The WinTD Swiss Pairing System
1-2, 3-4 Pairing System
In this pairing scheme, “natural” pairings have the highest ranked player playing the second highest, third playing fourth, etc.
This is a “fun” tournament format—the stronger players will generally play stronger opposition than the weaker ones will. It shouldn’t be used if any real prizes are at stake, as it is expected that at least some players will have fairly good scores with few games against the top players.
As with standard Swiss pairings, the ranking of players after round one is based first upon score, then upon rating. WinTD will do switches from the natural adjacent pairings to avoid duplicating earlier rounds, and also will switch to correct colors, subject to the same rules that govern Swisses.
WinTD implements the ratings-based Swiss System for pairing players described in the USCF Rule Book. However, it goes about computing the pairings in a very different way than a human does.
First, it’s important to understand that there is no way to guarantee that any program will find the “best” pairings in every situation. If you look at a 20 player score group, there are 3,628,800 (10!) ways to pair the ten top half players with the ten bottom half players. Examining every single one of those to find the “best” would take much longer than your players would like to wait. And the rulebook isn’t specific enough to define what best means anyway.
Suppose, for instance, that a score group can be paired with all colors correct in two different ways: in one, it requires both a 40 point swap and a 30 point swap, the other requires a single 45 point swap. Which is better? Either is acceptable, and no human TD upon finding one reasonable solution would likely keep looking to see if something a bit better was available.
Most pairing programs (including WinTD versions 2 and earlier) and most human TD’s pair by starting at the highest score group and working down. Where there is an odd number of players in a score group, or some other situation which prevents all the players from being paired within the group, the odd player or players are dropped. On occasion, the choice of whom to drop causes serious problems in a lower score group. A very good human TD will recognize the problem and go back up and change the dropped player to smooth the pairings out. However, the typical behavior of a pairing program is to push forward, even if it requires multiple drops at the lower level.
WinTD uses an approach which looks at the section as a whole. We have constructed a “penalty” function which measures how far the pairings differ from ideal pairings. What are “ideal” pairings?
- Everyone is playing someone with the same score.
- No previous pairings are duplicated and no pairing preferences (such as teammate or clubmate avoidance) are violated.
- In every score group, the top player is playing the next lower player.
- On every board, the colors are “right,” that is, everyone has as close to an equal number of whites and blacks as possible, and the alternate color from the preceding round.
The penalty value for ideal pairings is 0, which is almost impossible to achieve after the first round. The penalty function is designed so that lower values are “better” in the sense of being closer to ideal. For instance, the highest penalty is assigned to a pairing that has two players playing each other a second time. A lower penalty is assigned to a pairing which crosses score groups. A still lower penalty is assigned to pairings which have incorrect colors. And a rather small penalty is applied to pairings which change the natural pairing order slightly and involve a small rating change.
By finding a set of pairings which gives the smallest value for the penalty, we should end up with pairings which come as close to ideal as we can get. However, as noted above, there is no way that any program can look at all possible ways to pair any section with more than a very small number of players. Instead, WinTD uses the power of modern computers to find a “good” set of pairings. In testing this against earlier versions of WinTD and against other pairing programs, we found that WinTD almost invariably found superior pairings: more correct colors with smaller rating changes. In simple situations where a straightforward pairing process would work fine, WinTD would find the same solution.
The WinTD Color Balancing Procedure
In the first round, either WinTD or you will "flip a coin" to decide whether the higher ranked player will be White or Black on the first board. The color for the higher ranked player then alternates through the remaining boards.
In subsequent rounds, WinTD tries to determine which of two players has a better "claim" to a particular color. Within a given score group, WinTD will try to maximize the number of players who receive their "due" color, subject to the limits that you set in the Add/Edit a Section Dialog Box.
Given that two players are to be paired, the colors are assigned based upon the following priority list:
- If a player has not had equal numbers of each color, she will have priority for the color which she has had the fewest times. If both players are unequal on the same color, the color will go to the player who is most unequal. For instance, if Player A has had Black in both of the first two rounds, and Player B had a bye in round 1 and Black in round two, Player A will get White in round three.
- If rule 1 isn't sufficient, an attempt is made to give each player the color that they have had least recently. For instance, if Player A has had BWBW and Player B has had BWWB, Player A will get Black in round five, because A had White in round 4 and B had Black. If A has had BWW and B has had WBW, again A will get Black in the next round. (However, see note below).
- Rules 1 and 2 will only fail to assign a color if two players have identical color histories. In that case, WinTD provides you with two options for assigning the colors:
3a. WinTD gives the "due color" to the higher ranked player in any score group with even or plus scores, or to the lower ranked player in any minus score group. This is Variation 29I1 in the USCF Rule Book. Because it’s usually easier to correct any color problems in a large group, WinTD gives the correct color to the player likely to end up in the smaller group--the higher rated player (and thus likely winner) in a plus score group or the lower rated player (likely loser) in a minus score group. For last round pairings, however, there is no reason to favor one player over the other.
For the final round WinTD will use a "coin flip" to assign colors to players with the same history. This is Variation 29I4 in the rule book.
3b. Alternatively, WinTD gives the "due color" to the higher ranked player regardless of the score group.
Where possible, WinTD will also use transpositions and interchanges to improve color assignments, reducing the number of players who have to receive the "wrong" colors. See Color Corrections for details.
In most cases, the number of boards where one player or the other has to receive the “wrong” color can be reduced by making modest changes to the pairings. For each section, you specify an Equalization (or “high”) limit, and an Alternation (or “low”) limit for how large a pairing change you are willing to allow to improve colors.
The high limit covers the cases where, without changes, some players would receive one color at least two times more than the other. For instance, if two players have had WBW, without a change one will end up with WBWW. The standard high limit is 200. This may seem quite high, but if you fail to correct equalization problems in early rounds, you might run into much more serious problems in later rounds when the score groups are smaller and there are fewer possibilities for color correction.
The low limit covers the cases where some players would have the less serious problem of not having color alternation. For instance, WB versus WB means someone gets WBB. The standard low limit is 80.
If, in the Add/Edit a Section Dialog box, you check the None (FIDE style) box in the Ratings Limits section, the high and low limits are, in effect, infinite. WinTD will still prefer small changes to large, but will do whatever is necessary within a score group to correct as many colors as possible.