Modified Median Tiebreak (Harkness)

Modified Median

Definition

Modified Median (also known as the Harkness system) is a Swiss-system tiebreak method that sums the final scores of a player’s opponents, then discards extreme results depending on the player’s own final score. It is designed to smooth out the effect of having faced a single very strong or very weak opponent.

• If a player scores more than 50% of the possible points, discard only the lowest opponent score.
• If a player scores exactly 50%, discard both the highest and the lowest opponent scores.
• If a player scores less than 50%, discard only the highest opponent score.

The remaining opponent scores are added to produce the Modified Median tiebreak. It uses opponents’ final tournament scores (not their ratings), and the decision about what to discard is based on the player’s own total score.

How it is used in chess

In Swiss tournaments, many players often finish with the same point totals. Organizers apply a sequence of predefined tiebreaks to order tied players for prize distribution, standings, or qualification. Modified Median is a common early tiebreak in US Chess events (especially scholastic and local Swisses) and is supported by most pairing programs. It serves a similar purpose to Buchholz and Median-Buchholz, but with a different trimming rule that adapts to the player’s performance level.

Why organizers use it

• Reduces the impact of extreme pairings: A single opponent who scores far above or below the field won’t overly skew the tiebreak.
• Performance-sensitive: Players who did well are not heavily penalized for having met a very weak opponent; players who struggled are not unduly rewarded for having met a very strong opponent.
• Simple to compute once final scores are known.

Step-by-step calculation

1. List the final scores of all opponents the player actually faced.
2. Determine the player’s final score relative to 50% of the rounds (e.g., in 5 rounds, 50% is 2.5 points).
3. Discard opponent scores according to the rule:
   • Above 50%: drop the single lowest opponent score.
   • Exactly 50%: drop both the highest and the lowest opponent scores.
   • Below 50%: drop the single highest opponent score.
4. Sum the remaining opponent scores. The result is the Modified Median tiebreak.

Notes: Event regulations specify how to treat byes, forfeits, and unplayed rounds. Policies vary by federation and organizer; consult your event’s rules. Software usually applies the local rulebook automatically.

Examples

Assume a 5-round Swiss (so 50% = 2.5/5). Opponent scores below are their final results after the tournament ends.

• Player A scores 4.0/5 (> 50%). Opponents’ scores: 3.0, 2.0, 4.5, 1.5, 3.5.
  Drop the single lowest (1.5). Sum = 3.0 + 2.0 + 4.5 + 3.5 = 13.0. Modified Median = 13.0.
• Player B scores 2.5/5 (= 50%). Opponents’ scores: 4.0, 3.0, 2.0, 1.0, 3.5.
  Drop the highest (4.0) and the lowest (1.0). Sum = 3.0 + 2.0 + 3.5 = 8.5. Modified Median = 8.5.
• Player C scores 1.0/5 (< 50%). Opponents’ scores: 3.5, 2.5, 2.0, 4.5, 3.0.
  Drop the single highest (4.5). Sum = 3.5 + 2.5 + 2.0 + 3.0 = 11.0. Modified Median = 11.0.

Strategic and practical significance

• Pairing luck moderation: You can’t control who your early opponents are, but Modified Median dampens the “lottery” effect of a single outlier round.
• Tiebreak awareness: While you should never play only for tiebreaks, understanding them can inform late-round risk management (for example, knowing that your weakest opponent’s score might be dropped if you are above 50%).
• Comparison to Buchholz: Standard Buchholz sums all opponents without trimming; Modified Median trims based on performance. Median-Buchholz trims both extremes, regardless of the player’s score.

Historical notes

The method is attributed to Kenneth Harkness, a key figure in US Chess administration and rating development, hence its alternate name “Harkness system.” It became popular in American Swiss events where large fields and many ties are common. While FIDE events often prefer Buchholz-based systems, US tournaments frequently list Modified Median among their primary tiebreaks.

Common variations and related terms

• Median-Buchholz: Discard both highest and lowest opponent scores, regardless of the player’s result. Median-Buchholz
• Buchholz (Cut 1 / Cut 2): Discard a fixed number of the lowest opponent scores (e.g., cut 1 or cut 2). Buchholz
• Sonneborn–Berger: Uses weighted sums of defeated and drawn opponents’ scores; common in round-robins.
• Tiebreak order: Events define an ordered list (e.g., Modified Median, then Buchholz, then head-to-head). Always check the tournament’s advance notice. Tiebreak

Tips and caveats

• Finalized late: Because it uses opponents’ final results, your Modified Median can change after your game ends, as other boards finish.
• Byes/forfeits: Handled by local rules. Some organizers count certain unplayed rounds as specific fixed values; others ignore them. Confirm in the event bulletin.
• Small events: In very short tournaments (e.g., 3 rounds), trimming can remove a large fraction of data; organizers may choose different tiebreaks.