Best way to divide a group into 2 sections

Running Chess Tournaments
1

Last year was the first year that we expanded our City Championship Invitational from 6 qualifiers to 12. The format changed from one 6 man round robin to two sections. Each section plays a round robin with the winners of each section playing each other to decide the City Champion.

The first year the sections were divided like this:
Section A: 1,3,5,7,9,11
Section B: 2,4,6,8,10,12

The argument was made that this was unfair because Section A is harder even
though the relationship between 1 and 3 is similiar to the relationship between 2 and 4.

So this year the sections were divided like this:
Section A: 1,4,5,8,9,12
Section B: 2,3,6,7,10,11

Now the average ratings of each group is much closer.

Yet now also in Section A, the number 1 player doesn’t have to play anyone
higher than the number 4 ranked player in order to win his or her section.

So which of these systems to you think is fairer?
Or does anyone have a better way to split the groups?

Thanks

2

You can’t really do anything about the average ratings, just the seeds those ratings represent. Make sure the seed average is the same, and you’d be set.

Year one was clearly unfair. Year two has the same seed average, and looks fair enough.

Once the seed averages are the same, you want to try to get the variation between the seeds to be as smooth as possible.

Does 1,4,5,8,9,12 (which adds up to 39) seem smoother than 1, 3, 6, 7, 9, 12 (39)? Seems the same. I think either of these would work. Ben

3

WinTD has a Section-Divide Up function which takes the 12 players and breaks them into the two six player sections. The “Group to Equalize Ratings” choice would do the following:

  1. start with 1+4 in one section, 2+3 in the other.
  2. Add 5 to the section with the lowest average of the starting two, and 6 to the one with the higher average.
  3. Add 7 to the section with the lowest average for the first three, 8 to the other
    etc.

While it’s obviously easier to hand something like this off to a computer, it’s isn’t that difficult to do manually for just two sections. Note that this is designed to come close to equalizing the average ratings of the two sections. It won’t equalize the average CA of the players (which isn’t possible anyway). If there’s a big gap between #1 and #2, then the section with #1 will probably get the lower-rated addition in each pair down the line. That will compensate all those other players for their having to face by far the highest rated player, but, of course, makes life easier for player #1 vs the alternative of averaging seeds.

4

Why is it that you think Year one was clearly unfair?

At the time I considered it the fairest way of dividing the sections because if for example player 1 was 2000 rated and player 3 was say 1800 there was a 200 point rating difference in their game. In the other section Player 2 would be 1900 and playing player 4 a 1700 player, (these ratings are just to illustrate my point) again a 200 point rating difference.

So even though one group was stronger the Individual players have the same chance of winning.

5

Tom’s suggestion is good but fundamentally different that what I mentioned. Tom’s suggestion looks at the ratings of the players entered into the event. I thought you were looking for a fair system that you can publish every year saying these seeds are in section A and those seeds are in section B. However, as long as you’re following Tom’s algorithm, you’re being very fair (nearly equal averages) and impartial - done same way every year.

Tom’s method does have one potential pitfall. If the difference between seeds 1 + 4 were extremely large, Tom’s method might end up with 1, 4, 5, 7, 9, 11 vs. 2, 3, 6, 8, 10, 12 which on seed average is not very fair, favoring the second group, whereas the rating average has greater chance for equality than what I described in my earlier post.

What do you want more in your future events? Equal seed average, which can be published before invitees accept, or equal rating average, in which the bracket seeds have to wait until all spots are fulfilled?

I think this is factually incorrect, if barely. I think I see your point: even though seed #1 field is demonstrably tougher than seed#2’s field, it is still just as hard for someone to surpass him as the representative from that section. I don’t think I agree…he has the rating differential between seeds 3 and 4 to surpass (beating out the third seed should be harder than beating out the 4th seed) and if there are not many rounds, there is less chance that the top seed can outperform if the strength is higher. He may not be surpassed, per se, but with a tougher field there is a greater chance for a tie to occur. You don’t want to favor any seed with a system, but if you have to do something, you are going to want to make sure your top seed is happy, else he won’t play. Year one’s system favors seed #2 instead by making his path to the finals much easier than seed #1.

