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Bass wrote and asked:
Just so that we are clear on this, you seem to be saying that in your evaluation you have used the word phrase "Only a Player's Own Performance Affects His Direct Comparison Value" in such a sense that
1. If a change in a game's result would change the score, that is not "affecting". 2. If a change in pairings would change the score, that is not "affecting". 3. Your evaluation should only be applied in a context where by your definition it is impossible for anything to "affect" any scores whatsoever.
Please disprove at least point 3 by a counterexample.
My answer:
The phrase "Only a Player's Own Performance Affects His Direct Comparison Value" applies after the tournament's last round and when the final player ordering is being determined. Therefore (1) and (2) are not available within that context because after the tournament's last round neither any game result nor any pairing can still change.
Concerning (3), the phrase "Only a Player's Own Performance Affects His Direct Comparison Value" does not have an indefinite context but the one and only fixed context that we are after the tournament's last round and when the final player ordering is being determined. My "evaluation" is simply "calculation of the final player ordering due to the placement criteria that had been announced and set before the tournament start". The available "scores whatsoever" are the now fixed game results of the tournament and the various placement criteria values of exactly those placement criteria that had been announced and set before the tournament start. Since by definition of the context there is no further "anything" besides what I have just described, a counter-example does not exist.
I am not saying that one cannot also study other contexts but that I, with respect to my phrase, have not done it.
I urge you: keeping in line with your earlier arguments that
1. no alternative results may be considered, and 2. the evaluation may only be done after all the results are in,
please give one (1) example of anything affecting a Direct Comparison Value, or SOS, or MMS.
For your convenience, here are some dictionary entries for "affect", transitive verb sense:
You'll probably notice that when all the results are in, nothing has an influence on any of the mentioned scores, and nothing can cause them to change even the tiniest bit.
Therefore "Only a Player's Own Performance Affects His Direct Comparison Value" is true only in the remote sense that you are using "affects" in a manner that allows for nothing to ever affect anything.
After the last round, the direct comparison value of a player is affected by the player's games and only by the player's games according to the definition of direct comparison.
After the last round, the MMS value of a player is affected by 1) the player's starting MMS value and 2) the player's games.
After the last round (of a McMahon tournament), the SOS value of a player is affected by 1) each opponent's starting MMS value and 2) each opponent's games.
I think it is incorrect to say that only a player's performance can affect his DC. As I have written at the bottom of the discussion page on DC - a player exhausted by 8 tough opponent's in a row may lose to another granted 7 soft opponent's in a row. Sickness (an external factor) can produce an opposite reaction. Ill during round 1, lost that game, recovered and won all the rest. In both cases a different draw could have altered the DC. Therefore it does not strike me as absolutely only a player's own performance which plays a part. This is easy to miss if you ignore the rest of the tournament or indeed any non mathematical aspects.
The terminology in this discussion thread is hard to fathom.
BEFORE the end of the tournament, about everything, even an atomic bomb, can affect game results:)
yes and direct comparison is formed before the tournament ends.
Sigh. Let me be more precise: "before completion of the last round's games".
Here, you are redefining "affected by" to mean "calculated from". Please use words with their normal English meaning (Bass gave a list), not your own definitions.
Rewriting to use correct English, we get:
Definition of DC: Direct Comparison is calculated from only the results of the games between the tied players.
Advantage of DC: Direct Comparison is calculated from only the results of the games between the tied players.
Which is completely tautological, and hence without merit.
The great merit is, of course, that this means that DC does not depend on calculation from results of games in that the player was not involved. I.e., the player was entirely responsible for the size of his DC value. Quite like he was entirely responsible for his number of wins (and therefore his MMS or Swiss score). A great advantage of a placement criterion! An advantage that, in this clarity, opponent-score-dependent tiebreakers or lottery do not have.
The great merit is, of course, that this means that DC does not depend on calculation from results of games in that the player was not involved. I.e., the player was entirely responsible for the size of his DC value.
This is just a restatement of your earlier "DC is not affected" argument, and remains just as false. Third party games influence DC, as both Bass and I have already shown.
The same is not true for MMS (or, for that matter, something like CUSS).
