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Miscellaneous Topics / Tie Breakers for Prize Lists / Tie Breaker (FIDE Rules) |
These are the tie breaks available in WinTD that comply with FIDE rules.
A player's Buchholz is the sum of his or her opponents' scores. The Buchholz (possibly with cuts) is generally the first tie break for a FIDE Swiss. As an example, if A and B face opponents with the following scores:
Player A: 0,3,3,4,5
Player B: 3,2,5,3,3
Player A's Buchholz tie-break is 0+3+3+4+5=15, Player B's is 3+2+5+3+3=16 so B would have the higher tie break.
Many of the FIDE tie breaks include the possibility of modifiers which delete one or more of the summands. For instance, in the example above, Player A's first round opponent scored 0. It's very likely that A would have beaten someone better than that. A "Cut 1" Buchholz (Buchholz-C1) eliminates the lowest score. In the example above Player A would have 3+3+4+5=15 and Player B would have 3+5+3+3=14 so here A would have the higher tie break. A "Cut 2" drops the two smallest scores: for A 3+4+5=12, for B 3+5+3=11.
Median cuts eliminate both high and low scores. A "Median 1" Buchholz for A (Buchholz-M1) +would have 3+3+4=10 (dropping both the 0 and the 5). For B, it would be 3+3+3 (dropping the 2 and 5). A "Median 2" drops two scores from each end (four scores overall), which would never be used in a five round tournament.
"Fore" Buchholz is the Buchholz treating all paired last round games as if they were draws. This has the advantage (compared with the standard Buchholz) of allowing players to know where they stand on the tie break as they play the last round—in effect, you just need the previous round's full Buchholz plus the final round opponent's score. For the standard Buchholz, the final round results of all opponents of all potentially tied players will enter into the final tie break.
There are C1, C2, M1 and M2 variants of this.
Average Rating of Opponents (ARO)
This is the average rating of opponents with (pre-tournament) ratings. This is not to be used (in a FIDE tournament) when there are unrated players in the tournament (unless detailed rules on handling of unrated are established and published in advance, and WinTD would probably not be able to do those special calculations).
There are C1, C2, M1 and M2 variants of this.
The Sonneborn-Berger is the sum of 1 x (scores of opponents defeated) + .5 x (scores of opponents drawn). Compared with the Buchholz, this rewards scores against high-scoring opponents but does not penalize as severely failures to win against low-scoring opponents. It's commonly used as a tie break in Round Robin tournaments simply because it is one of the few that actually can break ties in a Round Robin. (Buchholz and related tie breaks will all be the same for players who tie in a Round Robin).
A player's Progressive Score is the sum of his or her scores at the ends of each round. If Player A won his first four and lost the last round, and Player B won two, lost the third round, and won the last two, the players scores at the ends of the rounds are:
Player A: 1,2,3,4,4
Player B: 1,2,2,3,4
Player A's Progressive Score is 1+2+3+4+4=14, Player B's is 1+2+2+3+4=12. The cumulative tie break measures strength of schedule indirectly. By Swiss System pairing rules, players who do not lose until later rounds (and thus have high progressive scores) will usually face tougher opponents than players who lose in early rounds (and thus have low progressives).
This has C1 and C2 variants, which here leave out the first round score (C1) or the scores for the first two rounds (C2). These are particularly helpful if you use accelerated pairings (where the first and second round pairings are different from standard Swiss).
Direct Encounter (Head-to-Head)
Direct encounter looks at the head-to-head results involving the players in a tie (through scores and any previous tie breaks). This can be inserted at any point in the tie break order and can be included more than once. Although Direct Encounter would typically be the first tie break, you can also do (for instance) Buchholz first then Direct Encounter to (attempt to) break any further ties.
In a Swiss, Direct Encounter is unlikely to be able to break ties among any but the smallest score groups as players will generally not play many of the other tied players. Unless all players have played each other (where they will be ordered by the points scored within the group), a player will only come out ahead on Direct Encounter if they would have more points no matter what results might occur in any "missing" games. For instance, if you have a four-way tie and A beats B and C, D draws B and loses to C and C draws B, then even if D beat A in a theoretical game, D could not have more than 1.5 points, so A's 2 points would come out on top. The tie break then looks at B, C and D, who have all played each other. In games involving those, C has 1.5 points, beating B's 1.0 points and D's 0.5. However, if you change this so D no longer plays B, then D could reach 2 points by beating A and B in filling out the gaps in the grid. In that case, Direct Encounter would fail to break any ties (the missing game calculation only applies if it produces a clear winner) and will be shown as 0's for all players.
Played Black/Wins (Full Pt Rounds)/Wins OTB/Wins Black/Rounds Elected to Play
These are straightforward statistics on each players' records. Wins (Full Pt Rounds) includes any round where the player received the score for a won game, whether played or not, while Wins OTB only counts played wins. Rounds Elected to Play counts any round where the player either played, received the pairing-assigned bye, or won when the opponent forfeited. It does not count rounds where a player took a requested bye (of any value) or himself was forfeited.
Average of Opponents' Buchholz(AOB)/Average of Opponents' FB(AOFB)
This is the average of the Buchholz values of the opponents or the average of their Fore Buchholz. This is a very indirect measure of strength of opposition—its advantage is that involves so many results that it is highly unlikely to come up the same for multiple players and thus can be useful as a late tie breaker.
FIDE TPR (Tournament Performance Rating)
This adds to the average rating of opponents an adjustment (up to +/-800) based upon the percentage score in played games to estimate a rating from this tournament in isolation. It will give an identical ordering to the ARO for players with the same score who have played all their games.
FIDE PTP (Perfect Tournament Performance)
This is a more complicated alternative to the TPR to estimate a tournament performance in isolation. It finds (using a search procedure) the lowest rating that a participant should have for their expected score to be greater than or equal to their tournament score. Unlike the TPR, where the ratings of opponents are simply averaged, this takes into account the actual ratings. 2000W, 2200W, 2400L will have a lower PTP than 1800W, 2400W, 2400L despite the average ratings of the opponents being identical, as the 2400W vs 2200W is more indicative of playing ability than 1800W vs 2000W, as both of those are the very likely result for a player in the 2300-2400 range.
Note that this calculation cannot be applied to players with all losses as the "lowest rating" that solves the expected score equals tournament score is -infinity. (Not that tie breaking players with all losses is going to matter in practice). Instead, it's computed as 800 less than the lowest rating of the opponents which is actually the highest rating that solves the problem. (The PTP for a player with all wins is 800 more than the highest rating of the opponent).
Average of Oppo TPR (APRO)/Average of Oppo PTP (APPO)
These are the average of the opponents' TPR's and average of their PTP's respectively. As with the other "average of opponents..." this is a very indirect measure of strength of schedules.
Random
This is basically a computerized coin flip. It should only be used as a final tie break.
Copyright © 2026 Thomas Doan