(I will admit top-seed bias, never much liking the swiss-system’s attempt to give seed #1 much harder pairings than seed #5 in a ten player section, but not reflecting that in the cash prizes if their final placement is the same.)

6

I’m just trying to figure out what would be best. This year I turned the decision over to someone who isn’t playing. Last year the division was made well before anyone qualified.

Pretend for a moment that there were only 4 people and you were dividing them into sections. Would you then go with 1 and 4 in one group and 2 and 3 in the other? This seems to me like it just gives 1 a free ticket to the top while 2 has to struggle to qualify.
Now with 1 vs 3 and 2 vs 4 both 1 and 2 have to work to qualify.

Or am I missing something?

7

With 4 people only, you have a perfect one-round, round one swiss pairing (if swiss pairings are perfect). Still, in the 4-player situation you have a choice of pairings that greatly favors either player 1 or player 2. When you add more players to the mix, you still must favor either #1 or #2 but the rest of the players can mitigate the extent of the favorism if you balance them correctly.

By the way, your concern about seed #2 struggling to qualify compared to seed #1 is not reflected in the NCAA basketball, NFL, NHL, NBA, MLB playoffs where the top seeds are given even more advantages. As I said, I have a top-seed bias.

8

The number one goal that I wish to achieve with the Invitational City Championship is to make it hard to win. Once a player has won they know that they earned it, they didn’t just catch the luck of the draw. I think this should apply to the number one seed as much as the lower seeds.

Each year the difficulty level of the Invitational has risen. For example this year instead of a single game play off between the two section winners there will be a two game match. If that is indecisive a third sudden death game will be played.

9

Apparently you think it should apply less to the #2 seed. Anyways, benefitting the #1 seed has the potential for the #2 seed to actually try to pick up rating points throughout the year by becoming a better player. Instead, the system you seem to espouse makes it more profitable for the #1 seed to shed a few rating points, thus becoming the new #2 seed.

Have it your way.

10

Your second version is what used to be known as the Holland System, the pre-Swiss method of pairing large groups. It was still used in the Olympiads until some time in the 80s. It has obvious drawbacks (every Olympiad someone complained that his group was tougher than the other ones), but it was the best that could be done. I think it still is. The problem with trying to equalize ratings between the sections is that it almost guarantees complaints about the seedings.

11

Actually I’m not that attached to either method.
I was planning on using the first method again this year until one of our members brought up to me his belief that it was unfair. Since the tournament hadn’t started yet at the time, we didn’t even have all the qualifiers, I told him he could decide on the division of the groups.

I can see the advantage of the Holland system when it is applied to more than two groups, say four. Because if I understand it it correctly, team 1 chooses then team 2 chooses, then team 3 chooses , then team 4 chooses twice, then team 3 chooses etc.

I only bring this up because one of the players in one of the groups thinks that the current years division is unfair.

So now I’m thinking of next year.

As far as the hardness thought goes it has more to do with the fact that I stumbled into winning the City Championship one year, simply by having a good run of games. But at the same time if you are good enough to be ranked number one, then you should be good enough to beat all comers.

Realize here locally we aren’t talking world class. The top rated player in the City Championship this year is 2000.

12

I realize that if we had not expanded the City Championship the division issue wouldn’t be a problem. But the the City Championship has evolved into a popular item. But expanding it from 6 to 12 actually dilutes it somewhat.

Maybe I can explain my issue with the division this way.
Pretend that next year for we have 16 qualifiers. We decide to go to a format that has 4 round robins to pick 4 players to play a round robin to decide the City Champion. Without playoff games that should only be 6 rounds.

So you have 16 players ranked 1 through 16. In reality players 1 thru 4 should all end up in the playoff round robin. Now the question is are the other players just window dressing?

