# Fine evaluation

The **fine scores for chess tournaments** are used when several players are tied and a ranking list should be created anyway.

## Individual ratings

### Scoring according to Sonneborn-Berger

The **Sonneborn-Berger number** or **SB number of** a player is the sum of the full number of points of the opponents against whom he won and half the number of points of the opponents against whom he played a draw. In the case of tied players, the one with the higher self-service number receives the better table position. The *Sonneborn-Berger rating* was developed for round-robin tournaments (of the form "everyone against everyone") when several players are tied at the end. It is also used in tournaments based on the Swiss system . This method weights a point gain against an opponent who is high in the table, higher than against an opponent who is lower, while it ignores the strength of the opponents in defeats. The player who has won against strong opponents more often or at least drawn draws, but has left the points with the weak opponents, while the player who wins against the weak opponents and loses against the strong ones, is rated higher .

In August 1873 the Austrian chess master Oscar Gelbfuhs developed this system. In 1882 William Sonneborn (* 1843, † 1906) and the Austrian master Johann Berger tried the system for the first time at a tournament in Liverpool and put it into practice in 1886.

Example: At the end of a round-robin tournament, the following cross table results (1 = win, ½ = draw, 0 = loss):

A B C D E F G Punkte

Spieler A - ½ ½ 1 1 1 1 5 B ½ - ½ ½ 1 1 1 4½ C ½ ½ - ½ ½ 1 1 4 D 0 ½ ½ - 1 1 1 4 E 0 0 ½ 0 - 1 1 2½ F 0 0 0 0 0 - 1 1 G 0 0 0 0 0 0 - 0

Players C and D are tied.

Player C receives the following self-service points:

Remis gegen A: 2½ Punkte (Hälfte von 5 Punkten von A) Remis gegen B: 2¼ Punkte Remis gegen D: 2 Punkte Remis gegen E: 1¼ Punkte Sieg gegen F: 1 Punkt (alle Punkte von F) Sieg gegen G: 0 Punkte Summe = 9 = SB-Zahl(C)

Player D receives the following self-service points:

Verlust gegen A: 0 Punkte Remis gegen B: 2¼ Punkte Remis gegen C: 2 Punkte Sieg gegen E: 2½ Punkte Sieg gegen F: 1 Punkt Sieg gegen G: 0 Punkte Summe = 7¾ = SB-Zahl(D)

For the difference in the SB number of two players, only those games are relevant in which the results of the two players against them differ. In the example, only the games against A and E are decisive.

C D C - D Punkte Produkt

Spieler A: ½ 0 ½ * 5 = 2½ Spieler E: ½ 1 -½ * 2½ = -1¼ SB-Zahl(C) - SB-Zahl(D) = SB-Zahl(C-D) = 1¼

Thus C has the higher SB number and is therefore in front of D.

In the example, the victories against G are worthless in the SB sense because G only has 0 points. On the other hand, the draw of C against top of the table A brings a high increase in SB.

The viewer-friendly advantage of this rating is that the spectacular fights between the strongest players make the difference and slips against weaker players in less attractive confrontations are less significant. Conversely, the sporting disadvantage is that consistently good play, even against weaker opponents, counts less than spectacular individual performances throughout the tournament.

### Buchholz rating

The **Buchholz number of** a player is the sum of the points of his opponents - regardless of the result of the games. The **refined Buchholz number of** a player is the sum of the Buchholz numbers of his opponents. Certain opponents often go unnoticed: the best and the worst ( *averaged* ) or the (one or two) worst ( *prank results* ). If there is a tie, the Buchholz number can be used to decide on the placement. In round-robin tournaments in which everyone plays against everyone else, the Buchholz number has no meaningfulness: it only differs in terms of its own number of points (since nobody played against themselves). Participants with equal points therefore always have the same Buchholz number. The Buchholz rating is used in tournaments according to the Swiss system , it was invented in 1932 by Bruno Buchholz from Magdeburg .

