xKinchRanks - A Modified KinchRanks that gives equal weighting to all events

[Kit Clement]

I've recently devised a new system for an overall ranking system, based on Daniel Sheppard's KinchRanks. While this system is incredibly robust and a massive improvement on the Sum of Ranks overall ranking method, it has some weaknesses that my rankings try to correct. These are:

1. Each event's individual KinchRanks distribution is highly influenced by the relative strength of the WR time. For events with WR times that are far better than the competition (MBLD, Clock, etc.) the center of the KinchRanks distribution will be far lower than other events. This makes it difficult to compare a score in one event to another event, as any comparison between events has to pass through the WR times in those two events.

I realize that this can easily be argued as a strength too, as it rewards the WR holder for dominating the event. However, I argue that the idea of overall rankings is to summarize the overall performance, and any instance of domination in an event will reduce the significance of skill in this event for everyone else, affecting any comparisons between two cubers that do not hold the WR.

2. The physical lower bound on the world record of an event greatly influences the distribution of KinchRanks. By the physical lower bound, I mean the best time time for an event that you can possibly achieve within physical limitations. For example, barring any astronomically, improbably easy scramble, solving a 5x5 in less than 5 seconds is not physically possible, where it is clearly possible for 3x3. KinchRanks use WR and PB as inputs, both of which are affected by this physical lower bound. Since the KinchRank output is WR/PB, any event with a higher lower bound on scores will be weighted higher in KinchRanks. Think about the relative difference in times between WR and your PB in a quick puzzle like 2x2 versus a long puzzle like 7x7, as an example.

To further illustrate why this is the case mathematically, we can illustrate the KinchRank as a function of several inputs. Consider n to be the physical lower bound for an event, k the distance between the current WR and the physical lower bound, and l the distance between PB and WR, then we would see WR/PB = (n+k)/(n+k+l). This fraction can be seen as an increasing function of n, meaning that higher n (physical lower bound) results in higher KinchRanks.

Now, to present the methods for xKinchRanks which will address these weaknesses. The idea is to use the 3x3 event as a baseline event, since it has the most competitors, and then smooth the distributions of KinchRanks for all other events to be of the same shape as the 3x3 KinchRanks distribution. Thus, the KinchRanks component for 3x3 will be identical to the xKinchRanks component for 3x3.

To compute the xKinchRank component for any other event (A) of a specific competitor (B), you follow this procedure:

1. Compute the percentage of competitors that are worst than competitor B in event A, that is, compute competitor B's percentile in event A.
2. Find the competitor (C) with the largest percentile in 3x3x3 that is still smaller than competitor B's percentile in event A.
3. Assign the KinchRank of competitor C in 3x3x3 to be competitor B's xKinchRank in event A.

This fixes the issue of having events not be comparable due to the strength of the WR in that event, because now every event has KinchRanks that follow the distribution of the KinchRanks for 3x3x3. What this does better than a straight percentile system is that it maintains the quality of KinchRanks that differentiates greatly those who are world class, while making less distinction toward the bottom of the rankings.

Of course, I don't mean to argue that xKinchRanks are superior to KinchRanks, just that they are an alternative overall ranking system that addresses a handful of weaknessess to the KinchRanks system. xKinchRanks comes with its own new weaknesses as a result of this system -- namely, that this system is incredibly volatile if a new 3x3x3 average WR is set. Also, because there are more competitors in 3x3x3 than any other event, the highest Kinch scores in 3x3x3 (besides 100) are often missing in other events since this percentile cannot be reached unless you have the WR already. I'm sure there are others, and I'd like to hear your thoughts on xKinchRanks as well.

Top 1000 for xKinchRanks are provided below (sorry about the Unicode errors, Windows localities suck.) Or you can view them in a google sheet here.

