SumoLyubo

Theoretical Sumo Tournaments

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I've lurked the Sumo Forum for a while, but now I've found occasion to post.

I spent some of my free time last week encoding sumo tournament scheduling as an integer linear programming (ILP) problem, largely as an excuse to play around with an ILP solver but also out of curiosity for figuring out certain theoretical possibilities for sumo tournaments, such as the lowest possible winning score without a tie, the largest possible tie, etc. I have posted my silly tool and written up some results here. Many of these bounds are, in retrospect, not too hard to figure out by hand: For example, if there are 315 total wins in a tournament, then there can be at most 315/8 = 39.375 (round down to 39) top-division wrestlers with a winning score, etc. Nevertheless, it is not obvious (at least to me) how to go from verifying one of these bounds to producing a specific tournament that fulfills those criteria. Note that the tool is pretty slow, so it's probably not a practical way to explore possible sumo tournaments.

I am curious as to whether others have worked these out on paper before and whether there are more results of this vein that I never considered. I am really bad with combinatorics, so I am also curious as to whether some of the problems I've stated are instances of "canonical problems" that I'm simply unaware of.

This was just a feverish first pass at the scheduling problem (also I don't have much prior experience with ILP solvers so I may just be encoding it badly), so I am also interested in extending or improving this solver. One thing I am curious about is whether trying to encode the typical scheduling customs (yokozuna and ozeki facing the komusubi and top maegashira in week 1 and then the sekiwake and each other in week 2, etc) might actually improve the performance of the solver, as it may reduce the search space. I would be curious if there are neat formulations of these rules I could try passing to the solver, either as hard constraints ("a yokozuna will never face M17E unless they're tied for the lead," etc) or soft ones ("minimize the distance in rank between the fighters in each bout"), that also seem realistic.

Another problem I would like to consider is sampling likely tournaments (schedules and outcomes), but I haven't worked out how to do it. A practical application of such a tool would be if one could judge the probability of a particular tournament as it unfolds. I'm curious if others have written up tools like that, as I'm sure someone's tried before.

Edited by SumoLyubo
grammar

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Buyuzan won the Juryo yusho (also fifteen day tournament) with a 9-6 record in 2001.

The lowest scoring Makunouchi yusho in the 15 day era is 11-4.

Of course in sumo games - such as Bench Sumo - which also operate on the fifteen day schedule, with different opponents each day - there have been several 10-5 yushos in both of the top divisions.

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This post is very interesting. I guess a rule-based system could be implemented, as a kind of expert system, since we have a lot of expert knowledge on bout scheduling with our experience as fans.

On 08/12/2020 at 06:23, SumoLyubo said:

 

Another problem I would like to consider is sampling likely tournaments (schedules and outcomes), but I haven't worked out how to do it. A practical application of such a tool would be if one could judge the probability of a particular tournament as it unfolds. I'm curious if others have written up tools like that, as I'm sure someone's tried before.

 

My intuition tells me that probability is too rigid for this kind of assessment, and the use of fuzzy sets or belief functions theories could be useful. Particularly to generate belief-plausibility intervals, way richer than "simple" probabilities.

Those are just random toughts, I haven't really studied the ins and the outs of such models...

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5 minutes ago, Nantonoyama said:

This post is very interesting. I guess a rule-based system could be implemented, as a kind of expert system, since we have a lot of expert knowledge on bout scheduling with our experience as fans.

My intuition tells me that probability is too rigid for this kind of assessment, and the use of fuzzy sets or belief functions theories could be useful. Particularly to generate belief-plausibility intervals, way richer than "simple" probabilities.

 Those are just random toughts, I haven't really studied the ins and the outs of such models...

Yeah, I'm digging through my old AI textbooks to figure out what would be a good approach. I had not thought about an expert system but that seems very promising.

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