I didn't expect to convince you or Bass after having explained it for only a 100 times:)
Did you expect to be convinced by either me or Bass, after we have explained it for only a 100 times?
I do not think Robert is interested in changing his mind.
No answer? It was a serious question.
RobertJasiek wrote:
The great merit is, of course, that this means that DC does not depend on calculation from results of games in that the player was not involved. I.e., the player was entirely responsible for the size of his DC value. Quite like he was entirely responsible for his number of wins (and therefore his MMS or Swiss score). A great advantage of a placement criterion! An advantage that, in this clarity, opponent-score-dependent tiebreakers or lottery do not have.
You are still wrong.
Here's my final attempt at explaining this.
# Name R1 R2 R3 R4 R5 MMS 1. Mr. One 15+ 10+ 2+ 3- 4+ 4
This line contains all the information about Mr One's performance in the tournament. What is his DC score?
You cannot calculate a person's DC value without knowing the MMS of all the other players. Also, if I told you the tie was a three-way, you still couldn't calculate the DC value for Mr. One, because you would need to look at the pairings to see whether 2 and 3 have played each other.
Robert, I am expecting a "I was wrong, sorry about wasting your time".
-Bass
Now finally we are making progress.
You are right that
Discussion is voluntary; if you don't want to waste your time, then don't discuss.
DC, when used for - only! - the purpose of determining the final player ordering, is a tiebreaker that is applied after completion of all games of the tournament. Your earlier references to game results and pairings were with a different meaning from that and from the one above: Earlier you referred to them as dynamic and spoke about DC as a sort of test variable for two or more tournaments.
After completion of all games of the one tournament, game results and pairings are no longer dynamic but they are fixed. So dynamic considerations do not discuss how good a tiebreaker is for the one tournament but they say something about variable behaviour of the tiebreaker in an abstract model set of more than one simulated tournaments. Although this is also interesting, it is something different from the static application of a final player ordering teibreaker applied after completion of all games of the one tournament.
Different aspects of MMS (or Number of Wins Score) or pairings are being considered for static application versus dynamic application. Static application looks at only the static MMS and the static who-has-played-whom information. Dynamic application looks at who-plays-whom, dynamically varying values of MMS and dynamically varying values of game results.
So now that we all know what we speak about, each of us can express his findings much more clearly (as soon as having time for it).
RobertJasiek wrote:
Discussion is voluntary; if you don't want to waste your time, then don't discuss.
Fair enough.
-Bass
DC measures something. MMS measures something. Many other tie-breaking systems measure something. They all have merit in that they help to resolve otherwise tied players. How should you decide a tie-breaking situation? It's just personal preference.
By definition, the people involved in a tie-breaking scenario are tied. The reason they are tied is because, by the normal scoring system (minus the tie-breaking method), they placed equally. Because of this fact, nobody can really complain about the final placement, provided that it is done in an unbiased and pre-announced fashion.
Any tie-breaking system is a means to determine a winner between two or more "equal" players. I think, then, that any system (DC, MMS, random tie-breaking, etc.) has merit.
Conversely, tie-breaking systems do not inherently prove that one of the tied players *should* be placed better than the other, except how is defined by the tie-breaking methodology at the beginning of the tournament.
If you announce it at the start of the tournament, a coin flip also has merit as a tie-breaking system.
Any of these systems have merit, because they establish a placement between two players that are otherwise tied. Without playing additional games, I don't believe that any tie-breaking system is "better" than another, as long as all players were given equal opportunity at the onset of the tournament.
Nah, it is not just all but peace. Some tiebreakers are clearly worse than others. E.g., SODOS directly after MMS is known to be flawed.
What was said at the KPMC 2008 was noteworthy as a basic spirit though: "The players cannot influence the tiebreakers!"
Kirby wrote:
Without playing additional games, I don't believe that any tie-breaking system is "better" than another, as long as all players were given equal opportunity at the onset of the tournament.
I do not share your opinion. I know it is not wise to bring an analogy to any discussion, but oh well.
Suppose that in a 100m dash competition two runners tie with a time of, say, 12.34. The clock can only measure hundreths, so the clock cannot determine the winner, and the result is a tie.
