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  2. Tie-breaking in Swiss-system tournaments - Wikipedia

    en.wikipedia.org/wiki/Tie-breaking_in_Swiss...

    For Swiss tournaments, he recommends the Buchholz system and the Cumulative system. [16] For Swiss tournaments for individuals (not teams), FIDE's 2019 recommendations are: [17] Buchholz Cut 1 (the Buchholz score reduced by the lowest score of the opponents); Buchholz (the sum of the scores of each of the opponents of a player);

  3. Buchholz system - Wikipedia

    en.wikipedia.org/wiki/Buchholz_system

    In the Median-Buchholz System the best and worst scores of a player's opponents are discarded, and the remaining scores summed. 'Buchholz cut 1' is a variant in which the score is calculated by adding together tournament scores of each opponent a player has faced, except the one with the lowest score (thus 'cut 1').

  4. Standard normal table - Wikipedia

    en.wikipedia.org/wiki/Standard_normal_table

    Example: To find 0.69, one would look down the rows to find 0.6 and then across the columns to 0.09 which would yield a probability of 0.25490 for a cumulative from mean table or 0.75490 from a cumulative table. To find a negative value such as -0.83, one could use a cumulative table for negative z-values [3] which yield a probability of 0.20327.

  5. Elo rating system - Wikipedia

    en.wikipedia.org/wiki/Elo_rating_system

    The USCF initially aimed for an average club player to have a rating of 1500 and Elo suggested scaling ratings so that a difference of 200 rating points in chess would mean that the stronger player has an expected score of approximately 0.75. A player's expected score is their probability of winning plus half their probability of drawing. Thus ...

  6. Sonneborn–Berger score - Wikipedia

    en.wikipedia.org/wiki/Sonneborn–Berger_score

    The Sonneborn–Berger score is the most popular tiebreaker method used in Round Robin tournaments.However in contrast to Swiss tournaments, where such tiebreaker scores indicate who had the stronger opponents according to final rankings, in Round Robin all players have the same opponents, so the logic is a lot less clear-cut.

  7. Studentized range distribution - Wikipedia

    en.wikipedia.org/wiki/Studentized_range_distribution

    The studentized range is used to calculate significance levels for results obtained by data mining, where one selectively seeks extreme differences in sample data, rather than only sampling randomly. The Studentized range distribution has applications to hypothesis testing and multiple comparisons procedures.

  8. Percentile rank - Wikipedia

    en.wikipedia.org/wiki/Percentile_rank

    where CF—the cumulative frequency—is the count of all scores less than or equal to the score of interest, F is the frequency for the score of interest, and N is the number of scores in the distribution. Alternatively, if CF ' is the count of all scores less than the score of interest, then

  9. Standard score - Wikipedia

    en.wikipedia.org/wiki/Standard_score

    Comparison of the various grading methods in a normal distribution, including: standard deviations, cumulative percentages, percentile equivalents, z-scores, T-scores. In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured.