winners are matched with winners, losers with losers. This naturally causes a situation whereby those who do well in the early rounds, will have relatively harder matches in the later rounds as they are paired off against eachother, and consequently building a stronger SoS than the rest of the field, but their prestige becomes increasingly harder to come by as they progress up the pyramid. In some ways the swiss systems punishes you for success whilst simulataneously rewarding you for failure in making your next round harder/easier respectively. This kind of catch up logic is apparent in the pairing system, but not in the final ranking system itself (except in the case of tiebreakers).
Often some of these players who have been playing in and around the top tables for the duration of swiss will miss the cut, replaced by someone who has relatively had a much easier ride on the mid tables who effectively sneaks in on the final swiss round. Whilst the strength of players faced is taken into account only in the case of tiebreakers, the Total Prestige method does not effectively weight the quality of the wins adequately. In other words all wins are equal under the current system.
One proposal could be to devise a metric weighted by SoS such as (Total Prestige* Sum(opponents prestige)/(N^2))/N = SoS* Prestige/N, using Total Prestige as the tiebreaker thereafter.
This has the property whereby the Prestige earned by a player is weighted by the average quality of the opponents attained he/she has played against over all rounds of swiss. For example, if Player A had scored 12 points and Player B 14 points in a 5 round tournament, and their SoS was 2.4 & 2 respectively, then Player A would finish above Player B on this metric (SoS* Prestige/N) with Player A obtaining a score of 5.76 vs Player Bs 5.6.
Running the numbers on the Worlds 2015 Swiss leads to some interesting changes. Lucas Li, whose phenomenal performance to accumulate 22 prestige in the context of a 3.05 SoS is recognised as the 3rd seed in Swiss, whilst Jen Erickson & Chris Dyer would also sneak into the cut on based on their SoSs of ~2.65. Notably a few of the late climbers such as Dave Hoyland would not make the revised cut, which could also be seen as a criticism that using a SoS weighted metric leads to a top table “club” which has its own intertia making it hard to break into if you have lost a few early rounds, increasing inevitability and reducing some of the excitement of the tournament. Conversely to this, one could argue that players who have been in and around the top tables all day, are to some extent are more deserving to be in the cut at the end, and a SoS weighted metric makes that more likely.
Interested to hear peoples thoughts.
Worlds 2015 Swiss (top 24 based on new rank are shown):
original rank name prestige sos prestige*SoS/N prestige new rank rank difference
1 Brandon Hauk 30 2.69 10.09 30 1 0
2 Minh Tran 26 2.61 8.48 26 2 0
16 Lucas Muxi Li 22 3.05 8.39 22 3 +13
5 Tim Fowler 24 2.69 8.07 24 4 +1
3 Dien Tran 26 2.42 7.87 26 5 -2
6 Noah McKee 24 2.61 7.83 24 6 0
7 Stjepan Pavuna 24 2.46 7.38 24 7 0
8 Gary Bowerbank 24 2.45 7.35 24 8 0
9 Dan D’argenio 24 2.39 7.17 24 9 0
10 Timmy Wong 24 2.39 7.17 24 10 0
4 Alan Noonan 25 2.25 7.03 25 11 -7
11 Chris McCulloch 24 2.34 7.02 24 12 -1
35 Jens Erickson 21 2.64 6.93 21 13 +22
12 Peter Hernandez 24 2.31 6.93 24 14 -2
17 Quinn Wongkew 22 2.45 6.74 22 15 2
37 Chris Dyer 20 2.66 6.65 20 16 +21
18 Joshua Wilson 22 2.41 6.6275 17 +1
19 Weston Odom 22 2.39 6.57 22 18 +1
13 Colin Hanna 24 2.19 6.57 24 19 -6
14 David Hoyland 24 2.19 6.57 24 20 -6
20 Nicholas Hansen 22 2.38 6.55 22 21 -1
21 Gregor Terrill 22 2.33 6.41 22 22 -1
15 Zach Eaton 23 2.2 6.33 23 23 -8
22 Mason Hans 22 2.28 6.27 22 24 -2
23 Jason Deng 22 2.27 6.2425 25 -2
24 Evan Hill 22 2.23 6.1325 26 -2
25 Spencer Healey 22 2.22 6.105 27 -2
26 Tomasz Fedorczyk 22 2.19 6.0225 28 -2
27 Kyle James 22 2.19 6.0225 29 -2
28 Keith Gaudry-Gardner 22 2.17 5.9675 30 -2
38 Travis Yeo 20 2.38 5.95 31 +7
39 Scott Pagliaroni 20 2.38 5.95 32 +7