Monday, November 19, 2012

Tie-breaks Explained

     Tie-break systems are used in many tournaments to determine the order of finish among players in the same score group. There is no perfect tie-break system. Each system carries a different bias and is subject to criticism. In events where time is not pressing, playoffs provide an alternative to the use of tie-break systems. Where playoffs are used, time controls are usually much faster than those used for regular tournament rounds.
     Scholastic events are often squeezed for time at the end of the day and tie-breaks are necessary to determine trophies or other non-cash awards. Tie-breaks systems are not used for cash prizes; cash prizes are divided evenly among tied players.
     Depending on the size of the event, more than one tie-break system may be needed to determine the order of finish. The sequence of tie-break systems to be used at a tournament should be posted before the first round. Unless a different method has been posted or announced before the first round, USCF rules indicate that players will expect the following sequence of tie-break systems to be employed as the first four individual tie-breakers:
1. Modified Median
2. Solkoff
3. Cumulative
4. Cumulative of Opposition
     Many of the primary tie-break systems are based in varying ways on the strength of your opponents' play. Generally speaking, the stronger the scores of your opponents, the better your tie-breaks.
     The following tie-break definitions are derived from the U.S. Chess Federation's Official Rules of Chess, Fourth Edition.

Individual Swiss tournament tie-break systems
The sum of all opponents' final scores.
Modified Median
·        The sum of opponents' scores (like Solkoff) but discarding some high or low scores:
  • ·        for players with "plus" scores (more wins than losses) -- the lowest scoring opponent is discarded.
  • ·        for players with "even" scores -- the highest and the lowest scoring opponents are discarded.
  • ·        for players with "minus" scores -- the highest scoring opponent is discarded.
  • ·        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.

·        These scores are adjusted for unplayed games (byes, forfeits, unplayed games), which count a half point each.
Median (Harkness System)
The sum of opponents' final scores, discarding the highest and lowest of these scores.
The sum of the cumulative (running) score for each round. One point is subtracted from the sum for each unplayed win or one-point bye.
For example, if a player's results over a five-round event were win, loss, win, draw, loss, the wallchart would show a cumulative score round by round as 1, 1, 2, 2 1/2, 2 1/2. Adding across, the cumulative tie-break total is 9.
Cumulative Scores of Opposition
The cumulative tie-break points for each opponent are calculated and then added together.
A player receives 4 tie-break points for a win, 2 for a draw, 1 for a loss, and 0 for an unplayed game. This system awards aggressive play by giving more credit for wins.
Result between Tied Players
Self-explanatory if two tie, but useful only when they are paired and did not draw. 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).
Most Blacks
Opposition's Performance
This method averages the performance ratings of the players' opposition. Performance ratings are calculated by crediting the player with the opponent's rating plus 400 points for a win, the opponent's rating minus 400 points for a loss, and the opponent's rating for a draw. Results of each opponent against the tied player should not be included, since this would give the higher-rated tied player an unfair advantage. This system may be difficult to use when unrated players are in the tournament.
Average Opposition
This system averages the ratings of the players' opponents, the better tie-break score going to the person who played the highest-rated average field.
Sonneborn-Berger (Partial Score Method)
Add the final scores of all the opponents the players defeated and half the final scores of all the opponents with whom the player drew. Nothing is added for the games the player lost or for unplayed games. This is the most common method used for round-robin events.

Modified Individual/Team tie-break systems
Many scholastic events used a modified individual/team tournament format. In this type of event, pairings are performed as in a normal individual Swiss tournament but often teammates (e.g., players from the same school) will not be paired against each other. At the end of the event, team points are accumulated (usually the top 4 players' scores are used for the team calculation) and team awards presented in addition to individual awards. For this type of tournament, the Team Cumulative tie-break may be employed in the overall tie-break sequence.

The sum of the cumulative (running) scores for each team member at the end of the tournament.
Team Cumulative
·        The sum of the cumulative (running) scores for each team member as the team is defined for each round.
·        This is different from the normal Cumulative tie-break only if there are more than 4 players on a team and the top 4 scores involve different sets of players for at least one round.

Most of the individual tie-break systems for individual Swiss tournaments described above are also suitable for modified individual/team events.

Team tie-break systems
In team tournaments, the team competes as a unit against other teams. The usual example is the 4-board team tournament in which 4 team members compete in each round against the 4 members of another team. Most of the individual tie-break systems for individual Swiss tournaments described above are also suitable for team events. USCF rules describe two other tie-break systems for team events.

Game (or Match) Points
The total game points earned by the team involved.
U.S. Amateur Team System
For each round, the final score of the opposing team is multiplied by the number of points scored against that team. For example, if Team A scored 2 1/2 - 1 1/2 against Team B, which finished the tournament with 3 match points, Team A's tie-break for that round is 2 1/2 X 3 = 7 1/2.

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