## 39958Real Good Luck and Real Bad Luck of Aki Basho!

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• Oct 2, 2013
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Dear Mensch of the Bench,

I am really sad that we have just witnessed the first Randomitsukigenous intai in Bench Sumo. In other words, my stupid MCP Standings, in particular the stats pertaining to "bad luck of the basho", were partially responsible for Ganzohnesushi's intai from the game. If there hadn't been this particular piece of stat, he would have simply (and erroneously) thought that he is a terrible Bench player...

In his last Bench will, Ganzohnesushi explained that he would love to see a cumulated bad luck (and good luck) standings for an entire year. I decided to do this after Kyushu Basho. However, there is a statistical problem: in general, Makuuchi is stronger than Juryo and Makushita, so one needs a higher MCP Score in order to get the same amount of wins. As a consequence, the bad luck (and good luck) standings are always slightly biased. Better players seem to have more bad luck, but in fact their only bad luck is that they play in a tougher division.

Therefore I devised a system that takes care of that, and in a stroke of genius I call it "real bad luck" (and "real good luck").

See the standings below if you just want to check whether you were lucky (near the top of the table) or unlucky (near the bottom). By the way, Ganzohnesushi was the unluckiest chap anyway.

Those who might be interested in the calculation should read this paragraph.
As the divisions are different in strength, I calculated the median MCP Scores per division (question to the uber-stattos: would you recommend using the arithmetic mean instead?).
Makuuchi had a median score of 8.297
Juryo had a median score of 7.214
Makushita had a median score of 7.029
In a first step I computed the difference between MCP and Median per person. For instance, Jejima had an MCP Score of 7.674. As he was playing in Makuuchi (median of 8.297), he trailed the Makuuchi median by -0.623 points. This means that he should have had 0.623 wins less than the average Makuuchi player. The average Makuuchi player (like the average player in any other division) should get 7.5 wins. That being said, the expected number of wins for Jejima in Makuuchi would have been 7.5 - 0.623 = 6.877 wins (see the columns below).
However, he had 11 wins instead, resulting in a difference of 4.123 wins. Voila, this is his RL (Real Luck) Score!

EW = Expected Wins (based on one's MCP Score, but taking into account one's division)
AW = Actual Wins
RL = Real Luck Score

Pos Shikona EW AW RL
====================================
1 Jejima 6,877 11 4,123
2 fujiyama 8,269 12 3,731
3 Fatakiyama 7,428 11 3,572
4 Furanohana 8,673 12 3,327
5 Holleshoryu 7,302 10 2,698
6 Fujisan 6,315 9 2,685
7 Achiyama 9,466 12 2,534
8 shimodahito 7,55 10 2,45
9 Kasamatsuri 9,55 12 2,45
9 Metzinowaka 8,578 11 2,422
11 Rubensan 6,792 9 2,208
12 Leonishiki 7,799 10 2,201
13 toonoryu 6,814 9 2,186
14 chabonowaka 5,943 8 2,057
14 Roundeye 6,102 8 1,898
14 Gohansazae 8,214 10 1,786
17 Hokuyutaka 6,286 8 1,714
18 iwakoko 4,439 6 1,561
18 Kintamayama 7,495 9 1,505
20 pandaazuma 7,506 9 1,494
21 Kitakachiyama 7,551 9 1,449
22 Gibuten 6,596 8 1,404
22 Yoohoo 5,673 7 1,327
24 Tosahayate 5,686 7 1,314
25 Fuheika 6,707 8 1,293
26 Rikishimiezi 7,741 9 1,259
27 Mariohana 7,888 9 1,112
28 Kintsubasa 7,92 9 1,08
29 kuroimori 6,926 8 1,074
29 Frinkanohana 6,945 8 1,055
31 Kaiomitsuki 8,956 10 1,044
32 Terarno 8,061 9 0,939
33 Chimatayama 9,084 10 0,916
34 chishafuwaku 8,19 9 0,81
35 Watashi 6,237 7 0,763
36 Takanorappa 7,398 8 0,602
37 Kyodaitimu 6,449 7 0,551
38 sekihiryu 7,455 8 0,545
39 Oskanohana 7,585 8 0,415
40 Damimonay 6,596 7 0,404
41 Heiyu 5,628 6 0,372
42 Marushiki 5,64 6 0,36
43 Maguroyama 6,641 7 0,36
44 Susanoo 8,911 9 0,089
45 Hakaso 7,933 8 0,067
47 VESHANA 7,977 8 0,023
48 Gaijingai 8,001 8 -0,001
49 tokugawa 8,001 8 -0,001
50 Jakusotsu 9,028 9 -0,028
51 ScreechingOwl 7,113 7 -0,113
51 Chocshoporyu 8,136 8 -0,136
53 mischashimaru 5,203 5 -0,203
54 Akokoneko 7,258 7 -0,258
55 Oshirokita 7,286 7 -0,286
56 Fuseigou 9,342 9 -0,342
57 Uoichiba 9,37 9 -0,37
58 Fujiko 5,381 5 -0,381
60 Haidouzo 4,522 4 -0,522
61 Taka 7,529 7 -0,529
62 Stowaway 8,538 8 -0,538
63 Yassier 9,583 9 -0,583
64 Boltbutthamma 7,731 7 -0,731
65 Basoyama 6,943 6 -0,943
65 Bunijiman 6,028 5 -1,028
67 Hironoumi 6,145 5 -1,145
68 andonishiki 8,169 7 -1,169
69 Chisaiyama 6,314 5 -1,314
70 Robocopthat 6,32 5 -1,32
71 Sebunshu 8,415 7 -1,415
72 Gawasukotto 7,449 6 -1,449
73 Kotononami 6,461 5 -1,461
74 Sherlockiama 7,522 6 -1,522
75 Zenjimoto 7,731 6 -1,731
76 Ruziklao 7,848 6 -1,848
76 Harumataikai 3,875 2 -1,875
78 Konosato 7,933 6 -1,933
79 Pitinosato 6,034 4 -2,034
80 Norizo 7,068 5 -2,068
81 tainosen 8,214 6 -2,214
82 Nekonishiki 8,302 6 -2,302
83 Aome 6,359 4 -2,359
84 Doitsuyama 10,443 8 -2,443
85 Itachi 7,484 5 -2,484
86 Rowitoro 8,684 6 -2,684
87 Tsunamiko 8,724 6 -2,724
88 Randomitsuki 8,81 6 -2,81
89 Bill 8,162 4 -4,162
90 Ganzohnesushi 7,477 2 -5,477

Randomitsuki
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