Could someone explain why "sum of ranks" is always calculated with the events one hasn't competed in equal to the number of competitors+1? For example, getting 70 "points" for 5BLD seems awfully generous. Should it really be a difference of 1 point between someone with a 5BLD success (a spectacular accomplishment) and the beginner who can only solve magic?

Not that it's a great alternative, but it makes more sense (to me) to set the score of non-competed in events to the total number of competitors overall. Um...20,583...that's a lot, but I'll still go with it =) Think of it as getting a huge bump in "sum of ranks" for doing hard events.

*Disclaimer: My rank would skyrocket under this alternative, so I'm not exactly a disinterested 3rd party, lol.
 
Uh, what? Then you'd have no chance of being on the top ten list unless you had competed in everything. I really don't like that idea. With the current "number of competitors plus one" it's basically considering everyone who doesn't have a success as having a DNF, and those are all equally ranked right below the worst solve.
 
On the contrary, it makes perfect sense to me that people who have invested time and effort into becoming good at everything should have a better ranking than those who compete only in the most popular events.
 
On the contrary, it makes perfect sense to me that people who have invested time and effort into becoming good at everything should have a better ranking than those who compete only in the most popular events.

I can only partially agree on this, Although it does seem more fair for those people who only compete in a few events to be penalised, it isn't always easy to compete in everything. For example, There are people who compete in 4BLD and 5BLD, but don't necessarily get successes, no matter how much time is put into practicing it, it doesn't seem fair to penalise these people for getting a DNF, over not competing at all. At least they tried. Also, some people might not be able to compete in a competition with the even that they are missing, for example, I want to compete in feet, and Edinburgh Open in Janurary will be my first opportunity since I started doing feet over the summer. Again, is it fair to penalise someone who just cant get to a competition with that event?
 
With the current "number of competitors plus one" it's basically considering everyone who doesn't have a success as having a DNF, and those are all equally ranked right below the worst solve.

Indeed. Shared next place with DNF or rather DNS is the idea. Number of successful competitors plus one is just the implementation of that idea. I should probably rewrite the documentation to point out the idea rather than its implementation.

But I intend to call the current version "absolute" ranks and offer an alternative "relative" ranks view, where the best in an event gets zero and the worst (people without a success) get 1 (or 100, depending on what looks better). Need to get other stuff done first, though.
 
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How many different people occupy the 2900 top hundred spots for events other than magic and master magic? What percentage of people with official results is this? Same questions for top 1000 and top 10.
 
How many different people occupy the 2900 top hundred spots for events other than magic and master magic? What percentage of people with official results is this? Same questions for top 1000 and top 10.
I've gone a bit crazy with the stats here, but I was having too much fun. I've used the latest WCA export, which is from 29/11/12

Top 100 Rankings Stats

891 people occupy the 2899 spots across the 29 Top 100 rankings. Ties (esp. in Fewest Moves) increase the number of Top 100 rankings and 5bld reduces it.
There are 20422 people in the database, which means 4.36% of people have at least 1 Top 100 ranking.

Most Top 100 rankings (min 10 lists)
1 Simon Westlund 28 (Not in One-handed average)
2 Yu Nakajima 26
3 Dan Cohen 25
4 Milán Baticz 24
4 Feliks Zemdegs 24
6 Bence Barát 23
7 Erik Akkersdijk 21
8 Mats Valk 19
8 Cornelius Dieckmann 19
10 Maarten Smit 18
10 Robert Yau 18
12 Yumu Tabuchi 16
12 Nipat Charoenpholphant 16
12 Daniel Sheppard 16
15 Rowe Hessler 15
15 Syuhei Omura 15
15 John Brechon 15
15 Louis Cormier 15
19 Edward Lin 14
19 Asia Konvittayayotin 14
19 Vincent Hartanto Utomo 14
22 Takumi Yoshida 13
22 Jong-Ho Jeong 13
22 Kailong Li 13
22 Emily Wang 13
26 Yu Sajima 12
26 Takahiro Tomisawa 12
26 Dániel Varga 12
26 Kevin Hays 12
26 Jan Bentlage 12
26 Alfrisa Diva Wandana 12
32 Henrik Buus Aagaard 11
32 Michael Gottlieb 11
32 Michał Halczuk 11
32 Timothy Sun 11
32 Michał Pleskowicz 11
32 Michael Röhrer 11
32 Weixing Zhang 11
32 Marcin Zalewski 11
40 Breandan Vallance 10
40 Sébastien Auroux 10
40 David Woner 10
40 Kamil Zieliński 10
40 Gabriel Dechichi Barbar 10
40 Weifeng Cheng 10
40 Congbiao Jiang 10
40 Howard Wong Jun Yen 10
40 Stephen Adhisaputra 10
40 Carlos Méndez GarcÃ*a-Barroso 10
40 Dmitry Kryuzban 10
40 Ivan Vynnyk 10
40 Kevin Costello III 10

