Re: Final day cheating?

[Rich Magahiz <MAGAHIZ@ernest.phys.cmu.edu>]

I compiled some statistics using Richard Webb's WWW pages for the
last three bashos.  I went through the records of makuuchi looking for
everyone who went into the last day with 7-7 records and came up with the
following

          1995 Haru Basho

	8-7 Winners on Senshuraku

          Maegashira 13 Kiraiho       Quality Index = -26  ***
 beat      Terao          (HM6: 8-7)  Quality Index = 12

          Maegashira 13 Kirishima     Quality Index = -24
 beat      Kasugafuji     (NM11: 7-8) Quality Index = -40

          Maegashira 11 Minatofuji    Quality Index = -27
 beat      Tomonohana     (HM7: 5-10) Quality Index = -31

	7-8 Losers on Senshuraku

          Maegashira 11 Kasugafuji    Quality Index = -40
 lost to   Kirishima      (HM13: 8-7) Quality Index = -24

          1995 Natsu Basho

	8-7 Winners on Senshuraku

          Maegashira 8 Tochinowaka    Quality Index = -6
 beat      Oginishiki     (NM15: 8-7) Quality Index = -24

          Maegashira 9 Kotobeppu      Quality Index = -24
 beat      Konishiki      (NM7: 5-10) Quality Index = -26

          Maegashira 11 Asanosho      Quality Index = -26
 beat      Asahiyutaka    (HM10: 6-9) Quality Index = -51

          Maegashira 11 Kyokudozan    Quality Index = -22
 beat      Hamanoshima    (NM10: 7-8) Quality Index = -42

          Maegashira 15 Daishi        Quality Index = -26  ***
 beat      Misugisato     (HM6: 8-7)  Quality Index = -12

	7-8 Losers on Senshuraku

          Sekiwake Akinoshima         Quality Index = -4
 lost to   Asanowaka      (NM5: 5-10) Quality Index = -23

          Maegashira 10 Hamanoshima   Quality Index = -42  ***
 lost to   Kyokudozan     (NM11: 8-7) Quality Index = -22

          Maegashira 16 Shikishima    Quality Index = -45  
 lost to   Tosanoumi      (HJ1: 14-1) Quality Index = none

	Nagoya Basho 1995

	8-7 Winners on Senshuraku

          Maegashira 1 Kotonishiki    Quality Index = 32
 beat      Daishoho (HM7: 6-9)        Quality Index = -21

 Maegashira 10 Asanowaka              Quality Index = -24
 beat Takamisugi (HM9: 6-9)           Quality Index = -48

 Maegashira 14 Daishi                 Quality Index = -36
 beat      Kasugafuji (NM11: 7-8)     Quality Index = -40

 Maegashira 12 Kirishima              Quality Index = -23
 beat      Tochinowaka (HM2: 3-12)    Quality Index = -35

 Maegashira 13 Mitoizumi              Quality Index = -23
 beat      Kiraiho (HM11: 6-9)        Quality Index = -49


	7-8 Losers on Senshuraku

 Maegashira 11 Kasugafuji             Quality Index = -40
 lost to   Daishi (HM14: 8-7)         Quality Index = -36

Summarizing:

Total number of bouts where one or more rikishi went in at 7-7: 15
(a couple are tabulated twice because both men were 7-7)

Total number where the QI of the winner was less than that of
the loser:  3  (as marked with stars)

So I would suggest that these numbers do not support the idea that
the winning percentage for 7-7 rikishi is way out of line because
of yaocho.  If anything, it would be consistent with the hypothesis
that the schedule-makers might be a little easier on 7-7 rikishi,
giving them typically opponents of equal or lesser worth.  Still,
going by the pure ranks, there seem to be plenty of instances where
the rikishi losing to the 8-7 rikishi have higher ranks, though
lower QI, so this isn't a very strong hypothesis IMHO.

Of course there is the caveat that the QI is computed after the
total record of a rikishi, so there would be a systematic
statistical bias pushing up the QI of the 8-7 wrestlers over
the 7-8 ones.  I frankly don't have to much of a feel for the
magnitude of this bias, maybe someone else can see how to make
the appropriate corrections.

Regards,

Rich
-- 
Richard A. Magahiz                  Physics Department
                                    Carnegie Mellon University
magahiz@ernest.phys.cmu.edu         5000 Forbes Ave.
rm6s+@andrew.cmu.edu                Pittsburgh, PA 15213-3890
http://www.contrib.andrew.cmu.edu/usr/rm6s/homepage.html