Spoiler

rank	id	name	333	222	444	555	666	777	333bf	333fm	333oh	333ft	minx	pyram	clock	sq1	skewb	444bf	555bf	333mbf	total
1	2009ZEMD01	Feliks Zemdegs	100.00	82.17	90.85	100.00	100.00	100.00	54.66	58.90	90.85	0.00	81.34	61.37	39.38	52.02	51.27	50.35	22.44	36.09	65.09
2	2012MCNE01	Jayden McNeill	84.09	91.36	65.75	61.20	51.03	44.15	66.70	78.95	75.35	46.64	56.68	71.51	58.27	70.49	81.96	33.84	16.49	49.96	61.36
3	2009LIUE01	Evan Liu	67.54	72.72	66.98	61.96	65.22	59.28	52.06	58.90	60.00	50.91	54.80	77.43	100.00	56.68	61.84	38.51	33.04	43.23	60.06
4	2007NAKA03	Yu Nakajima (<U+4E2D><U+5CF6><U+60A0>)	73.38	70.80	69.88	68.04	55.27	52.31	54.80	61.14	62.02	63.24	59.17	62.56	54.11	50.75	50.35	44.09	45.29	39.67	57.60
5	2010CANT02	Antoine Cantin	81.34	70.80	64.82	59.89	48.31	43.14	55.80	41.45	89.21	66.98	52.78	70.72	56.04	63.17	69.13	28.79	20.94	42.32	56.98
6	2010UTOM01	Vincent Hartanto Utomo	76.97	71.67	78.09	77.15	53.79	53.71	50.95	55.18	69.65	44.18	49.43	79.63	49.92	43.91	49.96	41.14	21.44	47.39	56.34
7	2009SHEP01	Daniel Sheppard	61.55	68.04	58.37	55.94	50.23	47.05	52.18	70.88	49.12	48.10	50.51	70.26	61.66	54.07	53.00	53.17	49.27	55.99	56.08
8	2013WALL03	Daniel Wallin	72.55	72.47	61.55	52.65	52.27	50.43	46.04	43.70	56.78	45.17	57.49	73.13	70.88	65.09	78.47	34.94	29.96	37.74	55.63
9	2014GERB01	Henri Gerber	72.31	69.43	63.17	57.64	54.71	51.35	52.74	49.58	66.02	59.45	74.31	64.76	52.74	49.73	65.55	37.39	22.78	32.96	55.37
10	2012SEVE01	Ainesh Sevellaraja	69.21	68.98	61.25	48.50	41.11	36.88	62.93	37.33	58.74	35.21	56.23	72.80	50.08	56.33	49.12	55.75	50.04	62.74	54.07
11	2012WESC01	Lucas Wesche	68.04	62.74	71.59	72.55	67.61	72.39	47.78	46.54	62.26	43.94	70.26	53.48	40.04	52.65	54.52	24.70	17.20	37.59	53.66
12	2009YAUR01	Robert Yau	78.56	73.30	71.67	68.84	61.72	56.98	43.00	64.31	69.13	43.03	65.75	67.75	47.29	60.85	54.52	0.00	0.00	24.76	52.86
13	2008JONG03	Jong-Ho Jeong (<U+C815><U+C885><U+D638>)	77.99	71.91	73.30	67.26	53.88	49.58	73.05	52.74	66.70	30.71	62.56	58.85	24.24	42.10	43.91	33.97	20.34	46.98	52.78
14	2011SBAH01	Rami Sbahi	84.87	91.36	63.61	44.27	35.48	26.33	40.49	78.95	54.52	58.74	66.43	77.71	44.98	54.80	74.14	10.96	0.00	41.94	52.75
15	2010BENT01	Jan Bentlage	61.60	70.80	51.11	45.42	41.06	40.44	47.96	70.88	54.85	47.36	48.17	61.72	52.83	58.21	59.45	43.61	38.90	51.64	52.56
16	2013GERH01	Kevin Gerhardt	87.76	83.33	71.75	65.82	58.42	52.52	42.02	64.31	75.00	32.61	67.75	74.39	34.62	57.90	76.79	0.00	0.00	0.00	52.50
17	2011WELC01	Walker Welch	62.08	71.35	57.38	52.91	47.25	48.68	43.46	78.85	57.85	38.88	50.39	62.50	54.94	54.48	56.98	32.63	23.47	43.73	52.10
18	2008BARA01	Bence Barát	67.82	75.79	59.45	61.72	59.01	66.02	57.44	70.88	53.39	27.26	48.75	54.52	34.81	49.46	53.71	34.36	21.62	41.69	52.10
19	2011RHEI01	Emanuel Rheinert	73.05	70.88	72.80	60.22	53.71	45.91	41.48	66.43	55.65	30.48	45.04	58.27	40.36	80.73	52.14	27.97	22.95	38.10	52.01
20	2012HALE01	Callum Hales-Jepp	68.40	69.13	55.60	52.14	42.66	41.11	50.00	43.70	57.44	56.33	52.06	49.39	54.38	43.67	53.31	46.54	46.44	50.12	51.80
21	2011BANS02	Shivam Bansal	65.88	72.47	48.64	48.03	46.64	37.90	71.43	43.70	56.93	35.04	40.90	73.38	42.72	53.88	51.56	45.91	24.51	71.27	51.71
22	2008WEST02	Simon Westlund	69.96	68.25	69.58	63.30	51.11	51.27	48.31	52.74	54.16	41.48	71.99	59.72	46.71	41.21	35.28	30.58	25.41	44.76	51.43
23	2010BREC01	John Brechon	70.18	69.65	66.02	62.02	62.87	60.06	45.29	49.58	55.08	25.45	57.38	64.37	45.07	52.57	46.30	30.94	15.82	23.83	50.14
24	2011KNOT01	Wojciech Knott	71.83	62.26	76.97	62.80	51.93	49.12	31.79	39.43	64.12	74.14	44.48	60.45	82.17	48.03	55.65	0.00	0.00	19.60	49.71
25	2010CORM02	Louis Cormier	71.75	72.72	64.24	59.17	50.87	52.78	31.93	52.74	61.84	57.90	78.09	67.97	48.97	39.89	46.74	0.00	0.00	31.36	49.39
26	2013EGDA02	Martin Vædele Egdal	71.04	94.44	58.06	54.71	41.96	42.94	38.60	52.74	69.06	26.48	53.31	78.56	47.43	64.76	70.96	0.00	0.00	14.47	48.86
27	2007VALK01	Mats Valk	94.44	76.24	84.87	79.43	60.17	57.23	37.09	58.90	73.13	19.15	36.24	52.83	33.47	55.56	38.30	0.00	0.00	10.96	48.22
28	2011FRES01	Linus Fresz	55.46	53.09	47.53	46.57	35.40	37.74	58.21	70.88	40.75	37.48	51.07	51.19	35.50	44.15	35.64	58.32	51.81	48.28	47.73
29	2007WONG02	Tim Wong	66.84	49.20	66.43	51.72	50.95	45.36	60.06	100.00	54.66	6.43	33.47	45.45	39.31	24.12	28.85	42.41	30.42	61.25	47.61
30	2008TAKA01	Yuhei Takagi (<U+9AD8><U+6728><U+4F51><U+5E73>)	63.05	51.23	54.57	47.85	37.79	38.53	56.78	52.74	66.91	71.67	44.70	52.48	35.64	36.54	32.04	40.93	38.23	34.49	47.56
31	2010WANG07	Yinghao Wang (<U+738B><U+9E70><U+8C6A>)	71.43	89.21	69.43	59.61	47.64	41.37	44.00	49.58	62.87	39.94	46.24	63.11	52.44	26.36	55.13	0.00	0.00	33.49	47.32
32	2011CAOS01	Sheng Cao (<U+66F9><U+665F>)	69.96	61.20	60.85	58.90	48.50	53.62	54.20	30.96	70.88	45.94	66.56	61.90	41.16	51.89	55.13	0.00	0.00	15.35	47.06
33	2012COST01	Kevin Costello III	88.36	68.98	81.34	70.41	63.67	59.17	30.60	39.43	71.67	34.62	53.66	52.91	33.75	28.98	50.04	0.00	0.00	10.29	46.55
