After promotion to which rank is KK the most difficult

[HenryK]

[EDIT] I attach the chart from post 10

A little stats exercise (that turned out to be less "little" than I had ancitipated) that works as follows: all basho since 1960, makuuchi only, look at rikishi who got promoted to rank X, and compute the share of rikishi that achieved KK at the new rank. Only promotions within makuuchi, promotions by at least a full rank, M13-Y (keeping in mind that above S the promotion rules are obiously different. Below M13 there are not enough observations.) I counted by hand, hence there are probably a few mistakes, but nothing major or systematic.

Here is the result

Rank-- #KK-- #MK-- %KK

M13-- 22-- 25-- 46.8

M12-- 30-- 39-- 43.5

M11-- 58-- 62-- 48.3

M10-- 65-- 79-- 45.1

M9-- 83-- 101-- 45.1

M8-- 91-- 122-- 42.7

M7-- 113-- 124-- 47.7

M6-- 91-- 164-- 35.7

M5-- 73-- 248-- 22.7

M4-- 62-- 272-- 18.6

M3-- 61-- 306-- 16.6

M2-- 83-- 342-- 19.5

M1-- 118-- 302-- 28.1

K-- 179-- 284-- 38.7

S-- 160-- 128-- 55.6

O-- 45-- 10-- 81.8

Y-- 21-- 2-- 91.2

Observations:

-- except for Y-S, the KK percentage is below 50 percent at all ranks. Hence the banzuke makers do in general "overpromote".

-- there is only slight overpromotion at the lower makuuchi ranks, however -- following a promotion to M7-M13, the KK percentage is about 45 percent

-- from M7 to M3, the KK percentage falls dramatically -- from 48 percent (M7) to 36 percent (M6) to 23 percent (M5) to 19 percent (M4) to a low of 17 percent (M3). Live in the meatgrinder is tough indeed. The fact that rikishi get tougher opponents with higher ranks clearly dominates the fact that they get better. According to these stats, M4 and arguably also M5 ought to be considered part of the meatgrinder.

-- from M3 to S the KK chances increase again -- 17 percent (M3), 20 percent (M2), 28 percent (M1), 39 percent (K), 56 percent (S). S-M3 fight the same opponents, but the quality of the rikishi increases. For O the KK percentage after promotion is 82 percent, for Y 91 percent, but of course these rikishi go through a more challenging vetting process.

-- all this is consistent with with intuition, but I found it interersting to see these effects confirmed that clearly by the numbers.

Edited November 21, 2008 by HenryK

[Doitsuyama]

-- except for Y-S, the KK percentage is below 50 percent at all ranks. Hence the banzuke makers do in general "overpromote".

That conclusion is a bit premature. I think you have to compare with the KK percentage of all rikishi at each rank - if it's below 50% too are all rikishi overpromoted?

[Asashosakari]

-- except for Y-S, the KK percentage is below 50 percent at all ranks. Hence the banzuke makers do in general "overpromote".

That conclusion is a bit premature. I think you have to compare with the KK percentage of all rikishi at each rank - if it's below 50% too are all rikishi overpromoted?

Another alternative explanation is that a significant percentage of KK rikishi may simply have overachieved, i.e. their talent level didn't support their KK in the first place, so they're always much less likely than 50% to repeat no matter how far they're promoted.

Edited November 21, 2008 by Asashosakari

[HenryK]

-- except for Y-S, the KK percentage is below 50 percent at all ranks. Hence the banzuke makers do in general "overpromote".

That conclusion is a bit premature. I think you have to compare with the KK percentage of all rikishi at each rank - if it's below 50% too are all rikishi overpromoted?

Another alternative explanation is that a significant percentage of KK rikishi may simply have overachieved, i.e. their talent level didn't support their KK in the first place, so they're always much less likely than 50% to repeat no matter how far they're promoted.

Both legit objections.

I had a criterion in mind that says "a rikishi is promoted to the right spot if he has a 50 percent chance of getting KK". If the specific rank hard to defend in the first place, a below-50 percent-chance may not point to overpromotion. And "overpromotion" and "overachievement" are of course impossible to separate.

[Gusoyama]

For the record, I guessed Komosubi. I would not have guessed M4 or M3. Interesting stats!

[HenryK]

To account for Doitsuyama's comment, I added the overall KK probability at each rank (last column) to the KK probability after opromotion (central column). At every rank except Yokozuna the overall KK probability is substantially higher than for promoted rikishi, suggesting that overpromotion (or -achievement) is common. The banzuke makers like to generate movement.

The overall rank-to-rank pattern is the same: M3 is the toughest spot on the banzuke, followed by M2/M4. Within the Yokozuna group, the Y1E stands out with a KK probability of 92 percent compared to about 85 percent for Y1W/Y2E. By contrast, there is little difference in KK percentages between Ozeki (around 85 percent for O1E-O2W). The detailed KK percentages at lower Sanyaku and below is: S1E (71.0), S1W (55.9), K1E (46.9), K1W (38.8), M1E (36.9), M1W (30.9), M2E (26.3), M2W (22.8), M3E (21.3). M3E is the absolute low point.