Since the refined Buchholz number refers to the same database as the Buchholz number, the results of both evaluations are unsatisfactory, so that the Sonneborn-Berger evaluation is usually used as the second evaluation .

The advantage of the Buchholz rating, which is generally felt to be fair, is that games against more successful players in the tournament bring advantages and thus a certain compensation is created for the fact that a player had the "misfortune" of playing against on average stronger players in the course of the tournament must as another participant with the same number of points. In addition, the Buchholz rating counteracts the tactic known as the “Swiss Gambit” of voluntarily drawing or even losing the first games in the “Swiss system” in order to roll up the field from further back with initially easier opponents. Without a Buchholz rating, this tactic is particularly useful in disputes with a high level of exhaustion.

Randomness has a big impact. If a player abandons a tournament or a player has a severe drop in performance, his opponents who have been played up to then have a disadvantage in the Buchholz number that is not justified in terms of sport. Likewise, particularly strong or particularly weak opponents randomly assigned in the first rounds can be decisive in the end, although this advantage or disadvantage in the “Swiss system” had long since been offset by the further course of the tournament. Sometimes it comes to sporty undesirable long-distance duels: If two top players have the same number of points and Buchholz at the end of their last games, the victory can be decided like a last game still in progress, in extreme cases that of the two weakest players in the tournament among themselves goes out. The winner of the tournament is the one who had the advantage in the first round of having drawn the better of the two.

A regular disadvantage is that extreme differences in the Buchholz number only lead to a fine evaluation and not to a point shift. It seems unfair that a player who has played one less win and one more draw than another player in the entire tournament, but had stronger opponents in all rounds, as the Buchholz number shows, is nevertheless rated lower. This disadvantage can be compensated for by a larger number of rounds to be played.

### Buchholz-Buchholz rating

In larger tournaments in particular, it often happens that several players do not only score evenly, but also score evenly. Then a third rating is required. This can then e.g. B. be another of the fine ratings mentioned here. The so-called "Buchholz-Buchholz number" can also be considered. This then does not compare how many game points the opponents had in a tournament in total, but how high the sum of the Buchholz numbers of the opponents in a tournament was. The logic is the same as with the Buchholz number itself: If you happened to have to compete against stronger opponents in a tournament, then an equally good final result should be rated higher and justify a higher final place. If the opponents of two tied players in the end have scored the same number of points, the Buchholz number is the same. But if the opponents of a player tied for points and Buchholz had "more luck" because they - measured against the Buchholz number - had the easier opponents, then the player who played against this preferred group obviously had against the easier opponents played. Therefore, the other player is preferred despite the same number of points and the same Buchholz number.

The disadvantages of this fine evaluation are also the same as with the Buchholz evaluation: the result depends on randomness. In addition, the Buchholz-Buchholz number is very large and is subject to considerable fluctuations until the last round. The Buchholz-Buchholz number is a way of avoiding the arbitrary lot for an order in the middle field, which is not very meaningful but is also regularly irrelevant for qualifications. Tackle fights are usually preferred for real qualification places.

The Buchholz-Buchholz number is z. B. applied at the German individual youth championships.

### Progress scoring

The *progress scoring* is used in tournaments according to the Swiss system , but mainly in larger open tournaments. For this evaluation, everyone gets their points scored up to then credited after each round as a fine evaluation. Wins or draws in the early rounds of a tournament are therefore rated more strongly than in the last rounds. The aim is to ensure that a player who has played in the top group for a long time, i.e. who has scored points very early in a tournament, is not overtaken in the final rounds by someone who has only played further back against probably weaker opponents . On top of that, the result is based only on his own results, the situation that often occurs with the Buchholz rating that the outcome of a game of completely uninvolved players has an impact on the Buchholz ratings and thus the ranking at the top is avoided.

