The Futagoyama effect on the Banzuke

[guje@nmr.lpc.ethz.ch]

T. Saimon wrote:
> Have you tried rationally arranging the Banzuke, its especially 
> difficult this time.  Muzukashii ne!

Actually I've made a program and tested it on some old banzuke. It worked quite
well. I used it last time for my banzuke guess and was not too far from the
best entries (that matched the real banzuke quite well). This time I gave up
on using the program and did it with paper and pencil from a very raw ordering
provided by the computer.

IMHO the problem is the Futagoyama effect, which is kind of a climate crisis in
sumo. The Futagoyama effect on the sanyaku ranks is a tendency to swell them.
The kinds of Takatoriki and Akinoshima (and for that matter Takanonami) have a
consistent advantage of at least 2 wins per basho that tends to prolong their
stays in sanyaku. Though being consistently high-ranked they can afford to lose
to some high-ranked maegashira more often, because they need not play one 
yokozuna and one ozeki (and of course each other). That in turn provides 
more high-ranked maegashira with kachikoshi than would be the case without 
the Futagoyama effect. The beautifully balanced system of the banzuke cannot
maintain its dynamic equilibrium since on average too many high-ranked rikishi
obtain kachikoshi by not fighting each other. After a sufficient time the 
sanyaku slots may be filled and nevertheless East-maegashira 1 may obtain kachi-
koshi.

The second consequence of the Futagoyama effect is a pronounced "maegashira
bouncing". This problem is more subtle and the theory is not yet satisfying.
However, the main reason seems to be that non-Futagoyama rikishi at m3 to m9
face a tougher schedule then would be normal for these ranks.

This research has been supported (unknowingly) by the Verein der Chemischen
Industrie Deutschlands ;-)

Gunnar

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