34	2014SCHO02	Cale Schoon	62.32	55.84	45.01	42.13	0.00	0.00	57.44	64.31	33.58	37.94	35.48	50.12	42.57	44.70	74.74	63.80	58.53	64.82	46.30
35	2012BUBE01	Reto Bubendorf	68.91	75.35	53.13	50.12	39.07	30.01	41.53	61.14	57.59	36.03	53.17	77.43	43.70	53.31	58.42	0.00	0.00	31.10	46.11
36	2005AKKE01	Erik Akkersdijk	73.38	67.33	71.35	59.39	48.61	43.52	39.91	61.14	51.44	49.96	52.61	58.48	42.72	34.53	34.58	9.21	0.00	26.18	45.80
37	2007WOOR01	Riley Woo	73.13	64.44	57.23	45.52	27.62	20.45	66.43	52.74	54.75	44.45	52.14	44.51	27.34	32.94	39.55	41.32	20.64	57.08	45.68
38	2011ETTE01	Lucas Etter	91.49	100.00	77.52	65.02	54.38	42.60	21.05	33.04	65.22	0.00	44.36	63.24	38.01	57.64	68.11	0.00	0.00	0.00	45.65
39	2010KILD02	Wilhelm Kilders	60.11	59.39	52.96	50.12	61.08	55.36	34.96	58.90	52.65	29.08	49.31	56.43	51.03	54.48	60.06	7.99	7.80	16.88	45.48
40	2015ROSE01	Daniel Rose-Levine	78.47	79.43	59.28	47.88	39.64	32.20	17.03	43.70	66.70	37.28	55.65	60.85	42.86	70.49	68.40	0.00	0.00	17.54	45.41
41	2011SAKO01	Corey Sakowski	57.38	54.20	46.24	42.55	36.38	27.92	53.35	43.70	49.62	27.23	43.00	63.80	37.43	53.13	57.95	42.91	33.54	46.84	45.40
42	2014FRIT02	Oliver Fritz	70.41	78.18	66.70	57.95	45.97	45.10	45.23	49.58	64.89	0.00	55.36	66.29	30.58	55.89	64.18	14.27	0.00	5.24	45.32
43	2013SAVA01	Harry Savage	67.05	74.65	52.91	40.46	32.76	21.63	52.48	46.54	51.03	32.30	37.92	76.79	32.63	66.43	66.84	32.89	0.00	30.45	45.32
44	2007COHE01	Dan Cohen	67.82	72.88	64.69	61.66	52.74	51.77	44.45	41.45	57.95	24.51	45.58	58.11	47.01	53.97	28.06	15.83	0.00	27.01	45.31
45	2012ZABR01	Ivan Zabrodin	59.61	63.92	54.66	48.13	46.27	45.17	39.23	49.58	47.64	40.36	43.73	52.87	58.11	31.79	61.02	24.62	12.96	35.21	45.27
46	2008SMIT04	Maarten Smit	63.99	65.62	54.80	47.88	36.54	29.19	46.34	55.18	53.13	10.50	58.69	58.11	61.66	53.88	31.14	27.58	16.23	44.39	45.27
47	2014CHER05	Clément Cherblanc	65.82	61.55	54.89	55.80	53.62	50.75	42.72	33.04	49.05	31.87	53.48	59.12	51.81	57.08	58.64	0.00	9.20	21.29	44.98
48	2014ZHAN11	Yunke Zhang (<U+5F20><U+4E91><U+67EF>)	60.11	54.29	55.89	51.35	47.36	47.57	38.72	64.31	56.28	18.84	51.85	51.31	63.92	47.18	57.54	11.62	11.05	20.42	44.98
49	2012WERB01	Sebastian Werb	65.15	66.84	56.53	41.91	35.89	33.84	53.04	17.80	53.84	40.80	37.87	51.89	27.00	61.72	46.50	37.05	22.62	53.26	44.64
50	2011WANN01	Daniel Wannamaker	81.75	77.34	69.50	64.37	55.41	50.12	28.58	35.02	61.02	21.25	58.58	59.78	49.69	49.31	40.75	0.00	0.00	0.00	44.58
51	2012ELLI01	Keaton Ellis	80.83	60.22	65.09	63.24	53.04	54.07	31.52	52.74	80.32	0.00	46.30	45.49	31.59	53.00	63.42	0.00	0.00	20.53	44.52
52	2014GOSL01	Raymond Goslow	58.85	55.99	45.29	42.52	42.21	33.73	46.77	52.74	51.03	51.44	37.01	64.18	33.58	35.44	46.67	32.12	22.10	48.57	44.46
53	2012BEAH01	Ciarán Beahan	77.43	61.90	77.06	73.30	72.47	67.33	17.79	27.48	62.08	39.04	51.15	73.97	0.00	48.79	50.04	0.00	0.00	0.00	44.43
54	2013DENN01	Andy Denney	80.83	86.11	66.77	50.99	48.13	42.43	40.44	41.45	55.80	0.00	71.04	60.28	31.85	49.46	58.06	0.00	0.00	14.65	44.35
55	2013FURL01	Mattia Furlan	74.74	59.94	71.19	75.17	79.24	73.55	28.70	0.00	58.27	0.00	73.30	54.61	56.63	35.79	55.13	0.00	0.00	0.00	44.24
56	2010GARC02	Carlos Méndez GarcÃa-Barroso	81.96	82.17	56.68	50.39	35.28	27.78	44.39	43.70	70.26	15.40	43.85	58.27	51.72	49.05	40.75	0.00	0.00	41.77	44.08
57	2011FIOL01	Alberto Pérez de Rada Fiol	61.31	64.69	50.83	49.43	43.85	44.24	37.59	58.90	49.62	45.39	42.66	66.91	40.21	33.88	55.89	20.03	0.00	27.52	44.05
58	2011DWYE02	Nathan Dwyer	69.06	64.69	61.49	61.02	49.85	46.47	34.79	52.74	55.51	0.00	47.60	55.18	50.35	68.40	48.35	0.00	0.00	25.14	43.92
59	2011KOGL01	Jakob Kogler	57.90	54.29	55.60	51.97	41.40	37.87	53.26	52.74	45.45	25.87	27.49	49.92	51.11	15.58	38.79	41.53	35.46	53.97	43.90
60	2009DIEC01	Cornelius Dieckmann	89.21	71.91	63.36	63.61	47.29	36.69	52.70	73.46	76.69	0.00	33.95	46.27	22.93	29.48	10.28	25.19	11.42	34.11	43.81
61	2010LANE02	Mitchell Lane	74.65	67.89	67.61	63.05	52.35	49.73	0.00	41.45	55.94	37.54	57.59	60.06	47.67	51.89	59.45	0.00	0.00	0.00	43.72
62	2012KALE01	Przemyslaw Kaleta	78.28	75.00	75.88	63.86	73.38	61.66	0.00	41.45	81.23	60.68	25.41	47.64	0.00	27.45	72.72	0.00	0.00	0.00	43.59
63	2011CHAP01	José Leonardo Chaparro Prieto	62.56	70.41	51.77	45.14	41.51	35.17	39.62	46.54	52.83	24.89	61.66	54.89	35.04	46.54	43.58	16.66	14.47	40.52	43.54
64	2005BATI01	Milán Baticz	74.31	69.81	63.42	56.09	47.67	45.97	52.83	49.58	58.37	24.25	52.02	54.80	44.24	38.28	0.00	17.91	0.00	28.34	43.22
65	2010KIPA01	Jakub Kipa	78.85	77.34	70.72	53.09	45.07	26.06	45.81	43.70	60.56	100.00	43.97	66.77	0.00	0.00	39.47	0.00	0.00	26.27	43.20
66	2009OLSO01	Christopher Olson	74.31	85.32	58.80	50.59	41.56	37.46	42.30	39.43	66.77	20.85	31.59	51.60	46.71	38.72	50.35	16.24	0.00	25.09	43.20
67	2013JOKI01	Kim Jokinen	77.99	75.35	61.72	47.81	23.83	22.99	44.21	41.45	72.15	12.98	34.40	75.00	50.00	49.20	50.19	16.16	0.00	22.10	43.20
68	2010BRAD01	Drew Brads	85.89	89.21	75.53	59.07	54.80	45.52	18.89	39.43	56.28	0.00	46.88	100.00	20.79	16.88	68.11	0.00	0.00	0.00	43.18