In my opinion it is of the utmost importance, that if a goal line camera is used to figure out the result to the thousandth of a second, then the tie is broken in the favor of the faster runner, not the slower one.
In my opinion, using the goal line camera to find the faster runner is a very good tie breaker. Doing the same and rewarding the slower runner is a very bad tie breaker.
So I do believe that some tie-breaking systems are better than others.
-Bass
Maybe there is a better analogy for the kind of tie breaker you have in mind. Imagine a jumpers tournament where each rider is assigned a course of random difficulty. If they arrive with the same number of faults, the difficulty of the course is the tie breaker (say Sum of Obstacles Scores :). Would they accept it as somehow equivalent to a goal line photography?
In body sports i see scoring / tie breaking methods according to difficulty of obstacles invariably only where people have a say about the difficulty (figure skating, diving etc.) of their obstacles.
Kirby: First, I am OK if we disagree on this point, so I hope that I'm not later blamed for "wasting your time".
Second, I think that there's an important difference between your analogy and the tie-breaking system discussion. In particular, the goal line camera and the clock are both measuring the same thing: who ran the fastest. The objective of a tournament placement is to determine an ordering for the players that performed the best. The tournament scoring system, excluding the tie-breaking system, defines what "performed the best" means. Tie-breaking systems attempt to measure/define "who performed best" in their own ways. But "who performed best" is not a universal definition, and tie-breaking systems that don't have additional games have no way of determining "performed best" by the tournament rule defined definition, since by the tournament definition of who "performed best", the two players performed equally well.
So to go back to your analogy, a tie-breaking system doesn't determine "who performed best" with greater accuracy - it merely adjusts the definition of "who performed best" (or, in the case of random placement, makes no attempt to adjust the definition). So I think a better analogy would be two runners that tie with a time of 12.34, and then using a measure of a DIFFERENT QUALITY (for example, who has a higher blood pressure) to determine the winner.
The point is, tie-breaking systems measure different attributes than the normal tournament scoring system. The scoring system defines "who performed best", and a tie-breaking system must use an alternate means to determine a winner.
Conclusion: None of the tie-breaking systems are measuring the same thing as the tournament scoring system - otherwise there would be no tie. "Who performed best" is an arbitrarily defined concept, which is contrary to measuring speed with greater accuracy.
I think that as SOS is composed of MMS (the tournament scoring system) we can safely suggest that it must be measuring something close to it.
Kirby wrote:
.. a tie-breaking system doesn't determine "who performed best" with greater accuracy ..
True, except when it does.
If you say that the only acceptable measure of performance are the collected MacMahon Points, then of course there is no way to break a tie meaningfully.
However, if you accept that performance might be described as "demonstrated ability to collect MMS", then you can indeed use tie breakers to gain greater accuracy.
But this is all off-topic on this page, so let's not get caught in it.
-Bass
Bass wrote:
However, if you accept that performance might be described as "demonstrated ability to collect MMS", then you can indeed use tie breakers to gain greater accuracy.
This is based on the assumption that Player A's "demonstrated ability to collect MMS" depends on how well Player A's opponents collected MMS. This is just one possible model of reality that can be used in a statistical analysis, and not everyone agrees with it.
For example, some people may not buy into the idea that the effort required for any particular game has any relation with previous or future games.
The wording on the page that you linked, which states that the SOS model is "obvious from a statistical estimation point of view", is some sneaky rhetoric that ignores the fact that a statistical estimation is only as good as the underlying model that's being used to measure the real world. In this case, not all people agree that opponents' performance on other games has anything to do whatsoever with performance on any particular game. Sure, you can make that assumption for your model. But who is to say that it is definitively true?
This is where preference comes into play. The choice of whether opponents' other games have anything to do with any given particular game depends on how one believes that "better performance" should be defined. There is no universal agreement on this definition.
Therefore, it is necessary to explicitly define what "better performance" means in the context of a particular tournament, both in the basic scoring system that's being used, as well as the tie-breaking system being used. This is why I believe that it is impossible to construct a model of reality only using assumptions that everybody agrees with, and hence, any tie-breaking system is OK to use as long as it is predefined, unbiased, and known in advance by all players in advance.
