Tie-Breaks

Running Chess Tournaments
1

Someone please speak to my thoughts about the following tie-breaks, as suggested by USCF rules.

  1. Modified Median
  2. Solkoff
  3. Cumulative
  4. Cumulative of Opposition

In a 5-round Team-Modified Swiss for scholastic players who will avoid playing each other as much as possible, are these the best? I’ve always preferred SOLKOFF followed by MOD MEDIAN in tournaments of less than six rounds, as MOD MED disregards the extremes, and in a 5-round swiss, we would end up using only 3 of 5 games with MM. Seems to me that SOLKOFF is better for that reason, but I would like more ideas.

CUMULATIVE, of course, in a T-MS, where players from the same school will not be playing each other, isn’t a good tie-break, IMO. But I’d like other opinions.

I realize that the rules aren’t compelling me to follow their suggestions, as I may post alternatives in pre-ads, but I’m still looking to learn.

Regards,

Terry Winchester

2

Others may disagree, but I think cumulative tiebreaks should no longer be used, especially in any tournament using a computer for pairing and tiebreaks.

The primary (possibly ONLY) virtue of the cumulative tiebreak was that it could be calculated before the last round ended.

I’ve said this before, but based on nearly 20 years of explaining tiebreaks to parents, common game is the tiebreak that parents most readily accept as being ‘fair’. Unfortunately, it only works in a two player tie, and then only if the two players played a game that didn’t end in a draw.

3

I believe that all tiebreak systems are unfair to someone. Having a playoff game(s) might seem fair until one realizes that a 40/90, G/30 tournament tie could get decided by a G/5 match. If it’s not one thing, it’s another?!

Tim

4

Definition: Tie break, a process, usually involving mathematics, designed to annoy the maximum number of players and parents.

5

Let’s face it… the title of the system is “TIE” break. The players are TIED, and if at all possible must be treated as equals! Why?.. Because they have proven that they ARE equals.

That being said… the unfortunate aspect of a SS tournament, of class prizes, etc… is that there will be times when breaking ties is necessary. Therefore, we need to acknowledge that fact and provide for it in the ‘rules’, and devise systems that can be applied equally to all participants so that there is very little opportunity for claims of favoritism.

I agree with Nolan, no tiebreak system will ever be agreed upon by all and can be “fair” especially when it involves a tie for first with a perfect or near-perfect score. (e.g. 5/5 or 4.5/5 and the draw was against each other.)
In that case, all of the listed systems are mathematically and statistically unsound, and I can prove it… but what’s the use. In fact, the higher rated player in the tie (even by just a few points) has a better chance of winning by this method (about 58%) than the player with the white pieces in a single game playoff (about 55%).

The use of opponents’ scores becomes much more meaningful for class prizes, with tied players having at least one loss or two.

BUT

Most of the rules committee (including T.J.) disagrees with me, therefore I must be wrong. I feel the only way to settle such a (perfect score) tie is a playoff, even if it needs to be g/5, though it should never need to be that extreme. (I would make the playoff for first place as full or 1/2 the original time control as a default, and if there’s time, two games one with each color, if not enough time, the higher “math” tiebreak gets white). I think that such a tie must be settled over the board, and not worse than an arbitrary coin toss.

However, getting back to the original post. Check the rule for the “modified median”. Those with a plus score lose only the lowest score (not both the highest and lowest), therefore have 4 scores to use (in a 5 round event). Only those with 2.5 use only three games. This makes the system slightly ‘better’ (though still not ‘good’)

Whatever you do, POST CLEARLY THE SYSTEM YOU ARE USING IN A PROMINANT LOCATION AT THE SITE! at the time of registration, and definately before the start of round 1.

No matter what system you choose (Rulebook default, or some other system) ALL sytstems are ‘fair’ if understood at the outset and applied without discrimination.
If the system you are going to use is different from the Rulebook default, (though, I agree with the rulebook default is the most accurate if a mathematical method is to be used, other than, possibly, performance rating.) state the system clearly in all advertising. You can still use full solkoff as your primary, if announced in such publicity.

Of course, unless specified otherwise (such as playoffs) all cash and cash-like prizes must be split among those tied.
Minor merchandise, trophies, or other unsplittable prizes may be decided by tie-break.
Even these you could offer essentially ‘duplicate’ prizes such as the lower tie-break getting the smaller trophy, but with the plate stating “co-champion” on both of trophies. Many such prizes are relatively inexpensive and can be duplicated if, for example, there is only one trophy offered for the prize.

Substantial, unbreakable prizes (like qualification to a closed or invitational event, or an unsplittable scholarship) is still open to debate. And will be, forever.

Hence, no matter what, BE SPECIFIC in pre-tournament announcements!

6

To answer your specific question, which, I failed to do. Here is my opinion regarding the listed systems:

Preferred: Don’t split ties if at all practical.

Median or modified median:
The best of the ‘simple’ mathematical systems, in particular for category prizes (falls apart with a perfect score.)
Cuts down on the sample size for a statistically significant determination.
But eliminates the first round pairing problem for opponents are ‘playing up’ and end up with 0 (or near zero) points.
Favors the higher rated player.
I prefer this to solkoff even in your example.

Solkoff:
uses all games, but has the problem of outliers (see above).
Strongly favors the higher rated player.
Not quite as good as modified median but much better than cumulative.

Cumulative:
Very poor, but easy and quick to compute. Since players who win earlier are paired with others of like score, they play ‘tougher’ competition throughout (well, in theory, anyway). Rarely works that way.

Opponent cumulative:
simply sucks. A coin toss would be better.

