Stats question

[HenryK 38]

Out of 100 rikishis getting past Mae-zumo, how many make it to Sanyaku, Maegashira, Juryo, Makushita etc. respectively? Say, in the past 20 years?

Edited December 4, 2007 by HenryK

[Doitsuyama 1,263]

Out of 100 rikishis getting past Mae-zumo, how many make it to Sanyaku, Maegashira, Juryo, Makushita etc. respectively? Say, in the past 20 years?

That's not easy to answer - which mae-zumo time frame would you like exactly? "Past 20 years" is impossible to answer as many, many rikishi out of these will reach higher grounds in the future, but we can't know exactly how many. Dewanosato can tell you that you must really go a long time back for a definite answer, but then again this answer may be outdated... ok, which time frame?

[HenryK 38]

Out of 100 rikishis getting past Mae-zumo, how many make it to Sanyaku, Maegashira, Juryo, Makushita etc. respectively? Say, in the past 20 years?

That's not easy to answer - which mae-zumo time frame would you like exactly? "Past 20 years" is impossible to answer as many, many rikishi out of these will reach higher grounds in the future, but we can't know exactly how many. Dewanosato can tell you that you must really go a long time back for a definite answer, but then again this answer may be outdated... ok, which time frame?

Would 1950-1990 make sense (taking your point that "past 20 years" results in a censoered sample)?

Edited December 4, 2007 by HenryK

[Doitsuyama 1,263]

Would 1950-1990 make sense (taking your point that "past 20 years" results in a censoered sample)?

I have complete banzuke only from Kyushu 1974 on, so I arbitrarily decided to go with the 20 year mae-zumo frame from Aki 1974 until Nagoya 1994. I guess there won't be that many rikishi reaching new high divisions in the future out of this group despite 88 rikishi still being active.

Now we get 3053 rikishi who entered the banzuke on jonokuchi and 36 more who started at makushita tsukedashi, not a bad sample size. The high divisions of the 3053 jonokuchi starters break down as follows:

Jonokuchi	512	16.77%
Jonidan	1147	37.57%
Sandanme	688	22.54%
Makushita	500	16.38%
Juryo	94	3.08%
Maegashira	62	2.03%
Komusubi	19	0.62%
Sekiwake	16	0.52%
Ozeki	7	0.23%
Yokozuna	8	0.26%

Some sums: sekitori 6.75%, makuuchi 3.67%, sanyaku 1.64%.

The makushita tsukedashi entrants in that time break down as 8 makushita, 6 juryo, 11 maegashira, 5 komusubi, 4 sekiwake and 2 ozeki (Asashio and Musoyama), 78% becoming sekitori. The only makushita tsukedashi ever to get to yokozuna was Wajima who entered a bit earlier in Hatsu 1970.

Edited December 4, 2007 by Doitsuyama

[HenryK 38]

Would 1950-1990 make sense (taking your point that "past 20 years" results in a censoered sample)?

I have complete banzuke only from Kyushu 1974 on, so I arbitrarily decided to go with the 20 year mae-zumo frame from Aki 1974 until Nagoya 1994. I guess there won't be that many rikishi reaching new high divisions in the future out of this group despite 88 rikishi still being active.

Now we get 3053 rikishi who entered the banzuke on jonokuchi and 36 more who started at makushita tsukedashi, not a bad sample size. The high divisions of the 3053 jonokuchi starters break down as follows:

Jonokuchi	512	16.77%
Jonidan	1147	37.57%
Sandanme	688	22.54%
Makushita	500	16.38%
Juryo	94	3.08%
Maegashira	62	2.03%
Komusubi	19	0.62%
Sekiwake	16	0.52%
Ozeki	7	0.23%
Yokozuna	8	0.26%

Some sums: sekitori 6.75%, makuuchi 3.67%, sanyaku 1.64%.

The makushita tsukedashi entrants in that time break down as 8 makushita, 6 juryo, 11 maegashira, 5 komusubi, 4 sekiwake and 2 ozeki (Asashio and Musoyama), 78% becoming sekitori. The only makushita tsukedashi ever to get to yokozuna was Wajima who entered a bit earlier in Hatsu 1970.

Awesome. Thanks very much. This provided answers to several questions of mine.

1) The "average" Jonokuchi entrant will never make it to Sandanme (!)

2) Making it to Makushita is a huge achievement: less than a quarter of all rikishis get there.

3) Only a tiny elite ever gets to Sekitori: less than 8 percent (including Makushita entrants)

4) However, once you are there advancing gets relatively easier: about 60 percent of all Juryo debutants will make it to Makuuchi

5) And almost half -- 45 percent -- of all Makuuchi debutants will obtain a Sanyaku rank (!)

6) About a quarter of all Sanyaku debutants will go on to Ozeki

7) Finally, almost every other Ozeki (8 out of 17) will go on to Yokozuna (!)