69	2008YOUN02	Michael Young	61.60	57.08	48.13	44.06	33.82	33.26	43.20	64.31	55.94	19.99	38.69	47.74	31.19	69.43	47.96	22.34	18.65	38.48	43.10
70	2011ZALE02	Marcin Zalewski	71.43	58.80	50.75	47.64	28.20	35.62	76.60	33.04	61.55	43.43	51.89	57.28	0.00	0.00	25.92	52.14	32.27	49.12	43.09
71	2010WUIF01	Yi-Fan Wu (<U+5433><U+4EA6><U+51E1>)	82.69	69.81	79.43	78.75	64.69	61.96	22.33	25.96	71.19	0.00	43.14	49.50	38.35	36.26	51.39	0.00	0.00	0.00	43.08
72	2011NARA02	Bhargav Narasimhan	69.96	65.62	52.96	40.31	21.38	24.19	47.64	46.54	76.06	49.46	59.56	43.61	27.41	41.16	54.07	24.27	0.00	29.44	42.98
73	2013FENG02	Zijia Feng (<U+51AF><U+5B50><U+7532>)	62.20	61.84	68.33	55.60	18.11	53.48	9.26	49.58	51.64	55.65	46.50	51.89	73.38	66.70	48.35	0.00	0.00	0.00	42.92
74	2008UENO01	Shuto Ueno (<U+4E0A><U+91CE><U+67CA><U+6597>)	66.02	62.80	59.78	53.31	24.39	22.74	44.89	58.90	63.80	23.46	21.67	58.85	38.12	48.90	42.97	30.70	14.73	35.67	42.87
75	2009HILD01	James Hildreth	58.06	60.62	51.93	56.88	59.28	58.27	42.43	49.58	54.61	25.67	37.05	40.19	35.83	37.01	48.50	19.09	0.00	32.15	42.62
76	2008YUDA01	Yu Da-Hyun (<U+C720><U+B2E4><U+D604>)	66.56	45.87	65.82	58.85	57.44	56.09	45.78	0.00	45.17	26.40	100.00	44.70	10.95	36.56	34.02	29.53	21.44	21.34	42.58
77	2010OMUL02	Matic Omulec	65.09	64.44	60.68	55.27	50.08	47.50	25.11	46.54	49.77	30.67	71.59	54.89	29.33	43.46	52.57	0.00	0.00	17.86	42.49
78	2011REED01	Austin Reed	69.73	71.11	57.90	49.39	39.74	34.79	38.81	41.45	48.46	31.82	41.40	55.41	38.53	59.01	47.50	9.73	0.00	30.04	42.49
79	2014KORO02	Vladimir Korovin	61.78	66.49	46.27	39.19	26.96	30.27	44.42	35.02	46.34	54.94	59.72	62.87	40.64	44.45	65.82	10.63	0.00	26.58	42.35
80	2008AURO01	Sébastien Auroux	54.38	66.43	47.05	38.01	29.86	30.60	40.16	73.46	41.21	36.28	32.03	60.28	58.85	33.03	46.54	28.59	8.52	36.73	42.33
81	2014BOYA01	Mark Boyanowski	51.89	48.24	36.01	29.29	27.19	33.28	65.82	65.42	35.95	15.29	43.09	45.62	16.92	36.40	28.24	49.09	53.84	79.43	42.28
82	2015ZHAR01	Alexey Zharikov	66.77	54.57	58.32	70.11	64.31	66.63	28.01	41.45	54.66	0.00	50.59	50.79	23.23	72.64	57.38	0.00	0.00	0.00	42.19
83	2012RUPE01	Akash Rupela	69.73	58.21	50.19	50.83	38.46	38.37	51.52	35.02	53.88	28.19	38.17	51.15	30.03	48.17	40.26	30.24	6.84	37.70	42.05
84	2010THOM03	Blake Thompson	79.14	72.96	60.34	51.44	47.53	44.79	0.00	55.18	54.57	20.06	49.58	57.95	41.72	64.18	57.38	0.00	0.00	0.00	42.05
85	2015BART01	LuboÅ¡ BartÃk	57.54	65.42	61.43	56.53	62.56	55.94	34.29	35.30	45.68	38.17	55.18	51.89	31.51	29.57	40.59	16.59	0.00	17.80	42.00
86	2011MAHT02	Natthaphat Mahtani (<U+0E13><U+0E31><U+0E10><U+0E20><U+0E31><U+0E17><U+0E23> <U+0E08><U+0E35> <U+0E21><U+0E32><U+0E17><U+0E32><U+0E19><U+0E35>)	79.43	70.41	73.05	58.00	39.99	30.70	32.89	27.48	61.43	27.14	47.32	50.04	36.07	38.01	61.66	0.00	0.00	21.46	41.95
87	2011MATA01	Jorge Castillo Matas	64.76	66.49	56.33	52.78	44.70	47.11	50.12	55.18	56.18	0.00	45.55	61.90	37.85	39.79	48.75	0.00	0.00	27.23	41.93
88	2011CAHY03	Hendry Cahyadi	71.59	66.29	61.43	54.66	36.71	34.49	45.49	27.48	58.37	42.43	35.00	62.56	52.02	0.00	54.99	20.12	0.00	29.83	41.86
89	2013SAVI01	Henry Savich	68.04	70.03	51.31	44.67	32.91	31.13	24.24	39.43	62.74	27.92	44.33	81.96	42.77	53.88	59.12	0.00	0.00	18.30	41.82
90	2012PATE01	Antonie Paterakis	77.71	90.46	64.44	55.18	45.78	39.55	23.94	39.43	58.90	18.56	45.49	65.88	26.28	41.16	59.28	0.00	0.00	0.00	41.78
91	2009BOZS01	Hunor Bózsing	75.79	66.84	65.48	61.31	52.83	49.65	25.24	46.54	68.76	0.00	45.01	56.48	36.13	33.37	60.11	0.00	0.00	7.55	41.73
92	2012POHL01	Andreas Pohl	55.03	58.58	40.24	37.68	16.87	15.07	57.08	61.14	39.57	35.27	26.12	45.49	38.53	41.96	44.54	48.68	42.38	46.04	41.68
93	2014WENW01	Wong Chong Wen	58.80	54.07	49.58	55.99	52.70	54.57	39.89	41.96	56.93	33.82	41.03	49.20	19.52	39.00	52.14	0.00	10.25	40.77	41.68
94	2011SALG01	Daniel Cano Salgado	66.22	60.39	60.85	50.91	42.80	40.19	33.33	35.02	58.21	39.59	49.73	50.31	53.13	39.91	43.00	0.00	0.00	25.83	41.64
95	2011MOLL01	James Molloy	59.12	55.84	52.70	47.85	40.87	39.69	31.14	55.18	49.01	30.18	39.19	39.11	59.17	48.68	58.27	14.78	0.00	26.94	41.54
96	2013DISA01	Edoardo Disarò	67.68	65.42	53.71	50.51	50.51	43.41	32.04	55.18	51.52	12.84	54.94	52.57	31.45	39.40	51.81	9.07	0.00	24.19	41.46
97	2014PETE03	Tobias Peter	57.85	64.82	47.67	47.50	33.61	31.52	48.61	39.43	57.59	0.00	37.43	62.08	51.15	44.21	51.44	25.76	0.00	43.64	41.35
98	2008CLAR01	Thompson Clarke	72.15	68.25	60.34	47.81	37.22	30.53	38.19	55.18	64.24	31.08	43.03	53.62	48.83	29.57	35.38	0.00	0.00	28.64	41.34
99	2014IRIA01	Julen Simón Iriarte	64.50	81.23	50.59	39.84	31.02	23.36	47.11	37.33	49.73	37.68	36.46	55.75	30.53	44.98	61.31	13.54	0.00	38.37	41.30
100	2012PONC02	Patrick Ponce	90.08	70.41	78.75	69.50	61.31	40.11	47.81	27.48	76.97	0.00	38.48	27.74	0.00	65.75	35.09	12.27	0.00	0.00	41.21
101	2010SUGA01	Sei Sugama (<U+6D32><U+938C><U+661F>)	77.15	66.43	73.46	71.04	45.62	45.87	51.11	33.04	66.02	0.00	50.04	50.04	10.44	14.88	17.80	27.77	7.00	33.40	41.17
102	2014LOPE04	Antonio López	63.67	53.09	53.00	55.18	57.64	61.43	47.99	30.96	51.93	24.17	58.00	50.16	18.29	37.03	39.00	0.00	0.00	38.55	41.12