Playoff:
Best used for first place only, unless there is a strong reason to apply to other, very substantial, unsplittable prizes.
Result decided over the board, always preferable (if possible).
In many cases there is not enough time allowed to implement at a reasonable time control.
Drags the end of a tournament on… most just want to ‘get it over with’.

Performance rating:
Not practical.
Probably the most fair of the mathematical methods, but as is usual with complex math too few players (and parents) understand, and is therefore not practical, even if using a computer.
Difficult to compute, and very difficult to tell ‘where do I stand (or my team stand) if…?’
Slightly favors the higher rated player.

(by the way, there are others, including head-to-head, S-B, not counting draws, who had more blacks, coin toss, etc…)

7

Thanks to all for replying and I’m still interested in more.

“Dont split ties…” Expand please?

email me, David. I’d be gald to hear your thoughts: winchester_t@yahoo.com

Terry Winchester

8

I’m hoping that a synopsis of David’s comments winds up here actually. Or David can email me as well! I’m glad you asked this question , Terry …

9

Great Topic!! I’m surprised it hasn’t come up earlier.

Head to Head seems the most obvious thing to look at when trying to determine a clear-winner.

I’m intrigued by the thoguht of who had more blacks. I had not thought of this. I don’t know if players would even except this at the onset of a competition. It seems unfair to 2 players who have a perfect scores, and one of them happens to have had 3 blacks (in a 5 Round Swiss). A playoff seems appropriate in this scenario. But I was never a big fan of the g/5 playoff when the tourney was a G/60 or above…

David, i also kindly request you please expand your thoughts here.

10

David’s advice about not breaking (or splitting) ties is not always practical.

In money tournaments, tiebreaks aren’t important because the money is pooled among the tied players, though the apportionment can get tricky, as several threads here have illustrated.

In trophy tournaments, the organizer/TD has a couple of choices for avoiding tiebreaks, all of which require either advance planning or extra work afterwards.

One is to order a few extra plates and put the right ones on before handing out the trophies. Another is to order and send out corrected plates afterwards.

I’ve heard that some large events, such as nationals, have had the trophy maker onsite to make up plates for tropies as needed, but that’s not practical for most events.

When there are prizes that cannot be split, such as a book or an entry into another event, that’s when tiebreaks are absolutely necessary.

11

I agree that there will always be someone unhappy when dealing with tie-breakers. Each system has it’s advantages and disadvantages. However, as long as you advertise the system in advance, there shouldn’t be too much room to argue.

I’ve never had an issue with it, because I’ve rarely seen anything other than cash as a prize for non-scholastic events. I played in one event in Mississippi where they awarded cash and trophy to the class winners, but every class had a clear winner so there were no problems.

12

Oops
what I meant was “Don’t BREAK ties if at all practical”

that is:
SPLIT prizes equally that can be split.
Give equal or duplicate prizes when economically possible.
Give equal titles (co-champions) and provide plates for trophies in that event (note; you may have to mail them after the event)
etc…

Use tiebreak only as the last resort or if the prizes cannot be split or duplicated.

For very large prizes that cannot be split, have a playoff (the preferred method even in the rulebook) if at all possible, and plan the event so that a playoff is possible. Publish the playoff conditions in advance and post at site.

Statistical significance of tie-break systems:
Complete analysis is not appropriate here due to the math involved and the length, but I can give you a summary.

modified median system:

The hypothesis is that by adding the scores of the opponents, it can be determined who played the ‘better’ competition within the event, thus earning the points against stronger opposition.

For a 1.96 sigma seperation (95% confidence) required for significance, adding the scores of the opponents, using 5 rounds (5 opponents, 4 scores counting) requires a tiebreak difference of at least 4.06 points.

It is rare that a title or trophy is decided by 4-1/2 tie-break points or more.

Solkoff:
Solkoff increases the sample size, thus reducing the difference required, but has the problem of including outliers (e.g. a 1200 rated player in a premier section that has several sections), thereby skewing the results. The effects of increasing the sampe size by one and the probability of meeting an outlier (and the effects thereof) are almost a trade-off. But when the outlier exists, the difference is large, indeed.

Statistical bias for the higher rated (first place ties, perfect score or perfect - .5)

Analysis can be summed up like this: The higher rated player is almost always paired against a higher rated opponent than a lower rated player in the same score group (given both players are in the top half of the group, for at least the first several rounds).
Those opponents of the higher rated player are going to score more (as a group) than the opponents of the lower rated player, therefore end up with a slightly better tie-break.
The lower rated player did not have the opportunity to meet those same players.
All you can say for sure is that both players are stronger than the players they met.

Cindy: “Hey, ma, I played in a chess tournament”
Ma: “Great, Cindy, How’d ya do?”
Cindy: “I won all my games”
Ma: “Wonderful… You won the tournament!”
Cindy: “Er… no. I lost”
Ma: “Huh?”

Hmmmm… doesn’t sound good, does it?

This arguement (an the subsequent analysis) diminishes as scores approach the middle of the pack. (e.g. 2.5/5), thus tie-break methods may be more meaningful for class or category prizes.

13

nolan said:

Very true.

and giving as equivalent prizes as possibe is sometimes more work than an organizer is willing to do (but I think it is worth it, when you do).

Sometimes tie-break systems are a necessary evil. Using the rulebook priority list diminishes that evil as much as possible, and still be workable.

That’s why they are in the rulebook at all.

Robgetty said:

My point, exactly, about being clear what is to be done, and publishing that in advance. Even if a system is unsound, if it is known and understood it is accepted and ‘fair’.