**PRINCIPLE: Sum
of Opposition's Scores**

**Buchholz (FIDE) or Solkoff (USCF)**
This is the sum of opponents' scores. The idea is that the same score is more
valuable if achieved against players with better performances in a given
tournament. Looks like an ideal tie-breaking method and has been used since the
Swiss system was invented. However it has some weaknesses which are addressed
by other methods (see Median-Buchholz, Progress, Berger).

**Median-Buchholz (FIDE) or Median
(USCF) or Harkness (USCF)**
Same as above but discarding the highest and the lowest opposition's scores.

Its idea is to eliminate distortions in Buchholz values caused by taking into
account games against run-away winners and bottom placed players.

**Modified Median (USCF)**
Same as Median-Buchholz *"for players who tie with even scores but modified for
other scores to disregard the only the lest significant opponent's scores. The
lowest scoring opponent is discarded for tied players with plus scores and the
highest scoring for tied players with minus scores.*

*For tournaments of nine or more rounds, the top two and bottom two scores are
discarded for even score ties, the bottom two scores for plus score ties, and
the top two scores for minus score ties." *(USCF
Rules)

**PRINCIPLE:
Player's Progressive Score**

**Progress (FIDE) or Cumulative (USCF)**
Calculated by adding points from a progress table eg if your scores were: Win,
Loss, Win, Draw then your progressive scores are 1, 1, 2, 2.5 and your Progress
tie-break value is 6.5

This is an attempt to put a higher value on scores which were achieved by
scoring better in the initial rounds than by finishing from behind. It is
common knowledge that the latter is usually much easier to achieve.

The problem is that the order of the Progress tie-breaks is known before the
last round (last round scores will change the actual value but not the order
within a point group). This may encourage some undesirable tournament "tactics"
in the last round.

Interestingly the USCF Official Rules of Chess considers the above feature of
the system an advantage on the grounds that it *"avoids the problem, comon in
Median and Solkoff, of having to wait for a lengthy last-round game between two
non-contenders to end for top prizes to be decided".*

**Cumulative Scores of Opposition
(USCF)**
*"The cumulative tie-break points of each opponent are calculated as in
Cumulative and these are added together."* (USCF
Rules)

An attempt to marry Cumulative with Solkoff. Rather strange.

**PRINCIPLE:
Opposition's Weighted Scores**

**Berger or Sonneborn-Berger (FIDE, USCF)**
This is calculated by adding scores of the opponets who were beaten by a given
player and half the scores of the opponents who she drew with. This has been
adopted from round-robin tournaments and is usually used as a secondary method.

**PRINCIPLE:
Number of Wins**

**Number of Wins (FIDE)**
Calculated by adding a point for a win and nothing for a loss or a draw.
Intended to discourage making quick draws. Popular in 70's and early 80's
(particularly in round-robins). In modern Swiss tournaments hardly justified.

**Kashdan (USCF)**
Similarly to the "Number of Wins" method rewards agressive play. A player
receives 4 tie-break points for a win, 2 for a draw, 1 for a loss and 0 for an
unplayed game. If there are no unplayed games this system reduces the "Number
of Wins".

Interestingly Kashdan can be used to calculate main scores rather than just
tie-breaks. In virtually all football (soccer) competitions in Europe teams
receive 3 points for a win, 1 for a draw and 0 for a loss.

**PRINCIPLE:
Opposition's Ratings**

**Opposition's Rating Sum (FIDE)**
Sum of the opponents' ratings. Uses the ratings ie presumed pre-tournament
strength of the opponents rather than their performance in a given tournament.
Also has the same problem with the last round as 'Progress'.

This is obviously an ill-conceived method. Ratings have been invented for other
purposes.

**Average Opposition (USCF)**
Averages the ratings of player's opponents. Effectively identical to FIDE's
Opposition's Rating Sum

**Opposition's Performance
(USCF)**
The concept a bit better than Opposition's Ratings but same comment applies.

**PRINCIPLE: Other**

**Result Between Tied Players
(USCF)**
Obvious if two tie but the USCF's interpretation of the situation where more
than two tie is interesting:

If more than two tie, all results among tied players should be considered, with
rank according to plus or minus, not percentage (3-1) beats (1-0).

This means that you can apply this tie-break even if not all tied players
played each other.

**Most Blacks (USCF)**
Number of games played with Black.