Edited December 4, 2007 by HenryK

[Asashosakari 20,297]

1) The "average" Jonokuchi entrant will never make it to Sandanme (!)

Keep in mind that those who never advance beyond Jonokuchi tend to be rikishi only for the fleetest of moments...for those 512 rikishi mentioned above, their average career length was only 4.4 tournaments, with more than three quarters (388 of 512) sticking around for 6 basho or less.

[HenryK 38]

Inspired the above stats I have computed a little transition matrix. "8.2" in the field "Mk-S/K", for example, means that 8.2 percent of all Makushita debutants ended up obtaining Sanyaku rank in their careers.

Ozumo Transition Matrix

(in percent)

[/td]	To	Y	O	S/K	M	J	Mk	Sd	Jd
From
Jk		0.6	2.0	4.3	7.6	24.0	46.3	83.4
Jd		0.3	0.7	2.4	5.2	9.1	28.8	55.5
Sd		0.6	1.2	4.3	9.4	16.4	51.9
Mk		1.1	2.3	8.2	18.1	31.5
J		3.4	7.3	26.1	57.3
M		6.0	12.7	45.5
S/K		13.1	27.9
O		47.1

[HenryK 38]

1) The "average" Jonokuchi entrant will never make it to Sandanme (!)

Keep in mind that those who never advance beyond Jonokuchi tend to be rikishi only for the fleetest of moments...for those 512 rikishi mentioned above, their average career length was only 4.4 tournaments, with more than three quarters (388 of 512) sticking around for 6 basho or less.

Sure. They are a relatively small part of the total (one-sixth), however -- 5 out of 6 Jonokuchis make it to Jonidan, but less than half make it to Sandame.

The transition matrix above suggests that the relatively most difficult career steps are (i) from Sekiwake/Komosubi to Ozeki (28 percent), and (ii) from Makushita to Juryo (31 percent). All other career steps have a conditional probability of about 50 percent, with the exception of Jonokuchi to Sonidan (5 out of 6).

[Asashosakari 20,297]

Sure. They are a relatively small part of the total (one-sixth), however -- 5 out of 6 Jonokuchis make it to Jonidan, but less than half make it to Sandame.

It's still significant though...while only 46% of all debutants reach Sandanme, it's 55% for those who stuck around for more than a year. Bump it up just a little bit more to a year and a half, and it's already 64%.

[Bealzbob 0]

Wow. Very interesting work guys. Nice job. Very interesting to me that nearly 1 in 10 makushita make it to sanyaku !! I wouldn't have guessed it that high. And also that nearly half of all maegashira make sanyaku, again that's higher than I'd have guessed.

[HenryK 38]

Sure. They are a relatively small part of the total (one-sixth), however -- 5 out of 6 Jonokuchis make it to Jonidan, but less than half make it to Sandame.

It's still significant though...while only 46% of all debutants reach Sandanme, it's 55% for those who stuck around for more than a year. Bump it up just a little bit more to a year and a half, and it's already 64%.

Absolultey. And I'm sure there are many ways how these stats could be refined.

[HenryK 38]

Wow. Very interesting work guys. Nice job. Very interesting to me that nearly 1 in 10 makushita make it to sanyaku !! I wouldn't have guessed it that high. And also that nearly half of all maegashira make sanyaku, again that's higher than I'd have guessed.

Sanyaku as such appears to be somewhat less exclusive than one would expect. Ozeki is the really huge hurdle (and, at a lower level, Juryo).

[Asashosakari 20,297]

Sanyaku as such appears to be somewhat less exclusive than one would expect.

It's all the "one and done" career-high Komusubi skewing the numbers. :-S Of the 24 in the sample, 15 had just one basho at the rank. (The others: 4x two basho, 4x three basho, 1x four basho.)

For comparison, the number of sanyaku basho by those 20 who topped out at sekiwake:

1

2

3 (twice)

4 (three times)

7

9

10

11

13

16

17

18

20

26 (twice)

27

34

[HenryK 38]

Sanyaku as such appears to be somewhat less exclusive than one would expect.

It's all the "one and done" career-high Komusubi skewing the numbers. :-S Of the 24 in the sample, 15 had just one basho at the rank. (The others: 4x two basho, 4x three basho, 1x four basho.)

For comparison, the number of sanyaku basho by those 20 who topped out at sekiwake:

1

2

3 (twice)

4 (three times)

7

9

10

11

13

16

17

18

20

26 (twice)

27

34

Implying: obtaining a Sanyaku rank is (relatively) easy, keeping it is hard.

[Zentoryu 154]

Wow. Very interesting work guys. Nice job. Very interesting to me that nearly 1 in 10 makushita make it to sanyaku !! I wouldn't have guessed it that high. And also that nearly half of all maegashira make sanyaku, again that's higher than I'd have guessed.

