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*To*: sumo@tosca.gnets.ncsu.edu*Subject*: Banzuke Stats (Long)*From*: John Szczepanski <johnski@iol.ie>*Date*: Tue, 15 Apr 1997 22:15:46 +0100*Sender*: owner-sumo@statgen.ncsu.edu

As further proof that I don't have a social life, I offer to the group the following statistics on banzuke listings, showing the typical promotion/demotion for each rank, given particular W-L records. I admit this is far from a scientific study, and vagaries of past banzuke prove that it's impossible to predict exactly where a rikishi will be placed given his previous performance. However, as you'll see here, there are indeed patterns to how banzuke rankings are determined, and, say, an 8-7 record may typically mean a jump of two places for a Maegashira-3, but a 5-place jump for a Maegashira-6. The following is based on a survey of 21 basho, where I had both the W-L records of one tournament and the subsequent banzuke rankings of the next. As I grouped together the East & West rikishi for each rank, I had a total pool of about 42 results for each rank. Thus, for some of the uncommon W-L records at the extreme ends of the range (say, 12-3 or 2-13), I ended up with only a few samples - so these statistics need to be read with a grain of salt (or, if you're Mitoizumi, a helluva lot of salt). HOW TO READ THE TABLES: I have grouped these by rank, starting with Sekiwake. The W-L records for the first tournament are listed along the left-hand margin, beside which are statistics for the subsequent promotion/demotion in the next basho. I first list the range of demotions/promotions, then the median, then the average. Checking all three of these will give you some indication of where a rikishi will rise/fall given his W-L record. To save typing time, rather than list the ranks by full name or even M-1, M-2, etc., I have typed just '1' or '2' (see below). I have indicated with asterisks (* / **) when I was drawing from limited sample pools. For example, I found one case where a Maegashira-7 was promoted to Sekiwake after going 12-3. However, that was the ONLY example of an M-7 going 12-3 I found in 21 basho. Thus, to say that the 'average' and 'median' promotion was to Sekiwake would be misleading. Therefore, I have indicated with ** cases where I found only 1 or 2 examples of a particular W-L record. Single asterisks (*) indicate where I found only 3 or 4 examples. Where I found NO examples, I have deleted that line from the list of possibilities (indicated by "N/A"). All this may be difficult to follow now, but please scroll down to see an example and it may be more understandable. 'Range,' 'Average' and 'Median' and What I Mean: Say I found five examples where an M-1 went 4-11; in two cases, the rikishi was demoted to M-9, in two other cases he was demoted to M-5 and in the last case he was demoted to M-7. The Range, then, would be from M-5 to M-9. By adding the ranks (9+9+5+5+7) and dividing by the number of samples (5) we would get 7.4 - which is the Average. To find the Median, we order the results from top to bottom (i.e. 5-5-7-9-9), and pick whatever number falls in the middle (here, it's the third of five numbers, or 7). Let me know if any of this is confusing and I'll attempt to clarify it later. Here's the results, which I hope you'll find of some reference. All the best, John "Peroginishiki" Szczepanski Starting Rank: SEKIWAKE 8-7 (or better) - remain at Sekiwake 7-8 Range: K-1 Median: K Average: (fall 83% to K) 6-9 Range: 1-2 Median: 1 Average: 1.2 5-10 N/A 4-11* Range: 2-3 Median: 3 Average: 2.7 3-12** Range: 4-6 Median: 5 Average: 5 2-13 N/A 1-14** Range: 7 Median: 7 Average: 7 Starting Rank: KOMUSUBI 12-3 N/A 11-4** Range: S Median: S Average: S 10-5 Range: S-K Median: S Average: (86% to S) 9-6 Range: S-K Median: K Average: (67% stay at K) 8-7 Range: S-K Median: K Average: (71% stay at K) 7-8 Range: K-1 Median: 1 Average: (83% to M-1) 6-9 Range: 1-2 Median: 2 Average: 1.3 5-10 Range: 2-4 Median: 3 Average: 3.1 4-11 Range: 3-6 Median: 4 Average: 4.2 3-12 Range: 5-9 Median: 7 Average: 6.6 2-13** Range: 5 Median: 5 Average: 5 1-14** Range: 7 Median: 7 Average: 7 Starting Rank: 1 12-3** Range: S Median: S Average: S 11-4** Range: S Median: S Average: S 10-5** Range: K Median: K Average: K 9-6 Range: S-K Median: K Average: (90% to K) 8-7* Range: S-1 Median: K Average: K 7-8* Range: 2-4 Median: 2 Average: 2.5 6-9 Range: 3-6 Median: 3 Average: 3.7 5-10 Range: 4-6 