Let me come clean and say that, at first, using my gut instinct, I thought the correct order would be: 1. A 2. B 3. C 4. D 5. E ...and my fantasy Legend for this was: A - Calzaghe B - Kessler C - Bute D - Mundine E - Inkin ...kind of...(with the emphasis on: KIND OF...)
My Dear Decebal, First let me congratulate you on a most interesting puzzle, indeed anything that can get Cross Trainer, China_Hand_Joe and C.M. Clay II on the same side is a most remarkable topic!! I would like to take issue with you, sir, if I may, on one specific point in your system. What we have been given is the results of a "Round Robin" tournament containing five contestants. You have rated a person with a win over the last place guy and a win over a guy in the middle of the pack (Designated "D") IN FRONT OF a guy with a win over the tournament winner and the last place finisher (Designated "C"). I should say that the latter CLEARLY had the better tournament and I can certainly assure you that in a ELO rated event - like a chess tournament - "C" would have the higher rating (His even score with D and win against a higher rated player). Is there a mathematical justification you have for choosing D over C that I have missed? With respect, I appreciate the work you have done and the importance of the issue. I simply cannot find an objective mathematical model that reproduces your "ideal". The introduction of the notion of "styles" to a tournament rating problem is quite unique. Kind Regards, Victor Von Vockerman
Haha, hey, mate! No need to address me so formally!:good You are undoubtedly right! It crossed my mind too that in a chess championship, C would get more points than his 4th place would suggest he should! And this goes for any method of ranking that goes by POINTS accumulated! And here was one of my points! I think this is the wrong way of going about ranking fighters. In my opinion, they should be ranked according to how good they are at present, given their past couple of performances and likely form as a result of those fights (e.g. including injuries, becoming "shot" etc...) Partly, the reason why I started this thread was to challenge those who will end up making ranking lists - they have to be aware of the weaknesses behind their own system of ranking, whatever it is! I think that we are not running an ATP or ELO points systme when ranking...or are we/should we? This is because in boxing, more than in other sports, it matters much more HOW that win was earned, and the manner in which the fighters have fought! So it is much more an art than any points system would allow for. As to this puzzle, the reason why D should be ranked above C is that D is a better fighter than C - beats him directly, and also, C's win over A shouldn't be overrated - it was as a result of his awkward style for A, not because he was that good! I think we have to accept, in boxing, that even a great Champ could be beaten by someone outside the very top, because of their very awkward style. But this shouldn't mean that that awkward fighter should be considered top, in a rankings list. The theory of boxing ranking is tough...and I am not pretending that I have made any inroads - but I am trying to shed some light on some caveats... I am aware that our top analysts will be able to do a great job by using their gut feel alone! This is why they are such good analysts in the first place. However, I think it would be useful if we established on what basis these rankings would be made, in the first place. You see...the problem is this...a top analyst should be able to decide whether A beats C or not, and so on...like in the question. But even if he predicts all the various combinations perfectly, it doesn't mean that he will know how to rank them accordingly! Say: A stands for Calzaghe B stands for Kessler C stands for Bute D stands for Mundine E stands for Inkin.... amd say that A could beat B, D and E but not C B could beat C and D, but not A or E C could beat A and E, but not B or D D could beat C and E, but not A or B E could beat B, but not A or C or D ....just like in the original question...and an analyst would correctly determine the outcomes of these fantasy match-ups... ....HOW should he rank them A-E? You saw yourself how many different answers we got, when looking at things theoretically using GIVEN fight results (taken as a given by all). Now, if people don't agree whether Calzaghe would beat Kessler or the other way around, there is very little chance that they will come to the same conclusion about the ranking... ...Sure, this is inevitable...that is why we have quite a few - to even things out. My point is, though...they have to think carefully about the assumptions that they make subconsciously, when ranking fighters...partly to this end, I have started this thread - to show people how many hidden assumptions there were - and how difficult it all is! :good