Most different people in a Top 100 list by Country
Rank Country Persons
1 USA 104
2 China 93
3 Indonesia 74
4 Poland 65
5 Japan 49
6 Germany 48
7 France 31
8 Hungary 28
8 Korea 28
8 Taiwan 28
11 Italy 27
11 Thailand 27
13 Sweden 26
14 Russia 25
15 Canada 23
16 Spain 21
17 United Kingdom 19
18 Brazil 18
19 Netherlands 16
19 Philippines 16
21 Hong Kong 13
21 Malaysia 13
23 Mexico 12
24 Austria 10
25 Australia 9
26 Chile 7
26 Denmark 7
28 Finland 6
29 Colombia 5
29 India 5
29 Norway 5
29 Vietnam 5
33 Ukraine 4
34 Belgium 3
34 Czech Republic 3
34 Slovenia 3
37 Iran 2
37 New Zealand 2
37 Switzerland 2
40 Argentina 1
40 Belize 1
40 Croatia 1
40 Israel 1
40 Kazakhstan 1
40 Macedonia 1
40 Peru 1
40 Portugal 1
40 Singapore 1

Most results in the Top 100 lists by Country
Rank Country Results
1 USA 346
2 China 276
3 Japan 214
4 Indonesia 208
5 Poland 187
6 Germany 186
7 Hungary 125
8 Thailand 104
9 Canada 101
10 Taiwan 97
11 France 91
12 Sweden 86
13 Netherlands 85
14 Russia 81
15 United Kingdom 74
16 Italy 69
16 Korea 69
18 Spain 52
19 Australia 46
20 Brazil 45
21 Philippines 44
22 Malaysia 42
23 Austria 38
24 Hong Kong 34
25 Denmark 29
26 Mexico 20
27 Norway 19
28 Finland 17
29 Ukraine 15
30 Vietnam 13
31 Chile 11
31 Slovenia 11
33 Colombia 9
34 New Zealand 8
35 Belize 6
35 Czech Republic 6
35 India 6
35 Kazakhstan 6
39 Singapore 5
40 Belgium 4
41 Switzerland 3
42 Croatia 2
42 Iran 2
42 Macedonia 2
42 Portugal 2
46 Argentina 1
46 Israel 1
46 Peru 1

Year in which people started competing
Year Persons Results
1982 2 2
2003 9 17
2004 10 21
2005 18 102
2006 39 140
2007 93 345
2008 149 590
2009 202 684
2010 193 584
2011 140 331
2012 36 83
For each event, the number of people who only appear in that list
Event Persons
333fm Single 39
333bf Single 31
222 Single 24
pyram Average 22
333mbf Single 20
222 Average 16
pyram Single 15
444bf Single 12
333 Single 10
333oh Average 9
333oh Single 8
sq1 Single 8
sq1 Average 8
clock Average 8
444 Average 6
minx Average 6
333ft Single 4
minx Single 4
clock Single 4
333ft Average 4
444 Single 3
333 Average 2
555 Average 2
555 Single 1
666 Single 1
555bf Single 1
666 Average 1
777 Single 0
777 Average 0
Number of people in top 100 for both Single and Average (for each event)
777 95
666 94
333ft 92
minx 89
clock 89
555 87
444 82
sq1 82
333oh 74
333 73
pyram 59
222 47
The top ranked person in any average list who does not make the top 100 singles is Ben Whitmore who is 6th in 2x2x2 average and 145th in 2x2x2 single
I'm sure you can guess the reverse of that statistic (highest ranking in single who does not make top 100 average). Hint: Think of the same event

Number of people in the Top 100 Average for random other pairs of events
222-333: 40
333-444: 53
444-555: 58
555-666: 65
666-777: 74
333-OH: 43
Megaminx-Pyraminx: 16
Feet-Sq-1-Clock: 5 :p

Top 10 Rankings Stats

147 people occupy the 293 spots across the 29 Top 10 rankings (Fewest Moves has ties), which means 0.72% of people have at least 1 Top 10 ranking
Most Top 10 Rankings (min 3)
Rank Name Top 10 Ranks
1 Feliks Zemdegs 15
2 Yu Nakajima 10
3 Mats Valk 8
4 Michał Halczuk 7
4 Dan Cohen 7
4 Lin Chen 7
7 Kevin Hays 6
8 Michał Pleskowicz 5
8 Daniel Sheppard 5
10 Erik Akkersdijk 4
10 Marcell Endrey 4
10 Rowe Hessler 4
10 Oscar Roth Andersen 4
10 Bence Barát 4
10 Kam Chor Kin 4
10 Yu Sajima 4
10 Congbiao Jiang 4
10 Asia Konvittayayotin 4
19 Yumu Tabuchi 3
19 Jong-Ho Jeong 3
19 Bingliang Li 3
19 Piotr Michał Padlewski 3
19 Muhammad Iril Khairul Anam 3
19 Nipat Charoenpholphant 3
19 Arifumi Fushimi 3