103	2014RAJE03	Anish Rajesh	63.30	77.43	65.95	71.75	56.63	61.20	0.00	29.03	58.42	27.01	34.02	48.35	35.36	34.13	77.06	0.00	0.00	0.00	41.09
104	2013CHIA02	Lee Chiang (<U+8523><U+792A>)	66.70	67.89	59.89	58.16	46.01	45.45	0.00	30.96	60.34	36.22	42.57	68.25	54.38	43.32	59.23	0.00	0.00	0.00	41.08
105	2009PLES01	Michal Pleskowicz	90.46	78.75	61.66	51.97	23.13	28.25	38.26	58.90	85.89	15.09	61.25	59.39	20.03	44.89	0.00	0.00	0.00	21.25	41.07
106	2014MEND02	Alexis Rodrigo Cazu Mendoza	61.25	53.31	54.80	63.80	62.14	56.83	13.39	29.03	62.44	34.49	53.97	64.76	34.16	46.34	48.17	0.00	0.00	0.00	41.05
107	2011ZHAN24	Chunyu Zhang (<U+5F20><U+6625><U+96E8>)	52.57	66.70	48.28	48.24	44.45	43.58	44.30	46.54	40.44	14.13	32.79	59.23	36.26	41.94	39.38	34.49	27.67	15.40	40.91
108	2011CHEN19	Qingbin Chen (<U+9648><U+5E86><U+658C>)	63.99	76.69	55.80	52.40	54.29	43.76	41.06	41.45	61.02	0.00	32.31	64.76	31.17	38.35	45.81	0.00	0.00	30.76	40.76
109	2011THOM01	Justin Thomas	61.25	59.07	62.80	54.75	59.72	48.57	40.36	35.02	51.31	0.00	49.01	50.51	45.26	48.28	32.71	0.00	0.00	34.85	40.75
110	2009BLAI01	AJ Blair	57.08	55.32	47.18	45.14	35.46	28.85	43.55	58.90	44.64	36.98	43.76	64.18	48.13	45.04	41.51	0.00	0.00	37.33	40.72
111	2014KARN02	Daniel Karnaukh	81.23	84.87	58.53	51.35	44.54	35.79	22.68	27.48	60.17	28.83	47.29	43.85	20.64	73.30	52.35	0.00	0.00	0.00	40.72
112	2011FERA01	Joshua Feran	59.34	50.51	45.33	43.82	40.19	40.77	36.96	39.43	41.48	41.96	53.31	64.37	71.59	26.00	51.81	0.00	0.00	25.70	40.70
113	2012CHOS01	SeungBeom Cho (<U+C870><U+C2B9><U+BC94>)	71.91	81.34	67.19	58.42	50.43	49.39	38.83	37.33	61.55	0.00	44.89	67.75	0.00	41.45	62.02	0.00	0.00	0.00	40.69
114	2012SORI01	Nathan Soria	71.75	68.76	70.11	54.02	46.34	43.20	24.74	25.96	71.59	0.00	37.37	56.33	44.39	50.51	65.55	0.00	0.00	0.00	40.59
115	2015MEDE01	Felipe Medel	63.74	53.17	58.80	49.09	45.10	37.50	29.38	21.59	51.03	28.68	47.11	51.89	53.53	59.01	55.99	0.00	0.00	24.65	40.57
116	2011SZAT01	Wojciech Szatanowski	63.80	64.44	53.57	39.62	29.96	30.18	50.47	64.31	56.58	29.57	33.28	57.49	38.17	22.72	45.33	9.46	0.00	41.14	40.56
117	2014MARS04	Ty Marshall	73.63	62.74	54.48	52.44	50.35	45.81	0.00	25.96	68.04	0.00	54.38	56.98	41.56	78.85	64.44	0.00	0.00	0.00	40.54
118	2011LINB01	Brandon Lin	59.83	56.28	50.95	38.17	26.50	16.04	38.97	33.04	53.75	15.13	53.79	46.84	45.49	100.00	43.70	9.86	8.67	32.12	40.51
119	2013KEJR01	Aryan Kejriwal	68.11	68.76	59.56	61.43	58.85	50.23	25.99	35.02	57.90	0.00	48.79	51.19	29.52	61.31	52.35	0.00	0.00	0.00	40.50
120	2013LANG03	Mason Langenderfer	60.06	68.04	46.27	39.69	31.57	26.29	30.15	35.02	48.94	40.44	36.61	55.65	42.97	45.39	68.11	16.45	7.94	28.81	40.47
121	2007SUNT01	Timothy Sun	63.86	56.68	48.83	46.40	19.83	18.52	48.64	52.74	42.69	46.07	31.39	41.16	44.98	39.16	28.10	34.64	28.28	35.93	40.44
122	2008HASH02	Wataru Hashimura (<U+7AEF><U+6751><U+822A>)	69.13	65.82	50.67	45.07	26.54	31.16	35.75	52.74	45.55	43.26	55.27	58.37	47.25	43.09	51.27	0.00	0.00	0.00	40.05
123	2014LANG02	Isaac Langer	71.75	65.02	55.41	49.81	33.01	25.60	32.79	35.02	63.67	21.18	62.26	55.18	28.28	60.34	60.85	0.00	0.00	0.00	40.01
124	2013LINK01	Kaijun Lin (<U+6797><U+607A><U+4FCA>)	76.79	62.87	47.43	40.85	0.00	0.00	100.00	0.00	57.44	0.00	25.10	67.75	0.00	0.00	0.00	100.00	69.06	72.72	40.00
125	2014SCHW02	Fabio Schwandt	64.89	71.51	51.15	47.67	43.91	43.35	22.03	43.70	51.11	16.00	39.67	58.27	45.58	54.16	66.56	0.00	0.00	0.00	39.97
126	2011JONA01	Andre Febrianto Jonathan	62.32	63.30	60.91	53.84	46.94	44.95	24.92	37.33	53.88	32.46	39.67	69.65	51.89	28.94	47.64	0.00	0.00	0.00	39.92
127	2006TABU02	Yumu Tabuchi (<U+7530><U+6E15><U+96C4><U+5922>)	78.18	56.04	58.90	58.74	25.86	19.05	49.01	46.54	60.79	46.94	24.95	43.00	18.73	39.86	18.82	27.30	11.96	33.09	39.88
128	2011TRON02	Sebastiano Tronto	61.25	61.72	37.76	34.70	19.63	16.41	70.03	70.88	63.42	0.00	23.57	40.14	37.85	15.46	37.85	45.65	34.62	46.37	39.85
129	2013EGDA01	Daniel Vædele Egdal	58.37	64.69	51.77	45.20	36.44	38.28	8.67	35.02	52.27	55.32	46.44	66.43	46.20	48.21	63.80	0.00	0.00	0.00	39.84
130	2013BROW04	Evan Brown	54.11	47.32	44.45	32.01	28.85	28.60	52.14	37.33	24.05	33.45	33.21	47.74	56.78	32.46	47.46	36.13	36.65	44.33	39.84
131	2013MUAT01	Matej Mužátko	62.93	77.80	47.88	48.50	37.41	38.12	53.84	49.58	38.21	0.00	13.13	41.11	53.04	14.70	53.44	25.36	6.25	50.71	39.56
132	2012BERG04	Nathaniel Berg	68.47	60.96	61.72	54.61	38.67	33.77	13.62	43.70	49.20	16.79	36.54	63.36	72.47	38.88	58.27	0.00	0.00	0.00	39.50
133	2013RUIX02	Xiaobin Rui (<U+82AE><U+6653><U+5F6C>)	65.68	52.06	68.47	56.98	47.11	44.67	27.53	33.04	58.48	23.13	44.45	49.92	44.67	43.85	50.59	0.00	0.00	0.00	39.48
134	2013NAHM01	Seung Hyuk Nahm (<U+B0A8><U+C2B9><U+D601>)	91.36	80.12	88.36	80.73	70.26	54.25	32.63	0.00	74.14	0.00	34.16	44.67	10.78	0.00	48.35	0.00	0.00	0.00	39.43
135	2013KATO01	Eva Kato	73.21	78.75	55.32	42.60	36.40	26.10	30.28	37.33	45.39	38.81	41.32	59.23	35.07	56.68	51.44	0.00	0.00	0.00	39.33