However, this rating has a number of weaknesses, since, for example, victories without a fight or a bye are rated as high as a real victory. It is not said that players who have the same number of points at the end of a tournament have had equally strong opponents in the opening round, for example. That is why the progress evaluation is preferred for tournaments with a set ranking list, in which there is extensive comparability of the nominal opponent strengths.

However, if a large number of players is assumed, this rating makes sense.

Player A and Player B both have roughly the same Elo rating, they both play in the first round against nominally stronger opponents because they are in the lower half of the draw. Player A draws and B loses. In round 2 player A plays again against a nominally stronger opponent, but B is now in the upper half of those who have 0 points and therefore gets a weaker opponent. A draws again and B wins. Both now have 1 point. However, A already has 1 1/2 progress in contrast to B, who only has 1 progress point. A is rewarded for getting his points earlier.

### Koya system

The *Koya system* is used in round-robin tournaments. The number of points that were scored against opponents who scored 50 percent or more of the achievable points in the tournament is used as a fine evaluation. It thus disadvantages players who limit themselves to victories against the weaker participants.

### Rating based on performance

A *fine evaluation according to performance* is occasionally used in tournaments according to the *Swiss system* , but mainly in smaller and high-class tournaments in which all participants have a uniform and meaningful rating - such as an Elo rating . For this evaluation, the average (or equivalent, the sum) of all known and established values of his opponents prior to the tournament is used for each player. The player whose opponent has a higher average rating has achieved a higher performance and thus a better performance in the tournament.

This type of fine scoring has various advantages over the Buchholz system or progress scoring. On the one hand, it is independent of the order in which everyone meets the opponents. On the other hand, the fine evaluation is already determined with the drawing of the pairings for the final round, so that this fine evaluation does not depend on random or manipulable results of the final round and is known to the players during the final round.

A disadvantage is that with a player with a high rating, his own rating is also included in the direct comparison and thus high ratings are indirectly punished. If, for example, a grandmaster with 2600 Elo and a player with 2400 Elo are equal in points and drawn against each other in the last round in all ratings, the player with 2400 Elo ends up in a draw in front of the Grandmaster, as he is assigned the 2600 Elo of his opponent.

The rating of performance is used as for some years at the German championships where virtually always all qualified participants have a meaningful Elo: *"In case of equality decides on the placement of the sum of the Elo ratings of the opponent, failing that, their DWZ in renewed equality the FIDE Buchholz valuation. "(Announcement for the German championship 2007)*

### Other ratings

In addition to the mathematical fine evaluations, other sporting aspects are also often used to enable differentiation. Often z. B. based on the *direct comparison* . If two players have played against each other in the tournament and they are tied at the end, the one who has won the game is rated higher. Less common is the variant that in a direct comparison the one who followed suit is rated higher in a direct comparison, i.e. who had to play with the slightly disadvantaged black pieces.

Another possibility of fine scoring is to score the games played. In some tournaments, suspension leads directly to disqualification. Where this is not the case and a missing player only loses a game without a fight, but can then play the next game again, this behavior, which is regularly perceived as unsportsmanlike, can be avoided by the winning opponent e.g. B. takes the opportunity to achieve DWZ, Elo, or Buchholz points, "punish" by first using the number of games played as a fine evaluation. That way, a losing game is still worth more than one that is not played.

Ultimately, the focus is always on *stabbing fights* instead of the fine evaluations that are perceived as not very transparent or fair. The problem with chess in particular is that a playoff lasts just as long as a regular game and that can take up to two days, depending on the tournament mode. Dodging a play-off in Blitz mode leads to a different distortion. In a tournament with long game mode, a player may win because he is the better or happier blitz player. This does not seem more convincing than a fine evaluation. The lead is particularly problematic if more than two players are rated equally before the playoff.

## Team ratings

### Berlin rating

The *Berlin rating* is used when a team fight ends in a draw and a decision is to be made. For a win on the last board, the team receives one point, on the penultimate two points, etc. On the first board, the winner receives as many points as there are boards. In the event of a draw, both teams each receive half of the points to be awarded on the board. In the event of a tie in the team match, the team wins the match that has achieved more points in the Berlin ranking.

