Median and Modified Median inequity with byes

Running Chess Tournaments
1

I hope this is the right forum to bring this up. It involves an inequity in the Median and Modified Median tiebreakers when a player has a bye (or perhaps other unplayed games).

When a player’s final score even or better, the Median and Modified Median systems drop the lowest score of his opponents, and a bye counts as a zero. This process usually helps the person who got a bye and hurts a person who does not get a bye. If a person had a bye, the lowest score that goes into the tie-break is a zero, and that is dropped. If a person doesn’t have a bye, a non-zero score is probably dropped. I checked the output of the WinTD software, and that is indeed how it is calculated. I think that the person receiving a bye is already getting an advantage by getting a full point for an unplayed game (I’m not arguing with that). However, if he has an even score or better, he gets an additional advantage when it comes to tie-breaks compared to others with the same score that don’t have byes.

I propose that for players with even or better scores, the lowest score of a played game should be dropped instead of the zero for the bye. This will help even it out.

Here is an example, although my proposal would not have made a difference in this case:

uschess.org/msa/XtblMain.php … 4-12922915

In the five-round primary section of this tournament, there were trophies for the first three places. There were nine players, so five out of nine got byes. #3 on tiebreaks (Todd) had a bye and #4 had no bye. In this case, my proposal would not have changed the places, but it could have.

In the elementary section of the same tournament
uschess.org/msa/XtblMain.php … 3-12922915
there were only seven players. One player elected to take a half-point bye, otherwise five of the seven players would have gotten a full-point bye and the situation could arise.

Now, the director probably should have combined these two sections, but that is not the point.

In this recent tournament, five of seven players got byes, so the situation could have arisen (but didn’t):
goldenisleschess.com/tournam … 060225.htm

It is not necessarily a small section that could have this problem.

To sum up, I propose that for Median and Modified Median tiebreakers with a player with an even score or better, the score of the lowest PLAYED game should be dropped from the sum, to not give the recipient of the bye an additional benefit as far as tie-breaks.

2

Wouldn’t it be easier simply to use Solkoff as the primary tie-break system? Under that system, no scores are dropped. Thus, players who earlier got a free point with the bye pay the price in the tie-break when the bye counts as zero. Just because the Rulebook recommends Modified Median as the first system doesn’t mean you have to use it.

– Hal Terrie

3

Yes, it would be easier to use Solkoff, but that isn’t my decision to make. So perhaps the recomended order of tie-break systems should be changed.

4

Jud,

First of all, any tie break method has flaws. The basic purpose of the Swiss System is to find a winner. Who finishes second as opposed to third or fourth etc becomes more a function of the luck of the draw with of course some skill thrown in.

I like to point out that under the modified median method it is only full point byes that count as zero, half point byes are assigned a score.

Under your proposal the player with the unplayed game would be penalized twice, i.e., by not having an opponent’s score for the unplayed game and by having an otherwise good result dropped from the calculation. Dropping the lowest score attempts to disregard an easy win for the plus scored players. Arbitrary? Perhaps, but it doesn’t penalize the player for not having an opponent. Maybe not the best method in all cases, but as I stated above no tie break system is perfect.

5

I once made the following statement when discussing tiebreaks:

“A tie break is a mathematical procedure designed to annoy the maximum number of players.”

6

According to the USCF rulebook, page 200, all unplayed games are counted as opponents with zero score (full point or half point byes and forfeits).

I know that the Swiss system is primarily to determine a winner, but tie-breaking can determine first place too.

I know that all tie breaking systems have problems, but Modified Median is given as the primary one, and I don’t think it should be that way (in the form it is in). Suppose two players are 3-2 and one has a full-point bye. The one without the bye has a 60% score in actual games, the one with the bye has only a 50% score in actual games. I think the tie-break should favor the 60% score over the 50% score, unless the one with the 50% score played sufficiently stronger opponents.