I think it has something to do with the fact that even a mid to low level maegashira regular can find himself at Komusubi if he has a good basho or a little banzuke luck, or both at the same time. Those are usually the "one and done" guys that Asashosakari mentioned.

[Asashosakari 20,297]

It's actually a nice little brain teaser: Name all eight currently active rikishi who have had just one basho in sanyaku. FWIW, I got six out of eight, and erroneously included one more guy who had more than one basho...

(For the solution, check here and here.)

Edited December 4, 2007 by Asashosakari

[Gusoyama 105]

The Ozeki-Yokozuna promotion guideline of 47% is pretty dead on, at least in the 6 basho/year period. Since 1958, there have been a total of 53 ozeki and yokozuna, and 25 of those made yokozuna, or 47.16%, very close to the 8/17 taken from the sample before.

[Doitsuyama 1,263]

The Ozeki-Yokozuna promotion guideline of 47% is pretty dead on, at least in the 6 basho/year period. Since 1958, there have been a total of 53 ozeki and yokozuna, and 25 of those made yokozuna, or 47.16%, very close to the 8/17 taken from the sample before.

Don't forget that we have four active ozeki - we need only (the expected) two of them becoming yokozuna to get over 50%. Then again... maybe statistical expectation isn't everything. :-S

[Bealzbob 0]

Then again... maybe statistical expectation isn't everything. ;-)

In this particular case, you've got that right :-S

[kaiguma 0]

Then again... maybe statistical expectation isn't everything. ;-)

In this particular case, you've got that right :-S

hah! Are you saying Kotooshu and Kotomitsuki are both expected to reach yokozuna? :-P

I know they both were at some point in their careers, but do most people still believe that now?

[Bealzbob 0]

Then again... maybe statistical expectation isn't everything. ;-)

In this particular case, you've got that right :-S

hah! Are you saying Kotooshu and Kotomitsuki are both expected to reach yokozuna? :-P

I know they both were at some point in their careers, but do most people still believe that now?

No you've got it the wrong way around. I'm saying that in this particular case, despite the statistics saying 50%, that I (and I assume Doitsuyama too based on the winking smiley) believe that precisely 0% of currently active ozeki's will reach yokozuna.

[higginbotham 0]

Don't forget that we have four active ozeki - we need only (the expected) two of them becoming yokozuna to get over 50%. Then again... maybe statistical expectation isn't everything. :-S

That expectation ( two of them becoming yokozuna) is statiscally inaccurate... The ratio is roughly 1/2...

[HenryK 38]

The Ozeki-Yokozuna promotion guideline of 47% is pretty dead on, at least in the 6 basho/year period. Since 1958, there have been a total of 53 ozeki and yokozuna, and 25 of those made yokozuna, or 47.16%, very close to the 8/17 taken from the sample before.

Don't forget that we have four active ozeki - we need only (the expected) two of them becoming yokozuna to get over 50%. Then again... maybe statistical expectation isn't everything. :-S

I don't want to split hair, but isn't the correct calculation that since, say, 1999 10 rikishi obtained Ozeki status -- Chiyotaikai, Dejima, Musoyama, Miyabiyama, Kaio, Tochiazuma, Asashoryu, Kotooshu, Hakuho, Kotomitsuki -- but only 2 made it to Yokozuna, instead of 4-5 one would statistically expect?

Edited December 5, 2007 by HenryK

[Zuikakuyama 1]

This latest batch of Ozeki are really a bunch of under-achiever, or is this due to the tightening of the promotion rules?

I think perhaps it is no accident that of this latest batch, 3 had 3 or more yushos behind them (Chiyotakai, Kaio, Tochiazuma). Since modern times, prior to this, only 1 ozeki ended their career with 3 or more yushos. That person is Konishiki, who could have been promoted too under the looser rule in place before Futahaguro. So it if say that these 3 should have been promoted (at least under the old rules), that would make 5 out of 10 ozekis promoted, then they are not so under-achieving after all.

[Randomitsuki 2,912]

A couple of days ago I tried to find out something that is related to this thread - I wanted to know what the average rank of an average rikishi in an average career might be. And barring some grave mistakes that I might have made I was really surprised how low it was. I expected the average rank to be somewhere in high or middle Jonidan, but in fact my data indicated the average rank of an average career to be Jonidan 121!!! Of course, the time frame I was looking at (1984-2007) included those years where Jonidan went down to 200, but still...

Doitsuyama, do you have means to confirm this? My analyses might contain a couple of errors because not all kaimei might have been tracked correctly. As for computing the ranks, I just numbered them from the highest rank (1) down to the banzuke-gai. The average number was 631.

Edit: The analyses excluded tsukedashi entrants.

Edited December 5, 2007 by Randomitsuki