The color distribution on the boards is partly done in such a way that the Berlin scoring cannot make a decision if all white players (or all black players) win their games. The players of a team then have the same color on boards 1 and 4 (and possibly 5 and 8).

As an example, play team M1 against team M2. The individual results look like this:

BW Brett 1: remis 2:2 Brett 2: 1:0 3:0 Brett 3: 0:1 0:2 Brett 4: remis 0,5:0,5 --------------- 2:2 5,5:4,5

The team fight ends 2-2. According to the Berlin rating it is 5.5: 4.5 - so team M1 wins.

### Olympiad Sonneborn Berger rating

Since the 2008 Chess Olympiad in Dresden, it is no longer the number of points on the board that decides on the better placement, but rather the number of match points (rating 1). There are two points for a match won against an opposing team, one for a tie and zero for a lost one. In the event of a tie in the match points, the so-called *Olympiad-Sonneborn-Berger evaluation* (Olympiad Pairing Rules, Section G. Tie Breaking) decides first . The board points achieved in each match are multiplied by the opponent's match points achieved during the entire tournament and then added. The match points of the "opponent with the fewest match points" are not included in the calculation; the very weakest participants should no longer have any influence on the outcome of the tournament and the subsequent medal distribution.

Interestingly, the Olympiad Sonneborn Berger rating is used as the second rating before the rating of the total board points (rating 3). This makes sense, because the strength of the over 100 teams from large and small nations is extremely different, so that if you simply add up the board points, those teams that get weak opponents would have an advantage. Since the Chess Olympiad is played in the Swiss system , especially at the beginning of the tournament, strong teams fighting for the gold medal could meet extremely weak opponents.

While the usual Sonneborn-Berger scoring used in non-team tournaments is only used in the event of a tie on the board points and thus only measures the ability to deliver unexpected, surprising results, the Olympics Sonneborn-Berger used before the board point scoring offers - Scoring a clever combination of two criteria. For one thing, it roughly corresponds to the goal difference in football. For the match points it is not decisive whether a team wins high, for example with 3.5: 0.5, or just barely with 2.5: 1.5; both give two match points. The height of the victory goes into the Olympiad-Sonneborn-Berger evaluation. Second, the Olympiad Sonneborn Berger rating recognizes that it is more difficult to score against strong opponents than against weak ones. It measures the strength of the opponents with the match points that they have already achieved and will still achieve during the entire tournament. The combination of these two criteria now means - to give an example - that a 2.5: 1.5 win against an opponent who scores 14 match points in the entire tournament is worth just as much as a 3.5: 0, 5 win against an opponent who collects only 10 match points, because 2.5 times 14 equals 35; 3.5 times 10 gives the same result.

### Olympiad Buchholz rating

At the 2008 Chess Olympiad, the following continued to apply: If there is still a tie after the Olympiad-Sonneborn-Berger scoring (scoring 2), the sum of the match points of all opponents except for the one with the fewest points (Olympiad Pairing Rules, Section G. Tie Breaking) . This rating corresponds to an *Olympiad Buchholz rating* . The number of board points achieved in all rounds (rating 4) would only be used if the Olympiad-Buchholz rating should not result in a decision. Since the Chess Olympiad 2010 , the scores 3 and 4 have been swapped, so now the total number of points on the board is determined before the Olympics Buchholz score.

Example: A 2.5: 1.5 win against an opponent with a total of 14 match points gives the Olympiade-Sonneborn-Berger rating as high as a 3.5: 0.5 win against an opponent with a total of only 10 match points. The Olympiad-Buchholz rating is decisive in favor of the team that had the stronger opponent: 14 opposing match points instead of just 10 are rated higher than the lower amount of victory (only 2.5 instead of 3.5 board points). Of course, this rating is only applied to the overall result after all rounds.