To exaggerate, one could say this,
Bob climbed mount everest in 1 day. Carol climbed the stairs to the first floor in 1 day.
Both achieved a climb in 1 day. However Carol's climb was harder as the stair's were pretty sticky and there was guy on them that kept on and on talking, and well you get the point.
This is what SOS basically says.
bad analogies everywhere:
bob climbed up to mount everest.
carol climbed up to nanga parbat.
mount everest is higher. we have some nice numbers to compare them... so award the victory to bob.
nanga parbat is however considered more difficult, but that doesn't fit into our scale so neatly.
cheers tapir.
To be clear, I think that SOS has a reasonable rationale, and I believe that this is one of the reasons that it is widely used as a tie-breaking system. It makes sense that if Carol indeed had a harder climb, then maybe her effort should be given more value.
But the rationale is still based on an assumption: there is a relationship between the amount of effort or skill required in a particular game and other games played during the same tournament.
Is this assumption reasonable? I don't think that there's a definitive answer. Some may think that the assumption is unreasonable since players' performance can fluctuate throughout the course of a tournament in complex ways. Others might think that it's a good way to define "better performance".
In my opinion, is SOS a reasonable tie-breaking method? Yes. Is DC a reasonable tie-breaking method? Yes. Neither definitively measure a universally accepted notion of "better performance", but rather define what "better performance" means in their own way.
You might have Mr. A say, "Well, I lost to Mr. B using DC, but I won against him using SOS". Does this mean that Mr. A inherently performed better than Mr. B? It just depends on how "performed better" is defined. All you can really say is that, by DC, Mr. B performed better than Mr. A, whereas by SOS Mr. A performed better than Mr. B.
Most tiebreakers have a rational basis, and it is not here that I, at least, seek to decree which one must be used. My interest is basically in seeing that each one is represented fairly, and not just that, but also represented in plain intelligible language.
It is correct that a tiebreaker should be both announced in advance and implemented in practice. I am not sure what DC measures beyond who won a single game in a tournament. Most other tiebreakers try to measure strength of opposition. Player's tied on MMS have obtained the same overall result. Tiebreakers that look at the strength of opposition suggest that there was a difference in effort required to obtain the result. DC-like tiebreakers (normally) suggest that one player is better than another on the basis of a single game result. For the most part then, it is a matter of preference for methodology. A (quickplay) play-off is another attractive methodolgy to use.
Kirby: I think that it is a matter of preference. Yes, tiebreakers that look at the strength of opposition suggest that there was a difference in effort required to obtain the same result, but it is still a redefinition of "who performed best", because in the case of the scenario where two players are *not* tied, the same definition of "who performed best" is not applied.
If I play in a tournament and have all losses, perhaps the reason is due to the effort required for my games. But the scoring system doesn't care about that in terms of "who performed best".
Such tie-breakers still certainly have merit because they specify a way to determine placement, even if it is not consistent with the determination of "who performed best" by the normal scoring rules.
DC may have merit, because it addresses the thought: "I had the same number of wins as that guy, and I even beat him... But he still places higher than me.". Some people may disagree that the single game result is an indication that he "should be" placed higher.
But I think that it's just preference. "Better performance" doesn't have a universal definition, and depends on the tournament and tie-breaking rules being used.
i am grateful that you joined in kirby...
mathematics, measurement and statistical understanding all this aside:
direct comparison appeals to moral judgement. (as is evidenced by quite a number of comments i have read about the egc2009 after catalin won his game against alexandre but still lost on SOS to just name one example.)
direct comparison offers a higher degree of suspense than other common tie breakers, namely SOS.
i feel we should add these properties as advantages as soon as we unlock the page.
It is better not to talk of advantages and disadvantages, but simply correctly state properties of the tiebreaker. One of the reasons these discussions (albeit, that they are mostly no longer centered on the actual verbatim content here on the page) continue for so long is that somebody insists on inaccurate advantages framed in pseudo mathematical lingo. There is no reason for the page to be locked anyway since it is not really the subject of an edit war.
the direct comparison score would be different if any (different result of a) third party game changes size or composition of the tied group.
you never get tired of your argument, don't you. all of you.