Question about pairing the odd man from a scoregroup

Running Chess Tournaments
1

Last month, this question came up in the fourth round pairings for our monthly club event.

Here is the wallchart after the first three rounds (with the player names anonymized):

Rd1 Rd2 Rd3 Rd4 1 Alpha W 7 B11 W 8 2375 25000001 0 1 2 2 Bravo B 8 W 5 H-- half point byte 2244 25000002 1 1 1½ 3 Charlie W 9 B 6 W 5 2138 25000003 1 2 3 4 Delta B10 W 7 H-- 2113 25000004 1 1 1½ 5 Echo W12 B 2 B 3 2102 25000005 1 2 2 6 Foxtrot B13 W 3 B 7 2002 25000006 1 1 2 7 Golf B 1 B 4 W 6 1988 25000007 1 2 2 8 Hotel W 2 B12 B 1 1930 25000008 0 1 1 9 India B 3 H-- -13 withdrawn 1832 25000009 0 ½ F ½ 10 Juliet W 4 B13 W11 1823 25000010 0 0 ½ 11 Kilo H-- W 1 B10 1822 25000011 ½ ½ 1 12 Lima B 5 W 8 bye 1700 25000012 0 0 1 13 Mike W 6 W10 - 9 zero point bye 1683 25000013 0 1 X 2

The TDs at the club would have paired round 4 as:

Alpha (1) - Charlie (3) Echo (5) - Golf (7) Foxtrot (6) - Delta (4) Hotel (8) - Kilo (11) Lima (12) - Juliet (10)

SwissSys produced these pairings:

Golf (7) - Charlie (3) Echo (5) - Foxtrot (6) Delta (4) - Alpha (1) Hotel (8) - Kilo (11) Lima (12) - Juliet (10)

Clearly, Charlie has to have an opponent from the 2 score group. Charlie has already met Echo and Foxtrot, so the only possibilities are Alpha and Golf. Pairing Charlie and Golf gives both players their due color; pairing Charlie and Alpha gives Charlie his due color but not Alpha. However, the rating difference between Alpha and Golf is 388 points.

Question 1: Is this switch justified? (SwissSys was configured with the USCF defaults of 80 points for alternation and 200 points for equalization. Please note that I’m not asking why SwissSys chose this pairing. I’m strictly asking whether this pairing complies with the rules.)

Question 2: Given the pairing Golf-Charlie, I would have expected either Echo-Alpha (treating Foxtrot as the odd man) and Foxtrot-Delta. Instead, SwissSys paired Echo-Foxtrot, treating Alpha as the odd man. Given that the rating difference between Alpha and Echo is 273 points, and the rating difference between Alpha and Foxtrot is 373 points, does this pairing comply with the rules? (Again, the question is not why SwissSys made this pairing.)

2
  1. In my opinion, no. I can’t see any justification in the rules for this pairing, though I would be interested in hearing other views. 2) This one is correct. The relevant rating difference is not between 1 and 5 (273), but between 5 and 4, the players actually being flipped (11). I have some reservations about this, but that’s what 29D1b seems to say.
3

I agree with the TDs at the club.
I entered the tournament into WinTD and it agrees with us.

For those that are interested, here is the pairing log:

[code]**************************************************

Pairing Section q, Round 4, on Fri Oct 21 20:45:55 2005

Options Used:
High (Equalize) Limit=200
Low (Alternate) Limit=80

**********Natural Pairings

Score Group 3.0
0 EQ OK Charlie(1:2138,B) vs Alpha(2:2375,B)
Drop 1.0 Points
Score Group 2.0
0 EQ OK Echo(3:2102,WW) vs Foxtrot(4:2002,W)
0 OK OK Golf(5:1988,W) vs Delta(6:2113,b)
Drop 0.5 Points Duplicate
Score Group 1.0
0 AL OK Hotel(7:1930,WW) vs Kilo(8:1822,w)
0 AL OK Lima(9:1700,b) vs Juliet(10:1823,BB)
Drop 0.5 Points

Total value 17346.125000
0001 Duplicate
0002 Wrong Equal
0002 Wrong Alternate
0003 Drops for 2.000000

**********Final Pairings

Score Group 3.0
0 EQ OK Charlie(1:2138,B) vs Alpha(2:2375,B)
Drop 1.0 Points
Score Group 2.0
0 EQ OK Echo(3:2102,WW) vs Golf(5:1988,W)
14 OK OK Foxtrot(4:2002,W) vs Delta(6:2113,b)
Drop 0.5 Points
Score Group 1.0
0 AL OK Hotel(7:1930,WW) vs Kilo(8:1822,w)
0 AL OK Lima(9:1700,b) vs Juliet(10:1823,BB)
Drop 0.5 Points

Total value 962.125488
0002 Wrong Equal
0002 Wrong Alternate
0003 Drops for 2.000000

Best Results Achieved on Pass 1[/code]

4

The switch from
Alpha-Charlie
Echo-Golf
to
Golf-Charlie
Echo-Alpha
is not Alpha-Golf=387, but rather Charlie-Echo=36.