136	2012HOLE01	Ray Leung Ka Ho (<U+6881><U+5BB6><U+6D69>)	66.70	57.80	63.17	60.62	54.61	46.20	37.81	39.43	59.23	0.00	39.50	54.38	41.45	35.69	49.85	0.00	0.00	0.00	39.25
137	2008SAJI01	Yu Sajima (<U+4F50><U+5CF6><U+512A>)	71.99	58.21	68.84	57.49	38.19	21.14	35.27	43.70	50.95	53.88	40.06	51.39	59.45	21.95	27.96	0.00	0.00	0.00	38.91
138	2015KOEN01	Christian König	61.72	60.06	45.10	42.18	38.95	33.13	31.31	41.45	52.52	51.68	37.79	60.96	34.68	36.67	56.09	0.00	0.00	15.89	38.90
139	2010GREG01	Jure Gregorc	72.64	65.42	55.46	52.70	39.45	38.67	30.99	37.33	53.57	0.00	49.54	64.76	47.25	36.86	44.15	0.00	0.00	11.40	38.90
140	2006GOTT01	Michael Gottlieb	61.37	52.06	59.50	59.45	45.87	53.04	35.46	46.84	58.00	0.00	51.27	50.59	44.42	43.76	38.26	0.00	0.00	0.00	38.88
141	2013BOTZ01	Alexander Botz	59.17	56.68	53.88	52.48	43.64	41.27	44.54	55.18	51.03	0.00	41.37	55.03	0.00	60.17	50.59	0.00	0.00	34.07	38.84
142	2006HALC01	Michal Halczuk	66.77	61.84	65.95	70.57	75.17	71.35	0.00	0.00	51.44	17.60	50.19	35.27	35.36	59.45	36.56	0.00	0.00	0.00	38.75
143	2015WANG09	Kai-Wen Wang (<U+738B><U+6977><U+6587>)	80.73	71.35	61.49	66.63	56.93	52.70	17.28	0.00	76.24	0.00	44.42	56.68	0.00	48.13	64.24	0.00	0.00	0.00	38.71
144	2015TELL01	Pedro Alejandro Condo Tellez	71.04	52.06	76.24	71.59	66.49	60.45	31.91	0.00	72.64	0.00	41.29	56.48	20.78	35.93	39.69	0.00	0.00	0.00	38.70
145	2011BILC01	Ihor Bilchenko (<U+0406><U+0433><U+043E><U+0440> <U+0411><U+0456><U+043B><U+044C><U+0447><U+0435><U+043D><U+043A><U+043E>)	72.07	65.75	61.20	49.20	42.52	31.43	30.57	46.54	56.93	14.79	26.90	56.73	43.35	23.38	50.95	0.00	0.00	23.64	38.66
146	2010WANG68	Bill Wang	90.85	81.44	86.11	73.97	52.96	0.00	61.02	0.00	82.17	0.00	36.98	0.00	0.00	0.00	0.00	65.88	48.46	15.18	38.61
147	2008WONE01	David Woner	65.35	60.85	53.53	52.02	28.59	17.49	30.06	52.74	52.96	21.51	44.15	56.73	53.22	50.27	34.46	0.00	0.00	21.07	38.61
148	2014MIAO02	Qijun Miao (<U+7F2A><U+5176><U+96BD>)	59.94	53.31	45.33	43.67	0.00	33.82	29.74	49.58	56.18	0.00	47.08	58.37	48.83	44.64	79.43	15.62	0.00	25.83	38.41
149	2010KRYU01	Dmitry Kryuzban	59.07	58.85	46.10	45.68	40.41	34.04	13.59	37.33	41.03	39.35	55.75	73.30	57.03	46.57	32.17	0.00	0.00	10.98	38.40
150	2009WHIT01	Ben Whitmore	65.55	72.47	48.39	43.29	29.57	33.33	36.71	37.33	50.47	15.06	39.99	50.31	37.52	56.88	41.77	8.66	7.18	15.91	38.36
151	2009ROTA01	Marco Rota	52.06	53.09	40.06	38.42	40.14	34.09	33.42	41.45	34.68	43.67	48.31	53.75	30.22	53.09	61.31	14.00	0.00	17.99	38.32
152	2007OMUR01	Syuhei Omura (<U+5927><U+6751><U+5468><U+5E73>)	66.98	58.58	60.79	62.26	51.56	50.91	44.79	35.02	59.34	20.67	47.81	38.74	20.12	15.02	19.67	8.51	7.35	20.83	38.27
153	2013ZHYH01	Vladyslav Zhyhailo (<U+0412><U+043B><U+0430><U+0434><U+0438><U+0441><U+043B><U+0430><U+0432> <U+0416><U+0438><U+0433><U+0430><U+0439><U+043B><U+043E>)	61.78	65.09	46.91	46.81	35.71	28.13	24.86	52.74	60.34	29.87	38.81	52.23	38.93	36.69	50.59	0.00	0.00	19.17	38.26
154	2012YANA01	Taku Yanai (<U+77E2><U+5185><U+62D3>)	54.99	45.97	35.48	27.08	11.05	9.38	67.40	49.58	46.84	30.57	21.94	56.93	17.04	41.75	40.64	46.88	40.34	44.45	38.24
155	2009SHEE01	Matthew Sheerin	48.13	52.35	42.49	40.49	31.54	27.95	54.02	49.58	32.01	0.00	34.81	35.11	20.40	42.74	36.50	47.53	47.08	45.29	38.22
156	2006BUUS01	Henrik Buus Aagaard	55.03	61.37	38.51	30.41	20.28	21.61	43.91	52.74	52.06	59.12	29.01	47.85	42.32	38.86	27.28	26.22	5.75	35.42	38.21
157	2013ESPA01	Jonathan Esparaz	76.15	65.02	67.54	56.78	39.67	33.54	28.53	27.48	69.88	0.00	44.39	53.57	25.41	50.79	48.86	0.00	0.00	0.00	38.20
158	2013VAKU01	Edward Vakula	61.78	64.82	43.49	39.50	27.04	22.84	17.68	37.33	45.71	37.87	41.91	70.88	43.17	51.27	63.11	0.00	0.00	18.90	38.18
159	2016CHAP04	Stanley Chapel	61.43	49.96	50.31	45.01	34.27	28.15	49.92	16.73	43.91	18.87	42.30	44.51	52.52	43.41	37.61	0.00	37.30	31.01	38.18
160	2011PARR02	Jhon Edinson Arias Parra	57.80	51.85	56.93	52.96	46.40	53.84	22.91	37.33	49.43	27.34	49.43	48.57	31.68	38.93	42.43	0.00	0.00	18.14	38.11
161	2012PENG05	Jiacheng Peng (<U+5F6D><U+5BB6><U+8BDA>)	54.80	46.77	54.38	52.06	46.84	43.85	35.25	33.04	36.38	27.75	31.33	41.40	33.33	31.85	56.33	28.28	0.00	30.53	38.01
162	2013YUSH01	Pavel Yushkevich	67.68	63.17	56.04	51.19	42.30	44.18	24.96	46.54	67.97	19.43	30.07	59.34	50.35	0.00	48.13	0.00	0.00	12.70	38.00
163	2015CHEA01	Andrey Che	78.47	71.91	53.79	43.73	30.45	26.84	0.00	39.43	72.80	0.00	57.23	51.72	38.32	62.08	56.33	0.00	0.00	0.00	37.95
164	2010WUJI01	Jiawen Wu (<U+5434><U+5609><U+6587>)	54.11	59.39	50.39	38.32	26.08	22.60	46.91	43.70	43.82	32.51	31.68	49.20	36.65	25.02	44.79	26.32	17.78	33.45	37.93
165	2013GALA04	Pavel Galaktionov	70.49	70.03	57.28	53.22	45.91	45.42	0.00	52.74	81.44	0.00	34.29	60.85	11.81	36.32	62.80	0.00	0.00	0.00	37.92
166	2010RAIH01	Fakhri Raihaan	63.55	68.04	53.62	43.38	26.64	19.80	45.84	0.00	50.27	59.94	30.32	61.66	34.29	21.75	23.13	30.14	13.45	36.34	37.90
167	2012CHON03	Zhao-Zhe Zhong (<U+937E><U+8087><U+54F2>)	63.36	62.74	60.62	55.22	46.54	44.42	26.37	33.04	44.64	15.43	33.51	48.35	44.24	43.82	59.72	0.00	0.00	0.00	37.89
