2004 NSC Pairing System Overview

[Updated 2004-07-28 to add a description of the Basic Approach]

The first 7 rounds (sessions 1 and 3/4 of 2) will be a Round Robin in groups of 8 players. The 8th round will be King-of-the-Hill based upon the initial ratings. Each group of 8 players will be chosen using the June 2004 ratings list, using a "snake" arrangement. The snake appellation comes from listing all the players (represented by transforming their June 2004 National SCRABBLE^® Association (NSA) rating into an ordinal number for each division) into 8 rows and x/8 columns (x=number of players in the division), with each odd-numbered row increasing numbers from left-to-right and each even-numbered row increasing numbers from right-to-left. The top row begins with #1. For example, if there are 96 players in your division, the first group will include the ordinals 1, 24, 25, 48, 49, 72, 73 and 96, all in the leftmost column, based on rating, where #1 is the highest-rated player. The top two rows would be:

 1  2  3  4  5  6  7  8  9 10 11 12
24 23 22 21 20 19 18 17 16 15 14 13

Dividing the group in this manner insures that the average rating of all players' opponents for all of the first 8 rounds is approximately even.

We will post only those rounds pertinent to each session. Each group will play at the same four boards and two tables, since there will be two boards at each table. This will ensure a minimum of movement. Note that in all later sessions, the numbers/ordinals below will represent the players' tournament standing among all the players in each division.

Subsequent sessions will be paired in groups of four (quads, unsnaked), and with each succeeding session these paired players will have win/loss records more similar than prior sessions. Also, define A = highest standing player in quad; B = 2nd highest in quad; C = 3rd highest; D = lowest.

Session 3 (Monday morning: 4 rounds) will pair from groups of 20, which means that the quads for the highest group of 20 will consist of (1, 6, 11, 16), (2, 7, 12, 17), (3, 8, 13, 18), (4, 9, 14, 19) and (5, 10, 15, 20), etc., and so on for all quads in each group of 20 in each division. The fourth round in the morning will pair A vs A1, B vs B1, C vs C1 and D vs D1, etc, where A1 is the A player in the adjacent quad.

Session 4 (Monday afternoon: 3 rounds) will pair from groups of 16, which means that the quads for the highest group of 16 will consist of (1, 5, 9, 13), (2, 6, 10, 14), (3, 7, 11, 15) and (4, 8, 12, 16) etc.

Session 5 (Tuesday morning: 4 rounds) paired as Session 3 except that quads will be formed from groups 12: (1, 4, 7, 10), (2, 5, 8, 11), (3, 6, 9, 12), etc., and repeats will be allowed.

Session 6 (Tuesday afternoon: 4 rounds) will be paired as Session 5 except that quads will be formed from groups of 8: (1, 3, 5, 7), (2, 4, 6, 8) etc.

Session 7 (Wednesday morning: 4 rounds) will be paired as Session 6 except that quads will be formed from groups of 4: (1, 2, 3, 4) etc.

Because there will be no repeat pairings until Round 16 (Tuesday afternoon), the computer program will adjust the quad pairings accordingly, with minimum adjustments.

Session 8, rounds 28-30, players in positions 41-bottom will be paired in King-of-the-Hill quads (41, 42, 43, 44) etc. so that they will know their opponents for all three rounds at the beginning of the afternoon. For players in the top 40 positions, each of the last three rounds will be paired individually and we will follow what we'll call the BASIC APPROACH, which is briefly summarized below. This system was created to accommodate the two-winner aspect of our NSC this year. "Threepeats" will be allowed.

In describing the BASIC APPROACH, we use the term GIBSONIZE, or a form of this invented word to represent a situation where a player has won enough games to guaranteed 1st place or a seat in the finals, no matter how many games s/he loses thereafter. By GIBSONIZING the player, the staff acknowledges that the player will be a finalist. Because a guaranteed finalist has little incentive to play their very best, instead of being paired with another top contender, s/he will be paired with the player who is in the highest position of the division who has no chance to finish among the top prizewinners. This will allow the remaining contenders to continue to play each other for the other prizewinning positions.

Note: Due to the fact that Division 7 currently has only about 40 players registered, there may be a last-minute change in its pairing procedure. We will announce any changes as soon as they become official. In all likelihood, the initial RR pairings will be adjusted to last closer to 19-20 rounds, with the whole division divided into two separate groups. This change will have the advantage over the current system of avoiding repeat pairings as much as possible.

BASIC APPROACH

Divisions 2-7: One Winner

For players in the top 40 positions, each of the last three rounds will be paired individually and will be king-of-the-hill, with threepeats allowed. However, for the top six players a modified pairing system will be used:

Rd 28: It will be determined if the player in the #5 spot has any legitimate chance to finish first by winning all his/her games (discounting spread). If so, then the top six will be paired 1 vs 4, 2 vs 5 and 3 vs 6 for Round 29. If #5 does not have a legitimate chance to finish first, then 1 vs 3 and 2 vs 4, while 5 vs 6.

For round 29: 5 vs 6. If #3 has a legitimate chance to finish first (as determined using same method for previous round for #5), then 1 vs 3 and 2 vs 4. If #3 doesn't have a legitimate chance to finish first then all of the top 40 will be king-of-the-hill.

Round 30: Top 40 = king-of-the-hill.

Division 1: Two Winners

For each of rounds 28, 29 and 30:

1. Determine whether any players can be "Gibsonized" according to a specific formula.

2. If less than 2 players are Gibsonized, then determine the "right" number of competitors to include in the top pairings flight with a few simple calculations.

3. The goal of these calculations will be to determine the size-of-flight "N" such that the top N (or N-1) players have a "reasonable" chance to finish 2nd or higher.

   The following restrictions apply: The number of players in the top flight will be limited to 12, 8, and 4 in rounds 28-30 if the two top positions are open, and 8, 4, and 2 in rounds 28-30 if only 1 top position remains open. Note that a player not in the top flight at rounds 28 or 29 may earn his/her way into the top flight for rounds 29 or 30.

4. After the flight size is determined, pairings within the top group match each player - in turn, starting at the group's top - to the lowest ranking player with potential of overtaking him/her in the overall standings.

5. For purposes of deciding whether or not a player is catchable by another player, we have applied the following win/spread limits:

   Games Left	Maximum Games Behind	Maximum Spread
   1	1	-500
   2	2	-800
   3	3	-900

   The philosophy behind applying spread limits is to ensure that only those players whose chances are reasonable be allowed into the top pairing flight. The numbers were chosen after much debate and analysis of past tournament results as being the outer limits of what was felt to be reasonable.

6. The system is also designed to create the right compromise between absolute perfection, and the need for it to be simple enough to implement manually.

These pairings were determined and agreed-upon by the NSA Pairings Committee, who were chosen by NSA Executive Director, John D. Williams, Jr., late in 2003. The committee members are: Steven Alexander (OR), David Boys (QC), John Chew (ONT), Joe Edley (NY), Gregg Foster (MA) and Jerry Lerman (CA).