Thus I can understand pulling Golf up to board 1 and making the 36-point change to equalize.

I don’t use Swiss-Sys, but I’m guessing that it first started with
Alpha-Charlie
Echo-Foxtrot
Golf-Delta
and then switched Alpha and Golf (eliminating the Alpha-Charlie pairing, the only one with both players requiring white to equalize) and then flipped the colors for Alpha and Delta. See 29E7, examples 2 and 5.

In this case, the real question is why it didn’t then switch Alpha and Foxtrot (Delta-Echo = and 11 point difference, which is well within the 200 point limit for Echo and Foxtrot’s equalization and the 80 point limit for Delta’s alternation).
It also overlooked the switch of Alpha and Echo (Delta-Foxtrot=111 which is within the 200 point limit for equalization of Foxtrot).

It looks like WinTD first brought Alpha up to the 3-point group before trying to equalize/alternate, and thus never looked at the Alpha-Golf switch.

5

Should the program (or TD) look only at the rating difference between the two players being switched, or should it (he/she) look also at the rating difference between the two opponents?

There are (at least) three cases.

Case A – a simple transposition within a score group. Example:

2000 BWB vs 1600 BWB 1900 WBW vs 1300 WBW
Switching the 1600 and 1300 would solve both color problems, but would apparently violate the 200-point rule. However, it really wouldn’t violate anything, because the opponents are within 200 points of each other. “29E5c. Evaluating transpositions. All transpositions should be evaluated based on the smaller of the two rating differences involved.”

Case B – an interchange within a score group. Example:

2000 BWB vs 1650 BWB 1700 WBW vs 1350 WBW
Here switching the 1650 and 1350 WOULD violate the 200-point rule, no matter which set of rating differences is considered. However, an interchange is also a possibility (switching a player in the top half with one in the bottom half). In this case, switching the 1700 and 1650 solves all color problems legally, and the rating difference between the opponents need not (should not) be considered. “29E5d. Evaluating interchanges. For an interchange, the director need only consider one rating difference rather than the smaller of two. The difference between the two players switched is the relevant difference.”

Case C – a transposition across score groups. Example:

1650 BWB (3.0) vs 2000 BWB (2.5) 1700 WBW (2.5) vs 1650 WBW (2.5)
Do we switch the 2000 and 1700? It’s an apparent violation of the 200-point rule, except that the opponents’ rating difference is zero! Here the rulebook contradicts itself: “29D1b. … In deciding whether to make a switch of either the odd player or the opponent, you should look only at the rating difference of the players being switched.” Yet, in example 5 (under 29E7), the book suggests that both sets of rating differences (the players’ and the opponents’) should be considered.

In the example that started this thread, it seems that WinTD followed the rule, while SwisSys followed the example.

Bill Smythe

6

The replies so far are very interesting, though I’m not sure I understand all the nuances yet.

I think I figured out a basic misunderstanding on my part. I’ve puzzled hard over rules 29A (Score groups and rank), 29D (The odd player), and 29E (Color allocation). Really hard. :slight_smile:

Rule 29A clearly defines “score group” and “group” as “players having the same score, even if there is only one player within a group.” On page 147, in rule 29E5: “A transposition is the practice of changing the order of players within the upper half or the lower half of a group. An interchange involves switching a player from the bottom of the upper half with a player from the top of the lower half.”

Based on the text in 29E5, I deduce that transpositions and interchanges only apply to players in the same score group. Based on the definition in 29A, I’m not thinking of the odd player as being inserted into a score group.

In other words, while I understand John Hillary’s and Jeff Wiewel’s logic in their explanations, I can’t find the justification in the rules for the procedure. My interpretation of the switches described in 29D1b was to consider the rating difference between players in the higher score group (deciding which player to treat as the odd player) or the rating difference between players in the lower score group (deciding which player will be the opponent of the odd player). I couldn’t find the justification for considering the rating difference between Delta and Echo (in John’s explanation) or between Charlie and Echo (in Jeff’s explanation).