168	2013KAMI03	Vladislav Kaminskiy	69.06	69.43	53.31	49.65	46.57	36.90	20.47	39.43	64.69	21.99	38.21	49.69	33.20	20.53	49.31	0.00	0.00	19.03	37.86
169	2012ROQU01	Pedro Henrique da Silva Roque	80.12	56.98	74.83	68.54	58.11	37.05	27.92	46.54	62.02	35.89	43.38	32.01	0.00	19.31	21.42	0.00	0.00	16.84	37.83
170	2011LOHR01	Fritz Löhr	48.90	41.75	45.74	41.03	39.55	40.59	34.13	70.88	36.30	28.50	37.74	40.64	32.15	26.42	52.23	21.06	10.53	32.28	37.80
171	2011ZVYA01	Dmitry Zvyagintsev	70.41	65.02	65.75	58.21	53.39	54.43	27.02	39.43	69.35	0.00	37.61	48.94	15.24	34.02	41.37	0.00	0.00	0.00	37.79
172	2013BURL01	Lukasz Burliga	72.31	72.72	58.85	51.68	36.32	17.37	0.00	41.45	60.85	0.00	39.69	63.67	26.94	37.99	100.00	0.00	0.00	0.00	37.77
173	2011HUNG02	Shao-Heng Hung (<U+6D2A><U+7D39><U+6046>)	60.85	62.02	59.39	50.75	44.48	35.52	0.00	23.01	38.74	45.81	41.59	59.17	67.61	38.74	52.14	0.00	0.00	0.00	37.77
174	2014MAUR06	Lorenzo Mauro	53.79	68.25	46.57	38.01	37.50	25.22	51.15	39.43	47.32	0.00	40.19	68.76	28.72	41.27	44.67	33.01	0.00	15.70	37.75
175	2014CORD04	Freddy Fernández Córdova	62.68	62.74	52.27	48.53	36.88	32.67	32.46	30.96	45.58	0.00	45.97	72.80	30.70	49.31	52.44	0.00	0.00	22.05	37.67
176	2008CLEM01	Kit Clement	46.40	54.94	36.96	30.20	23.34	20.52	45.04	70.88	35.21	22.12	30.45	46.37	62.14	39.74	53.00	20.89	4.74	34.79	37.65
177	2015ANTO04	Manuel Prieto de Antón	59.67	62.02	45.74	38.67	22.19	16.11	33.88	37.33	43.35	29.53	45.20	65.09	38.03	46.94	72.96	0.00	0.00	20.87	37.64
178	2005REYN01	Tim Reynolds	54.48	59.94	42.35	40.21	29.19	22.78	40.06	61.14	34.92	0.00	30.89	58.69	47.67	27.49	45.39	26.12	17.93	37.99	37.63
179	2014YASH01	Artem Yashkov	63.99	64.44	59.72	56.68	39.33	33.16	0.00	33.04	61.31	0.00	48.53	57.95	43.52	47.32	66.70	0.00	0.00	0.00	37.54
180	2013GHOD01	Abhijeet Ghodgaonkar	57.33	47.11	45.10	44.57	26.93	22.12	56.88	37.33	44.30	7.73	35.05	44.48	10.13	10.23	24.92	52.70	55.08	52.52	37.47
181	2013CRON01	Conor Cronin	50.75	55.08	41.43	41.64	30.22	32.06	35.93	35.02	37.87	23.57	32.69	55.27	54.80	42.10	48.90	18.13	11.83	27.04	37.46
182	2008VARG01	Dániel Varga	58.27	59.94	50.79	46.77	38.05	37.33	35.99	46.54	50.59	25.83	35.13	54.16	30.83	35.07	36.59	0.00	0.00	31.63	37.42
183	2010RONK01	Niko Ronkainen	60.22	66.29	48.17	42.16	37.15	32.46	0.00	55.18	47.60	37.74	23.25	57.28	66.02	36.50	62.08	0.00	0.00	0.00	37.34
184	2009HAYS01	Kevin Hays	76.97	64.69	80.73	84.87	82.17	78.28	26.34	15.58	53.13	0.00	40.09	32.44	11.61	15.38	0.00	0.00	0.00	8.16	37.25
185	2011MELI01	Artem Melikian (<U+0410><U+0440><U+0442><U+0435><U+043C> <U+041C><U+0435><U+043B><U+0456><U+043A><U+044F><U+043D>)	59.94	49.96	52.14	34.64	25.13	19.77	31.08	55.18	52.35	54.66	36.36	58.11	30.30	22.97	60.00	3.60	0.00	24.08	37.24
186	2012CARL03	Alexandre Carlier	87.40	74.39	80.12	72.15	51.23	44.54	26.38	41.45	63.67	0.00	42.49	60.79	0.00	0.00	24.87	0.00	0.00	0.00	37.19
187	2014LAFO01	Anthony Lafourcade	61.49	59.94	52.70	38.39	19.00	16.85	24.42	49.58	58.53	0.00	20.69	76.24	51.39	39.31	84.20	0.00	0.00	16.59	37.18
188	2007HESS01	Rowe Hessler	78.75	73.55	68.47	51.93	21.00	15.43	47.57	41.45	69.50	0.00	56.53	35.15	6.00	71.83	0.00	0.00	0.00	30.34	37.08
189	2013OWCZ01	Bartlomiej Owczarek	74.83	75.00	55.56	49.92	39.16	35.89	0.00	23.01	53.57	38.37	42.46	57.03	29.44	33.35	59.50	0.00	0.00	0.00	37.06
190	2012HAMA03	Brock Hamann	58.96	67.89	47.05	48.97	37.03	36.07	39.55	30.96	41.75	0.00	18.49	35.15	39.57	40.93	32.04	28.69	19.71	43.88	37.04
191	2011ANIS01	Dmitry Aniskin	70.72	64.44	59.17	47.96	30.47	28.90	17.15	39.43	61.72	0.00	50.75	52.78	39.50	45.55	48.68	0.00	0.00	8.59	36.99
192	2011CAST02	Michael Andres Castillo Lemus	69.28	62.26	66.29	53.48	38.12	37.57	0.00	37.33	52.18	23.09	60.17	52.10	18.40	46.91	48.28	0.00	0.00	0.00	36.97
193	2009ZHAN53	Weixing Zhang (<U+5F20><U+709C><U+661F>)	76.33	66.29	79.14	68.33	58.27	56.28	19.39	39.43	50.83	15.52	28.34	43.09	0.00	28.07	28.51	0.00	0.00	6.89	36.93
194	2011WALL02	Chris Wall	48.64	45.20	41.53	42.89	32.61	39.16	23.12	41.45	44.33	32.79	64.89	47.74	45.36	34.68	53.13	15.42	0.00	11.14	36.89
195	2013SZUM01	Grzegorz Szumigaj	52.74	61.55	45.20	51.77	45.29	42.72	25.87	33.04	43.00	49.62	36.90	59.45	0.00	55.99	60.39	0.00	0.00	0.00	36.86
196	2014BHAT09	Alaik Bhatia	61.72	49.12	51.11	51.23	34.88	29.89	52.52	46.54	40.19	13.92	26.50	48.68	31.59	57.38	45.33	0.00	0.00	20.67	36.74
197	2010ADHI01	Stephen Adhisaputra	72.72	63.92	56.28	49.92	16.48	21.02	38.79	64.31	61.20	34.13	28.36	53.75	36.34	6.56	13.92	20.44	0.00	21.41	36.64
198	2009KONV01	Asia Konvittayayotin (<U+0E40><U+0E2D><U+0E40><U+0E0A><U+0E35><U+0E22> <U+0E01><U+0E23><U+0E27><U+0E34><U+0E17><U+0E22><U+0E42><U+0E22><U+0E18><U+0E34><U+0E19>)	75.88	65.42	70.88	76.60	53.22	54.94	15.34	27.48	61.72	21.88	38.10	50.87	16.19	11.50	18.96	0.00	0.00	0.00	36.61
199	2010UBAL01	John Edison Ubaldo	56.83	48.17	54.52	49.88	43.03	40.98	53.09	41.45	41.72	17.13	54.34	38.01	23.73	38.03	33.70	0.00	0.00	23.79	36.58
200	2013WEAV01	Sydney Weaver	61.90	52.35	57.90	53.71	43.29	30.80	49.54	7.00	38.23	28.09	56.98	55.89	36.26	12.81	21.50	27.38	12.34	12.32	36.57