Median: 5 Average: 5.3 4-11* Range: 6-9 Median: 7 Average: 7.3 3-12 Range: 6-13 Median: 8 Average: 8.6 2-13** Range: 12 Median: 12 Average: 12 1-14** Range: 14 Median: 14 Average: 14 Starting Rank: 2 >10-5 N/A 9-6* Range: K Median: K Average: K 8-7 Range: K-1 Median: K Average: (80% to K) 7-8** Range: 3 Median: 3 Average: 3 6-9 Range: 4-6 Median: 5 Average: 4.9 5-10 Range: 4-9 Median: 6 Average: 6.2 4-11 Range: 6-10 Median: 7 Average: 7.4 3-12 Range: 8-12 Median: 11 Average: 10.3 2-13** Range: 13 Median: 13 Average: 13 1-14** Range: 15 Median: 15 Average: 15 Starting Rank: 3 >11-4 N/A 10-5** Range: S Median: S Average: S 9-6** Range: K-1 Median: K-1 Average: K-1 8-7 Range: 1-2 Median: 1 Average: 1.3 7-8 Range: 3-4 Median: 4 Average: 3.8 6-9 Range: 4-6 Median: 5 Average: 5 5-10 Range: 6-10 Median: 7 Average: 7.5 4-11 Range: 7-10 Median: 9 Average: 8.7 3-12* Range: 10-13 Median: 12 Average: 11.8 2-13 Range: 12-15 Median: 13 Average: 13.3 1-14 N/A Starting Rank: 4 12-3** Range: S Median: S Average: S 11-4* Range: S-K Median: K Average: (67% to K) 10-5** Range: K Median: K Average: K 9-6** Range: K-1 Median: K-1 Average: K-1 8-7* Range: K-2 Median: K Average: 0.75 (50% to K) 7-8* Range: 4-6 Median: 6 Average: 5.3 6-9 Range: 6-10 Median: 7 Average: 7.5 5-10 Range: 7-10 Median: 9 Average: 8.6 4-11 Range: 8-14 Median: 11 Average: 10.5 3-12 Range: 11-15 Median: 13 Average: 12.8 <2-13 N/A Starting Rank: 5 >11-4 N/A 10-5** Range: K-1 Median: K-1 Average: K-1 (50% to K) 9-6** Range: K-2 Median: 1 Average: 1 8-7 Range: K-3 Median: 1 Average: 1 7-8* Range: 6-7 Median: 6 Average: 6.3 6-9 Range: 6-12 Median: 8 Average: 8.3 5-10 Range: 9-10 Median: 10 Average: 9.8 4-11* Range: 11-14 Median: 12 Average: 12.3 3-12* Range: 14-15 Median: 15 Average: 14.7 <2-13 N/A Starting Rank: 6 >10-5 N/A 9-6 Range: K-3 Median: 1 Average: 1 8-7 Range: 1-2 Median: 1 Average: 1.3 7-8* Range: 6-9 Median: 7-8 Average: 7.5 6-9 Range: 8-13 Median: 10 Average: 9.0 5-10 Range: 10-13 Median: 12 Average: 11.9 4-11 Range: 13-15 Median: 14 Average: 14.2 3-12** Range: 15 Median: 15 Average: 15 2-13** Range: 14 Median: 14 Average: 14 1-14 N/A Starting Rank: 7 12-3** Range: S Median: S Average: S 11-4 N/A 10-5* Range: K-2 Median: 1 Average: 1 9-6* Range: K-2 Median: 1 Average: 1 8-7 Range: 1-4 Median: 2 Average: 2.2 7-8 Range: 8-10 Median: 8 Average: 8.7 6-9 Range: 10-12 Median: 11 Average: 10.9 5-10 Range: 13-14 Median: 13 Average: 13.2 <4-11 N/A Starting Rank: 8 12-3 N/A 11-4 Range: 1 Median: 1 Average: 1 10-5 N/A 9-6* Range: 2 Median: 2 Average: 2 8-7 Range: 1-5 Median: 3 Average: 3.2 7-8 Range: 9-11 Median: 10 Average: 10 6-9 Range: 10-14 Median: 12 Average: 12.1 5-10** Range: 13-14 Median: 13-14 Average: 13.5 <4-11 N/A Starting Rank: 9 12-3 N/A 11-4** Range: 2 Median: 2 Average: 2 10-5 N/A 9-6 Range: 1-3 Median: 2 Average: 1.9 8-7 Range: 1-6 Median: 4 Average: 3.9 7-8 Range: 11-12 Median: 11 Average: 11.4 6-9 Range: 12-15 Median: 13 Average: 13.4 <5-10 N/A Starting Rank: 10 >11-4 N/A 10-5** Range: 1-2 Median: 1-2 Average: 1.5 9-6 Range: 2-4 Median: 3 Average: 2.9 8-7 Range: 2-8 Median: 5 Average: 5.5 7-8 Range: 11-13 Median: 12 Average: 12 6-9* Range: 14-15 Median: 14-15 Average: 14.5 5-10 N/A 4-11 N/A 3-12** Range: J2 Median: J2 Average: J2 <2-13 N/A Starting Rank: 11 12-3 N/A 11-4** Range: K Median: K Average: K 10-5* Range: 3-4 Median: 3 Average: 3.7 9-6 Range: 3-5 Median: 4 Average: 4.3 8-7 Range: 2-9 Median: 7 Average: 6.4 7-8 Range: 12-15 Median: 13 Average: 13.3 6-9 Range: 14-15 Median: 14 Average: 14.7 5-10 N/A 4-11** Range: J3 Median: J3 Average: J3 3-12 N/A 2-13** Range: J4 Median: J4 Average: J4 1-14 N/A Starting Rank: 12 12-3** Range: 1 Median: 1 Average: 1 11-4** Range: 4 Median: 4 Average: 4 10-5** Range: 3 Median: 3 Average: 3 9-6 Range: 2-10 Median: 6 Average: 6 8-7 Range: 3-11 Median: 8 Average: 7.6 7-8* Range: 13-16 Median: 14 Average: 14.3 6-9 N/A 5-10** Range: J2 Median: J2 Average: J2 4-11** Range: J5 Median: J5 Average: J5 3-12 N/A 2-13** Range: J4 Median: J4 Average: J4 1-14 N/A Starting Rank: 13 12-3** Range: 1 Median: 1 Average: 1 11-4** Range: 3 Median: 3 Average: 3 10-5** Range: 4 Median: 4 Average: 4 9-6 Range: 5-11 Median: 7 Average: 7.6 8-7 Range: 7-12 Median: 10 Average: 10.1 7-8** Range: 15-16 Median: 15-16 Average: 15.5 6-9 N/A 5-10** Range: J1 Median: J1 Average: J1 <4-11 N/A (Beyond this point the sample pools are too small to show any reliable patterns.)

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