On the other hand, I may be reading the rules too literally. In 29D, I read: “At least one player, and possibly more, will have to be dropped to play in a lower score group.” That seems to contradict the definition of “score group” in 29A.

Also, the rules do seem to say the odd player is paired against a player in a lower score group. I’m afraid I couldn’t understand John’s explanation without pulling Delta up from the 1.5 score group into the 2 score group.

My mental model for dealing with an odd player has been to determine a pairing for the odd player by selecting an opponent from the next lower score group, setting that pairing aside, and then pairing the remaining players in the lower score group. The explanations so far suggest the procedure should be to pair the odd player, then pair the remaining players in the lower score group by “natural” pairings, and then look at all the pairings (including the pairing with the odd player) in evaluating transpositions and interchanges for improving color allocation.

I hope I’m not being impossibly legalistic here. I’m afraid my education was in pure mathematics, and I’m a software engineer by vocatiion. Some days it’s a marvel that I can decide which shoe to tie first! :slight_smile:

Actually, my real excuse is that the senior TD certification exam has instilled The Fear of The Rulebook and The TDCC in me for when the time comes to take the ANTD exam. :slight_smile:

Thank you for the discussion so far.

7

I think you’re overlooking 29D1b (“If the conditions in A cannot be met …”). One of the conditions in A is “… the color consequences are acceptable.” If the colors don’t match when you drop the odd man, you are supposed to look down (or up) to see if the total number of balanced colors can be improved, but only within the 80- and 200-point limits. That being said, the treatment of the odd man with regard to color has always been a fuzzy area in the rules, and the 5th edition, while an improvement, has not fully solved the problem.

8

Looking at it more closely with pairing cards, I now agree that the pairings on boards 2 and 3 were just wrong (bad colors in both games). This looks like a program bug. The rating differences are irrelevant, since (given the first board pairing) switches do not improve colors.

9

Has anybody tried reproducing this pairing with another copy of SwisSys?

10

I’ve actually been communicating with Thad Suits about these pairings. He’s looking at it in more detail.

That’s why I was focusing on the rules in my question. Thad agrees that the pairings are suboptimal. I was trying to examine whether the rules allowed SwissSys to make the pairings it did.

11

Actually, in the topic titled “Controversial pairings from SwissSys” (http://www.uschess.org/forums/viewtopic.php?t=686), I did mention that three TDs (two senior TDs and a National TD) had a long discussion about what “acceptable color consequences” meant. Obviously, I haven’t learned yet. :slight_smile:

Thanks again for the discussion so far.

12

Yes. It produces the same pairings. That’s why I’m pretty sure it’s a program bug (rather than a leftover setting of pairing flags, which was my first thought).

13

The basic question is to what extent, and in what manner, the 80- and 200-point rules apply to cross-score pairings. It is clear that the authors of the 5th edition made a serious effort to resolve this, but they didn’t quite succeed.

14

Pairing the lowest 3.0 against the highest 2.5 is (as you point out) NOT a transposition. It’s just a simple consequence of a law of mathematics, which says that unfortunately odd numbers exist.

Pairing the lowest 3.0 against the SECOND-highest 2.5, however, IS a transposition. But the two players being transposed are the two highest players in the 2.5 group – so it doesn’t violate your concept that a transposition necessarily involves players in the SAME score group.

Likewise, pairing the SECOND-lowest 3.0 against the highest 2.5 is also a transposition. But, again, the two players being transposed are in the SAME score group (the lowest two players in the 3.0 group).

So all we’re doing is applying transpositions (of players in the SAME score group) to situations requiring odd players.

I think you should first determine who the odd player is. It shouldn’t necessarily be the lowest-rated. For example, sometimes you can make colors work better in BOTH score groups (3.0 and 2.5) by using another player (such as the second-lowest) as the odd player.

This requires a look-ahead philosophy rather than a top-down philosophy. If, for example, before you make ANY pairings, you notice that the 3.0 group has extra “due-whites” and the 2.5 group has extra “due-blacks”, then it makes a lot of sense to pair a 3.0 due-white against a 2.5 due-black.

Bill Smythe

15

There are some places where the rules are still fuzzy (including some transposition issues), but this isn’t one of them.

Under “29D. The odd player”, it says:

“29D1b. … switches to correct colors should stay within the appropriate limits (29E5). …”

– and 29E5 consists of the 80-point rule (29E5a) and the 200-point rule (29E5b).

In other words, color transpositions involving the odd player are subject to the same limits as color transpositions within a score group – 200 points to equalize, 80 points to alternate. That doesn’t sound “fuzzy” to me.

Bill Smythe