Consider the Modified Median versus the Solkoff in this situation. Suppose one player had opponents with adjusted scores of 5, 4, 3, 2, 2 and the other had a bye and had opponents with scores 5, 4, 3, 2.5. Modified Median puts the one with the bye ahead of the other player, Solkoff puts the one without the bye ahead. Under the Modified Median, the player with the bye benefits twice - once by getting the bye and secondly in the tie-breaks. Under Solkoff he gets the benefit of the bye but then that is offset partially in the tie-break.

I think Solkoff should be preferred over Modified Median.

7

I am at a bit of a disadvantage since I don’t have my current rulebook at home, so if the rule changed since the 4th edition I will take your word for it. I tend to rely on the skill of Thad Suits and Tom Doan to program tie break methods correctly.

They don’t determine first place, they only determine who gets nondivisable prizes.

It does favor the one with the 60% score since he has results from five opponent’s where the player with the bye only has four.

As Hal Terrie pointed out, you are free to use Solkoff.

8

It is in the 5th edition.

Like the trophy (and title?) for first place.

Not compared to Solkoff.

No, I am not free to use Solkoff. (1) I am not the director. (2) Even if I was, it applies to all tournaments, not just ones I’m involved with, (3) the rulebook, page 199, says that Modified Median is to be used first, unless otherwise anounced.

Intuitively, it seems that Solkoff would be better than any form of Median. You are throwing away information with Median. Since all of the games count in the final score, why don’t all of the opponent’s scores
count in the tie-break?

Actually, the problem is bigger than just the issue of unplayed games.

Suppose that two players are both 3-2 (or 4-1). One played against opponents whose scores were 5, 4, 3, 2, 2. The other played against ones with scores 5, 4, 3, 2.5, 0. I would say that the first one did better than the second one, and Solkoff ranks them that way, but Modified Median ranks the second player higher.

The upshot is that I think Solkoff should be preferred over Modified Median.

9

All tie-break systems are unfair and often end up simply being a way of using tournament results rather than a coin-flip. There can be countless examples cited to show that one system or the other is better (below are a couple including one where I feel Modified Median is definitely better in that case). One major reason for using Modified Median (with the ignoring of the least significant opponent) rather than Solkoff is to reduce the “lottery effect” of the first round pairings when it may be virtually random as to which players were paired against lower rated players who either were or were not scoring well after that round.

To slightly modify your example and increase the apparent inequity of Solkoff, if one played against players (in round-sequence) with scores of 0, 3, 2.5, 4, 5 and the other played against players with scores of 1 (from a last-round bye), 3, 2, 4, 5 then Solkoff favors the player whose opponents scored fewer points in actual play while Modified Median favors the opponent who had apparently stronger competition after the gross mis-matches of the first round. The actual results are so close that it is roughly the same as a coin flip.

A different example is where 4-1 players have opponents with the following scores: 0, 4, 4, 4. 5 versus 3.5, 3.5, 3.5, 3.5, 3.5. In this case, the first player played the tournament winner and three of the players that were one point back while by chance being paired in round one with a player having a terrible tournament (maybe suffering from a bad cold), while the second player played none of the other top final scorers. Modified Median strongly favors the first player (17 to 14) while Solkoff slightly favors the second (17.5 to 17).

10

I assumed since you posted to the Tournament Direction forum area, that you were the director. I would say if you want to change the rulebook you need to post to the USCF Issues area.

I am not sure how intuitive it is that Solkoff is better. Hopefully it is bad data that is being thrown away under Modified Median.

Lets assume that in the first round I get an easy pairing against someone who ends up 0-5, and you get an easy pairing against someone who ends up 2-3. We both got easy pairings and we both won. But somehow you deserve the prize over me based on the luck of the draw in the first round? I rather have the games from the later rounds count more. Indirectly Modify Median takes this into account.

I understand that.

11

Not true.

Regarding Modified Median: In a 5-round tournament, the player with the bye has to count 4 of 4 played opponents. A player without a bye gets to count the best 4 of 5 played opponents.

If a player happens to get a first round full-point bye because he is the odd player, I don’t think that he should automatically be at the bottom of the tie-break order.

-Kevin Hyde

[size=75]“Anything is fair if it declared prior to the event and all players enter the event with full knowledge.”[/size]

12

In most cases (unless the tournament conditions specify otherwise), a title is shared by the co-champions.