Most different people in a Top 10 list by Country
Rank Country Persons
1 China 17
2 USA 15
3 Japan 13
4 Poland 10
5 Indonesia 8
5 Thailand 8
7 Germany 7
7 Italy 7
9 Canada 5
9 Hungary 5
9 Korea 5
9 Netherlands 5
9 Russia 5
14 Australia 4
14 Finland 4
14 France 4
14 Malaysia 4
18 Brazil 3
18 Spain 3
18 Taiwan 3
18 United Kingdom 3
22 Austria 2
22 Denmark 2
24 Belgium 1
24 Mexico 1
24 Philippines 1
24 Slovenia 1
24 Sweden 1

Most results in the Top 10 lists by Country
Rank Country Results
1 China 36
2 USA 32
2 Japan 32
4 Poland 24
5 Australia 20
6 Thailand 16
6 Netherlands 16
8 Indonesia 13
8 Hungary 13
10 Germany 11
11 Italy 8
11 Korea 8
11 United Kingdom 8
14 Canada 7
15 Russia 6
15 Finland 6
15 France 6
15 Denmark 6
19 Malaysia 4
19 Brazil 4
19 Spain 4
22 Taiwan 3
22 Austria 3
24 Mexico 2
24 Sweden 2
26 Belgium 1
26 Philippines 1
26 Slovenia 1
 
Patterns in official averages: Best/Worst solves and DNF/DNS

Sorry for another long post, but I get carried away by numbers.

Prompted by MLSTRM asking whether there are patterns within my official averages, I have done some calculations across all results.

These were run on 29/11/12 export. I filtered for rounds that were averages of 5 (removing people cutoff after 2 solves etc). That left 214590 averages to play around with.

Number of times each solve is the best/worst within the average:
# Best Worst
1 40650 46420
2 42639 43062
3 42734 42514
4 43831 41263
5 44736 41331

1540 averages are monotonic increasing (getting worse every solve)
2005 averages are monotonic decreasing (improving every solve)

This table and figures following certainly have statistical significance, given the large data volume. This improvement in performance could be down to a number of factors, of which I will list a three: a) Warming up (physically and mentally) through the solves b) Nerves calming down as the solves go on c) Real improvement in events that people rarely practise!

In the table above, there is one figure that does not follow the pattern - there are more worst 5th solves than 4th solves. This can easily be explained by the increase in DNFs and DNSs on the 5th solve due to people giving up:
# DNF DNS
1 7264 54
2 6953 197
3 7061 517
4 7229 818
5 8547 1063


Going down another route, I have this idea in my head that a really good solve is often followed by a terrible one, so I tried to test it out by looking at all cases where the best solve was not the 5th solve.
25.06% (42562 out of 169854) of averages had the worst solve following the best one, which is extremely close to the expected value of 25%.
23.1% (25 out of 108) of WR single solves were followed by the worst solve (again, ignoring where the 5th solve was the best). So this suggests that a WR doesn't make you more likely to do a terrible solve.
26.6% (812 out of 2056) of record single solves (NR/CR/WR) were followed by the worst solve, which could be seen as a small indication of the effect.

Here are the number of times that single solve records have been set on each solve number. Remember that this is only counting solves within averages of 5, so records in single-only events and where they were set during a mean of 3 etc have not been included.
# WR NR/CR/WR
1 29 682
2 26 747
3 24 781
4 29 846
5 34 843

This shows the same sort of behaviour as the first statistic did - the later solves are more likely to be better!
 
highest sq1 single to average ratio? and the other way around.
Largest ratio of Sq-1 average to single
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Smallest ratio of Sq-1 average to single
21n2lc8.png

I've done them as images because I'm fed up with tables not appearing in columns
 
what about sq1 to 3x3 ratios? if you dont mind

All people with faster Sq-1 single than 3x3x3 single (or equal!)
25p2ya8.png
All people with faster Sq-1 average than 3x3x3 average
10r4mrr.png
All people with 3x3x3 single >10 times faster than Sq-1 single
jpk45z.png
All people with 3x3x3 average >10 times faster than Sq-1 average
30idiyq.png

Lastly, I got this human verification when I was uploading that last picture :p
14wc84l.png
 
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