Code for xKinchRanks in R:

Spoiler

library(reshape)
setwd("C:/Users/kitcl/Desktop/xKinch")
singles = read.csv("WCA_export_RanksSingle.tsv", sep="\t")
averages = read.csv("WCA_export_RanksAverage.tsv", sep="\t")
people = read.csv("WCA_export_Persons.tsv", sep="\t", encoding="UTF-8")

lowRank_Single = aggregate(worldRank ~ eventId, singles, max)
lowRank_Average = aggregate(worldRank ~ eventId, averages, max)

names(lowRank_Single)[2] = "n"
names(lowRank_Average)[2] = "n"

WR333 = min(averages$best[averages$eventId=="333"])

(3600 - (x %% 1000000)/100)/3600

mbf = function(x) {99-(x %/% 10000000) + (3600 - (x %% 1000000)/100)/3600}
singles$best[singles$eventId == "333mbf"] = lapply(singles$best[singles$eventId == "333mbf"], mbf)
record_Single$best[record_Single$eventId == "333mbf"] = mbf(record_Single$best[record_Single$eventId == "333mbf"])

singles2 = merge(lowRank_Single, singles, by='eventId')
averages2 = merge(lowRank_Average, averages, by='eventId')

singles2$percentile = (singles2$n-singles2$worldRank+1)/(singles2$n)
averages2$percentile = (averages2$n-averages2$worldRank+1)/(averages2$n)

lookup333 = averages2[averages$eventId=="333",c(4, 8)]
lookup333$kinch = WR333/lookup333$best*100
lookup333 = lookup333[,c(2,3)]
lookup333 = rbind(lookup333, c(0, 0))
lookup333 = lookup333[nrow(lookup333):1,]

averages2$index = findInterval(averages2$percentile, lookup333$percentile)
averages2$xKinch = lookup333$kinch[averages2$index]

singles2$index = findInterval(singles2$percentile, lookup333$percentile)
singles2$xKinch = lookup333$kinch[singles2$index]

singlesRed = singles2[singles2$eventId %in% c("444bf", "555bf", "333mbf", "333fm", "333bf"),]
SinAvgCombined = rbind(singlesRed, averages2)

peopleSub = people[people$subid==1, c(1, 3)]

xKinch = cast(SinAvgCombined, personId ~ eventId, value="xKinch", fill=0, fun.aggregate=max)
xKinch$total = rowMeans(xKinch[,-1])

xKinchNames = merge(peopleSub, xKinch, by.x="id", by.y='personId')
xKinchNames = xKinchNames[order(-xKinchNames$total), c(1, 2, 4, 3, 10, 12, 14, 15, 5, 6, 9, 7, 17, 18, 16, 20, 19, 11, 13, 8, 21)]

con <- file("xKinch.csv", open="w", encoding="UTF-8")
write.table(xKinchNames, con, sep=",",row.names=FALSE, fileEncoding = "UTF-8")
close(con)

 

[Torch]

Obviously I have to support this, since I jump from 61st (in KinchRanks) to 52nd!

Seriously though, I'd be interested to think about what the general factors are that cause somebody to be ranked much higher/lower in xKinch than Kinch. I feel like it's something more subtle than the difference between SoR and KinchRanks.

 

[DGCubes]

Bumps me up 5 places, so that's nice.

Very cool concept. I'd like to see what happens when 3x3 WR average is broken.

 

[AlexMaass]

seems interesting and nice, maybe this will make it worth it for me to pick myself in Pyraminx in fantasy cubing now haha
name suggestion: Kitch Ranks?

 

[Cale S]

I'm the same world ranking as regular Kinchranks, interesting

 

[JustinTimeCuber]

I'm too stupid to understand this, which is odd because I'm usually good at that kind of thing.

 

[Kit Clement]

seems interesting and nice, maybe this will make it worth it for me to pick myself in Pyraminx in fantasy cubing now haha

The idea for this was definitely fantasy-motivated, but I think that the current system is already too complicated for understanding and making picks. This isn't exactly an improvement on that.

 

[AlphaSheep]

What I really like about the KinchRanks is that I can calculate my own score (rank isn't as meaningful when you're miles from the top) with nothing but my PBs and the world records. With xKinchRanks, I need the entire database export to calculate my score, and I can't quickly estimate how my score for an event will change when I set a new PB at a comp.

Also, I really don't like that changes in the distribution of 3x3, especially lower down in the rankings, have a significant impact on the scores in other events.

I also worry about the tail end of the distributions using 3x3 as the reference distribution. Most other events often have cut offs and time limits which certainly affect the distribution of real end competitors, whereas 3x3 cut offs and time limits are usually generous and rarely reached. The extreme example is FMC. The level of skill required to get a tail end FMC result (80 moves) is significantly higher than the level of skill required to get a tail end 3x3 result (say 3 minutes).

This has a much greater affect on those at the bottom of the rankings, so I think the ranking of the top 100 or so is probably a slighty fairer ranking than KinchRanks.

So basically, I don't see this as a replacement for KinchRanks. I just see it as a different ranking system with a different objective.

 

[uyneb2000]

lol I went from 329th to 392nd with this, did anyone else see a big drop like that?

 

[Kit Clement]

What I really like about the KinchRanks is that I can calculate my own score (rank isn't as meaningful when you're miles from the top) with nothing but my PBs and the world records. With xKinchRanks, I need the entire database export to calculate my score, and I can't quickly estimate how my score for an event will change when I set a new PB at a comp.

Also, I really don't like that changes in the distribution of 3x3, especially lower down in the rankings, have a significant impact on the scores in other events.

I also worry about the tail end of the distributions using 3x3 as the reference distribution. Most other events often have cut offs and time limits which certainly affect the distribution of real end competitors, whereas 3x3 cut offs and time limits are usually generous and rarely reached. The extreme example is FMC. The level of skill required to get a tail end FMC result (80 moves) is significantly higher than the level of skill required to get a tail end 3x3 result (say 3 minutes).

This has a much greater affect on those at the bottom of the rankings, so I think the ranking of the top 100 or so is probably a slighty fairer ranking than KinchRanks.

So basically, I don't see this as a replacement for KinchRanks. I just see it as a different ranking system with a different objective.

Lots of good feedback here -- thanks!

The ease of computation of KinchRanks is definitely a plus for that system which I didn't mention, but have definitely considered. I originally thought of this new system as a way to level the playing field for events in fantasy cubing, but obviously this is too complicated to be used as a fantasy cubing scoring method due to the difficulty in calculating a projection when building a team. Still thought it was an interesting idea to pursue as a ranking system for the purposes of equal weighting.

Your idea about cutoffs pertaining to 3x3 as the base event and the level of skill for a success in certain events is certainly a good one, and one I hadn't thought about, so thanks for that point. I don't know if there's really a good fix for that, and as you say, it really only affects those toward the middle and bottom of the rankings, which isn't necessarily the goal of doing an overall ranking system. However, it does affect the goal of having scores in each event comparable to another to some degree, even if the distributions are identical -- lots of people would have a 4x4 average without cutoffs, but just barely making a cutoff would put you at a very low percentile. But to be fair, missing the cutoff in normal KinchRanks would give you a score of 0, where barely making the cutoff would also give you a score similarly low to xKinch, so maybe this effect isn't as bothersome as thought previously.

And yes, of course, I don't see this as a replacement to KinchRanks at all, just a different perspective upon the system that addresses some flaws and creates some new ones. Another idea that could simplify this system while removing the volatility based on 3x3 would be to just define an appropriate function that maps the interval [0, 1] to [0, 100] that closely mimics the process of mapping quantiles to KinchRanks. This would result in ranks that are not just relative, but also absolute. This is the current empirical "function" that was used to map KinchRank scores to all of the non-3x3 events -- looks almost like a logit function:

 

[TheCoolMinxer]

The thing I always disliked about Kinchranks and isn't improved in this one, is that BLD events are weighted way too much imo. Even Ainesh, who has a 7:0x 5bld, has just a score of 50. In bld it's just way harder to get a really good score, other than clock or fmc.
Top100 in 5bld is around 4x the WR, and I think SOR is just better for that.

 

[mark49152]

In my opinion, the two alleged weaknesses of KinchRanks are not weaknesses at all. Dominance of a WR holder can be seen instead as the rest of the field being relatively weak because they are further away from reaching the limits proven to be humanly possible, and that justifies their lower scores.

Also, if your objective is to normalise the score distributions across events, why not simply use linear rankings, and normalise to the number of 3x3 competitors? Or just 100? That would be a whole lot simpler and less arbitrary than normalising to the 3x3 distribution of KinchRank scores.

 

[AlexMaass]

The idea for this was definitely fantasy-motivated, but I think that the current system is already too complicated for understanding and making picks. This isn't exactly an improvement on that.

i dont see how the current system is complicated though, just estimate the average of wr/result cr/result nr/result