Things that generally cannot be shared and must be decided by some kind of tie-break procedure (including a playoff):

Trophies, medals, plaques, ribbons, etc.
Book, set or clock prizes
Qualification slots for some other event
Scholarships (depending on the scholarship grantor’s specifications)

13

I said I didn’t know if this was the right forum. I’ll move it over there, after replying here.

That seems like more of a problem with the cumulative system.

14

He is not automatically at the bottom of the tie-break. In one of the examples I gave in the first message, the one with the bye would have finished at the top of the tiebreak, even with the change I proposed.

When a player has even or better score, the lowest score is dropped in Median and Modified Median. For a player with an unplayed game, this is a zero anyway, so it doesn’t hurt. For the player with no unplayed games, the score dropped is probably not zero, so he is disadvantaged.

15

I misread your question. What you describe are just “the breaks”. Instead, what I’m converned are systematic biases in the system. What if one player gives away a rook and the other has an easy round - that jsut the breaks.

16

Now that we’ve determined that this is the correct forum:
As GrantPerks noted, tie-break systems are all imperfect by nature. Which one is “better” is going to depend on how you define your terms. If you’re looking for a tie-break system that correlates well with performance rating, why not just use performance rating itself? That’s probably the best tie-break system we can come up with, and there’s no question of any bias with respect to byes. With computers available to figure the tie-breaks, we don’t have as much of a need for those that are easiest to calculate (like cumulative).

The organizer can use whatever tie-break system he wants, as long as he lets the players know in advance. You don’t need a rule change if you can convince the organizers that there’s a better system.

17

What is “the formula” you used to determine the winner? If the highest rated always won then I would assume your results will have a certain bias. I have run similar scenarios in the past to test the effect of accelerated pairings on final results. In my test I would pre-rank hypothetical players based on strength, and then add ratings in a slightly different order, i.e. the highest rated was not necessarily the best player. What I found was that the final tie-break order is closer to actual with accelerated pairings as opposed to normal pairings.

This is a bit out of my field of study, but why is the comparison to performance rating the key to evaluating the various methods? Seems like the measure of success should be against some predetermined strength criteria at the beginning of the event. I see performance rating for that one event just as biased as the tie-break methods.

In “The Official Chess Handbook” by Kenneth Harkness he describes the “Harkness Median System” as well as Solkoff, Kashdan etc. He compares Solkoff to Harkness and shows the advantages Harkness has over Solkoff.

18

When you want to award prizes for an event, the awards should be based on the performance in that event – not awarded to whichever player is strongest at the beginning. Otherwise, why play?

Arguably, (and IMHO) performance rating is the best measure of that performance – even better than the actual score in the event – IF the ratings are reasonably accurate to begin with.

But then, I should also admit that I consider any tie-break method to be little better than flipping a coin.

19

The reason performance rating is not considered the best tie-break method is, I think, because the pairings are arbitrary to a certain extent, so the way you performed is not as important as how the people you beat performed (for some of the tie-break methods). It could be that you beat a very high rated player that you were lucky to be paired against who was having a really bad streak and lost all his games. Your performance rating for that game would be great, but it does not reflect how little trouble that high rated player gave you.

20

I agree that the awards should be based solely on the performance for that event. This is why performance ratings shouldn’t be used as a tie-break method. Compare two players who tie at 4-1. One of them was the highest in the section at the start of the tournament, the other the lowest. Since the highest will get “paired down” against lower rated opponents in the early rounds, and the lowest rated player will get “paired up” in the early rounds the performance rating for the higher rated player for those rounds will be lower than for the lower rated player. We might as well award ties based on pre-tournament ratings, lowest first.

I know one TD who breaks ties based on date of birth, the youngest first. A method I find better than performance rating.

If a 2700 goes 5-0 against a field of 1800’s his performance rating would be 2200’s. Any of the 1800’s who lose to him would get a 2300 performance for that game. Thus, the 4-1 1800 would have a higher performance rating than the 2700 who went 5-0.

While there are flaws with any tie-break system, there is a good degree of correlation between performance and each of the common methods.