tag:blogger.com,1999:blog-8734744291040505450.post459213197559010019..comments2019-07-02T07:14:28.502-07:00Comments on The Art of Logic: Network graph theory and debate tournamentsRussell Haneshttp://www.blogger.com/profile/13594411930757264086noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-8734744291040505450.post-13120598489486591712009-12-23T07:01:52.402-08:002009-12-23T07:01:52.402-08:00For those who are interested in this topic, I sugg...For those who are interested in this topic, I suggest reading A Numbers Game's page: http://code.google.com/p/anumbersgame/wiki/TournamentCharts. There's a lot of different considerations of how to best "resolve" upsets.<br /><br />I think Anonymous raises a good suggestion; once I have a working program, I need to run some simulations to test it out.<br /><br />Just to clarify, I think schedule strength should be relatively equalized within a bracket, not across the whole tournament. Teams in the top bracket should have higher opp. wins than teams at the bottom. My whole point is if the opp. wins are fairly equalized within a bracket, then we can be more sure of the reliability of a win-loss record as a good indicator of a team's strength. <br /><br />Thanks for the Colley matrix paper!Russell Haneshttps://www.blogger.com/profile/13594411930757264086noreply@blogger.comtag:blogger.com,1999:blog-8734744291040505450.post-34674141684551867512009-10-04T07:06:50.303-07:002009-10-04T07:06:50.303-07:00Hi Russell, Wow! I've been thinking about this...Hi Russell, Wow! I've been thinking about this problem awhile and I'm glad to see that you and others are attacking it. Great work! A few comments. First, I think it would be helpful to generate a mock tournament and assign strength values to your mock contestants. Then ask your algorithm to generate strength values after your matching. You can then compare the difference between the hidden starting strength and your algorithm's estimation. This would provide with a quantitative measure of your algorithms. For example, I can intuitively understand why you would want to normalize strength of schedule by the end of the tournament but this may not be the most efficient for ranking (or strength estimation). It should be tested and I'm not sure it is best to rely upon actual tournament results because there is always uncertainty if the better team won any specific round.<br />Also, your virtual tournaments should not be entirely deterministic, meaning that a contestant with a strength of .9 vs one with .45 should have a probability of winning 2/3 of the time not winning 100% of the time.<br /><br />Also, My second suggestion would be to look at the Colley matrix. http://www.colleyrankings.com/matrate.pdf This seems like the most straightforward method to assign values to a network based upon a binary output (win or loss). You seem fairly fluent in math and programming so I hope you might be able to implement this.<br /><br />If we assume the Colley matrix is the best ranking system; the big question is what is the best way to match the later rounds. (Does anybody know this?!)<br /><br />Implementing the first suggestion will give you comparable results. <br /><br />Lastly, this seems like a very academic mathematical exercise. Have you been able to find any good math papers on this topic? Pubget.com is a good place to start.<br /><br />Also, I'm not very math literate. If you could decode the most relevant math papers, It'd be incredibly appreciated.<br /><br />Wow! Good luck Russell! I hope you have the energy and enthusiasm (and time!) to see this through. :)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8734744291040505450.post-7855821445180448812009-08-11T10:28:12.800-07:002009-08-11T10:28:12.800-07:00It occurred to me that there's an easier way t...It occurred to me that there's an easier way to describe the same procedure that I used for breaking a round robin tie.<br /><br />Using the same example as before, there's a three-way tie between B, C, and D. Imagine that these three teams were your entire tournament. B's record against C and D is 1-1, C's record against B and D is 0-2, and D's record against B and C is 2-0. Your rankings would go {D, B, C}. That is the same method I described before, just an easier way to conceptualize what it is doing.Russell Haneshttps://www.blogger.com/profile/13594411930757264086noreply@blogger.com