Below M13 the KK probability falls again. At M16 its 49 percent -- presumably because at the bottom end of the banzuke rikishi tend, on average, get to fight higher ranked opponents than themselves, just as at K-M3.

M13 - 46.8 -- 58.1

M12 - 43.5 -- 58.5

M11 - 48.3 -- 61.7

M10 - 45.1 -- 60.1

M9 -- 45.1 -- 57.1

M8 -- 42.7 -- 54.9

M7 -- 47.7 -- 56.8

M6 -- 35.7 -- 45.8

M5 -- 22.7 -- 37.2

M4 -- 18.6 -- 30.1

M3 -- 16.6 -- 22.3

M2 -- 19.5 -- 24.6

M1 -- 28.1 -- 33.8

K --- 38.7 -- 43.6

S --- 55.6 -- 62.6

O --- 81.8 -- 84.8

Y --- 91.2 -- 87.4

Edited November 21, 2008 by HenryK

[Andreas]

It might seem as if Komusubi have the lowest kk chance, but I think the reason for this is that they get more attention than upper Maegashira (compare Goeido and Futeno).

If You face the facts, all rikishi from m3 upwards usually face each other, and the m3 are the weakest of the group (except for upcoming talents who wont stay at this rank for long). m4 might already get less sanyaku opponents, thus improving their chances for more wins. The slightly higher winning percentage of m1 rikishi (compared to m2 and m3) might be a result of "traffic jams" because of filled sanyaku slots.

[Harry]

I too thought the shinkomusubi curse would be the toughest place to get KK. Goeido certainly had that curse put upon him; for some reason I thought he would do better.

I think you also get rikishi demoted FROM sanyaku in m1 so they might do better than ones promoted up.

Overall it is a mixed blessing getting a promotion in sumo and some reach a level where they just bounce up and down between a rank where they do well and a rank where they don't do well, never able to break through. The highest ranks have protections against this of course, otherwise you wouldn't have long tenures at ozeki. In some ways, long tenures at sekiwake are more impressive as they don't have kadoban protection though of course if they are really good they should make it to ozeki one day where an even higher bar exists but which, when passed, offers the ultimate protection as no demotion is possible.

This feeds into the sumo games where you ask youself if you want to pick someone who has fallen from a high place who should do well at a lower rank, or did they fall for a reason like an injury which will likely see them fall further? Should you pick an up and comer in a new high rank expecting them to keep going up or avoid them for a basho to see if they're going to have a bad makekoshi basho at that new high rank? As my performance this basho shows, I have not figured this out yet.

[HenryK]

Here I try to upload a chart shwing above percentages (I do this the first time, hence I may go wrong)

Edited November 21, 2008 by HenryK

[Doitsuyama]

I too thought the shinkomusubi curse would be the toughest place to get KK. Goeido certainly had that curse put upon him; for some reason I thought he would do better.

It's not a matter of shin-komusubi as not new high ranks were the topic but any kk leading to the rank (if I understood that correctly). New high ranks would be interesting too.

[HenryK]

I too thought the shinkomusubi curse would be the toughest place to get KK. Goeido certainly had that curse put upon him; for some reason I thought he would do better.

I think you also get rikishi demoted FROM sanyaku in m1 so they might do better than ones promoted up.

Overall it is a mixed blessing getting a promotion in sumo and some reach a level where they just bounce up and down between a rank where they do well and a rank where they don't do well, never able to break through. The highest ranks have protections against this of course, otherwise you wouldn't have long tenures at ozeki. In some ways, long tenures at sekiwake are more impressive as they don't have kadoban protection though of course if they are really good they should make it to ozeki one day where an even higher bar exists but which, when passed, offers the ultimate protection as no demotion is possible.

This feeds into the sumo games where you ask youself if you want to pick someone who has fallen from a high place who should do well at a lower rank, or did they fall for a reason like an injury which will likely see them fall further? Should you pick an up and comer in a new high rank expecting them to keep going up or avoid them for a basho to see if they're going to have a bad makekoshi basho at that new high rank? As my performance this basho shows, I have not figured this out yet.

I find several results surprising at first sight but perfectly plausible when thinking it through. For example, KK probability is above 50 percent for Y-S, below 50 Percent for K-M6 or so. Well, in the standard banzuke (2Y 4O 2S 2K) the S1W has 7 guys ranked above him and 8 below, the K1E 8 above and 7 below. Thus, if the banzuke makers get on average the relative rikishi strenght right, the S1W should get KK in more than 50 percent of the cases, the K1E in less than 50. And this is exactly how it is.

[Bealzbob]

I think it is perfectly logical that the M4-M3-M2 area would be the toughest initial KK because this is the area where you become potential joi-jin and therefore are included in the regular torikumi of the top sanyaku. Something you were protected from to that point. Thanks for the chart though Henry. As a fellow stat-nut I can vouch for these things never being as 'little' as they appear beforehand (Detective...)

[Charlemagne]

Really interesting observations here. Do keep up the good work.