If we divide the sections by the Holland Method we would end up with the following (Sections go vertical like 1,8,9,16 is a section)
1 - 2 - 3 - 4
8 - 7 - 6 - 5
9 - 10 - 11- 12
16- 15 - 14- 13

Seems a touch unfair to #4 having to play #5
#1 gets like super easy opponents.

Now using the other method that I have no name for
(section again is vertical 1st section is 1,5,9,13)
1 - 2 - 3 - 4
5 - 6 - 7 - 8
9 - 10 - 11 - 12
13 - 14 - 15 - 16

123 and 4 all should win their groups and we will
end up with the same end result as the first division
but 123 and 4 are all going to have to work equally hard to get there.

Maybe I’m just dense but I don’t see the Sequential Method as being unfair.
Unless it is unfair to make the stronger players work to maintain their status.

13

Isn’t it unfair to 5?

He is rated between 4 and 6 and so should have a probability of reaching the finals somewhere between their probabilities. That is correct when he is in the group with 4, but very incorrect when in the group with 1.

In general the probability of qualifying for each player is roughly decreasing steadily by ranking when using the the Holland method distribution, but is jumping all over the place using the Sequential method.

It seems to make sense that each players probability of reaching the finals should correlate well with their rankings - and that is much better with the Holland method. Possibly the distribution described for WinTD would provide an even better correlation between probability of qualification and rating if that was desired.

14

The second, by far.

This doesn’t make sense. Why would it be fair, through pairing manipulation, to give a 1400 player the same winning probability as a 2000 player, given that the (ultimate) total field is the same?

Whichever player, 1 or 2, is paired against 3, has more of a struggle on his hands than the one who is paired against 4. Player 2 has no more inherent right to avoid this struggle than player 1.

As long as we’re pretending, let’s suppose we have 8 players rated 2000, 1820, 1810, 1800, 1400, 1220, 1210, 1200, and that (for some reason) our only concern is finding sections that are “fair” to the 2000 and the 1400. By your criterion, you would consider sections of 2000-1820-1820-1800 and 1400-1220-1210-1200 fair, because the 2000 and 1400 are each playing opponents rated 180, 190, and 200 points below themselves.

bbentrup stated that he has a #1 seed bias. Obviously, you have exactly the opposite bias – stick it to the stronger player. What about making the weaker players work, too?

Bill Smythe

15

There is probably a certain amount of truth to that.

Right now if I were to make a suggestion for a change for next year it would be to go to 8 qualifiers and to have just one section.

This would tighten back up the Invitational Idea, yet still is an expansion of the original 6. Now there is no necessity of a playoff at the end unless there is a tie, so 7 rounds would handle everything.

16

I think this would be much preferable for fairness’ sake.

17

The city championship can be opened up to a larger pool of players while allowing only six or eight qualifiers by making one or more seeds available to be earned at another existing event (s) .

18

I’m not sure I understand what you are saying.

19

I don’t know how the six qualifiers in the past were identified, but let’s assume that it is was the six highest-rated city residents who were interested in playing. Two more spots could be awarded to the highest-finishing not-otherwise-qualified players from a swiss that occurs before the city championship. An existing tournament may serve this purpose if you do not wish to organize another. This allows a city resident who does not qualify by rating to still have a chance of getting into the championship.

20

Originally the 6 were from the following:
Previous years City Champion
Top finishing local player from the Greater Peoria Open
The Fall Qualifer event held on Monday Nights
The Winter Qualifer event again held on Monday Nights
Something we called the Class Championship from Monday Nights
The Highest rated local player that can be convinced to play.

The city championship has been played on weekends and over a series of
Monday Nights. Lately The Monday Nights has been the norm.

When it was expanded the Qualifiers went to
Defending Champion
Top two from Greater Peoria Open
Top two from The Fall Qualifier
Top two from The Winter Qualifier
Top two from The Class
Again the top rated that could be convinced to play.
And two additional chosen by committe for various reasons.

We actually get a little more attendance at the Qualifing events through the year. The reality is that with the size of our club most people that want to play for the City Championship can qualify in one way or another, especially now that it has been expanded to 12.