What follows is a dendrogram, or family tree, of a sample of 100 kdicers. What it intends to show is relatedness of players to each other. For any two players, the highest value of "h", or height, between them, is a measure of dissimilarity between the two. If you find yourself in the tree, offer comments on the similarities or difference between you and your "relatives".

This particular sample of 100 players is hemidemiskrumic, meaning, four equally spaced groups of 25 players spanning skrum's group (page 56 on the leaderboard) and the top group (page 1). The other intervening groups are page 37 and page 19.

From your comments and my analysis I will try to come up with a comprehensive taxonomic system for the classification of kdicers.


[Update 29 January 2009]

The stat work for this analysis was done by an online website, the official citation of is:
Wessa, P., (2008), Hierarchical Clustering (v1.0.2) in Free Statistics Software (v1.1.23-r3), Office for Research Development and Education, URL http://www.wessa.net/rwasp_hierarchicalclustering.wasp/

The Ward method was used because it minimizes variance, which is the same as saying it uses as much of the information as possible. I used the raw percentage data for first through seventh place finishes to compute these results. Since in theory we have only six independent variables, I should need to use only six of the seven levels of finishes. So I ran the data with seventh place omitted. Some of the branches got moved around, including those belonging to MadHat_Sam, moondust, and fiero600. I also did a run with fourth place, instead of seventh place, removed. In theory the results should be the same no matter which place was removed, but such did not turn out to be the case. There is a greater variance in fourth place finishes than seventh place. Though fourth place makes the least contribution to overall kdice score, it can be argued that two players who have significantly different percentages for fourth, though their other percentages show similar shapes, have different playing styles and should be classified as different.

One source of error in the data is the truncation of the percentages by Ryan. This leads to a range in percentage sums from 95% to 100% for all seven places. To correct for this, I did a run with all seven places, but normalized by player percentage sum. This supposedly minor adjustment rearranged many of the minor branches of the trees, but left the leaf pairings undisturbed. Conclusion: the data must be normalized.

[end 29 January update]

Run with all seven places of finish, unnormalized:

--[dendrogram w/ 2 branches and 100 members at h = 1.39]
|--[dendrogram w/ 2 branches and 6 members at h = 0.371]
| |--[dendrogram w/ 2 branches and 3 members at h = 0.238]
| | |--leaf "boilerjon"
| | `--[dendrogram w/ 2 branches and 2 members at h = 0.169]
| | |--leaf "pulver toast man"
| | `--leaf "jimmcguinn"
| `--[dendrogram w/ 2 branches and 3 members at h = 0.323]
| |--leaf "YevgenyBk"
| `--[dendrogram w/ 2 branches and 2 members at h = 0.199]
| |--leaf "hjdfgeteyr"
| `--leaf "jim2674"
`--[dendrogram w/ 2 branches and 94 members at h = 1.29]
|--[dendrogram w/ 2 branches and 41 members at h = 0.631]
| |--[dendrogram w/ 2 branches and 13 members at h = 0.44]
| | |--[dendrogram w/ 2 branches and 3 members at h = 0.197]
| | | |--leaf "fiero600"
| | | `--[dendrogram w/ 2 branches and 2 members at h = 0.119]
| | | |--leaf "jurlyk"
| | | `--leaf "Pharao"
| | `--[dendrogram w/ 2 branches and 10 members at h = 0.226]
| | |--[dendrogram w/ 2 branches and 4 members at h = 0.129]
| | | |--leaf "komando80"
| | | `--[dendrogram w/ 2 branches and 3 members at h = 0.0697]
| | | |--leaf "Akila"
| | | `--[dendrogram w/ 2 branches and 2 members at h = 0.0424]
| | | |--leaf "mmmboobies"
| | | `--leaf "mangoo"
| | `--[dendrogram w/ 2 branches and 6 members at h = 0.199]
| | |--leaf "aardvarks"
| | `--[dendrogram w/ 2 branches and 5 members at h = 0.143]
| | |--leaf "Pifi"
| | `--[dendrogram w/ 2 branches and 4 members at h = 0.103]
| | |--[dendrogram w/ 2 branches and 2 members at h = 0.0648]
| | | |--leaf "brisk"
| | | `--leaf "skrumgaer"
| | `--[dendrogram w/ 2 branches and 2 members at h = 0.0671]
| | |--leaf "lala123456"
| | `--leaf "Mirabilis"
| `--[dendrogram w/ 2 branches and 28 members at h = 0.544]
| |--[dendrogram w/ 2 branches and 11 members at h = 0.272]
| | |--[dendrogram w/ 2 branches and 5 members at h = 0.128]
| | | |--[dendrogram w/ 2 branches and 3 members at h = 0.0556]
| | | | |--leaf "fcuku"
| | | | `--[dendrogram w/ 2 branches and 2 members at h = 0.0436]
| | | | |--leaf "Gdott"
| | | | `--leaf "Dr Leech"
| | | `--[dendrogram w/ 2 branches and 2 members at h = 0.0632]
| | | |--leaf "beyazguvercinus"
| | | `--leaf "GG.Schönebörger"
| | `--[dendrogram w/ 2 branches and 6 members at h = 0.136]
| | |--leaf "eurasianbro"
| | `--[dendrogram w/ 2 branches and 5 members at h = 0.127]
| | |--[dendrogram w/ 2 branches and 3 members at h = 0.0648]
| | | |--leaf "MsCat"
| | | `--[dendrogram w/ 2 branches and 2 members at h = 0.049]
| | | |--leaf "ji-jo"
| | | `--leaf "Luin"
| | `--[dendrogram w/ 2 branches and 2 members at h = 0.0825]
| | |--leaf "mr Kruezfeld"
| | `--leaf "Moroccan Jasmine"
| `--[dendrogram w/ 2 branches and 17 members at h = 0.418]
| |--[dendrogram w/ 2 branches and 9 members at h = 0.179]
| | |--[dendrogram w/ 2 branches and 3 members at h = 0.106]
| | | |--leaf "Shevar"
| | | `--[dendrogram w/ 2 branches and 2 members at h = 0.0624]
| | | |--leaf "lesplaydices"
| | | `--leaf "jpc4p"
| | `--[dendrogram w/ 2 branches and 6 members at h = 0.145]
| | |--[dendrogram w/ 2 branches and 2 members at h = 0.0361]
| | | |--leaf "cnkcnk"
| | | `--leaf "Raubritter"
| | `--[dendrogram w/ 2 branches and 4 members at h = 0.0704]
| | |--[dendrogram w/ 2 branches and 2 members at h = 0.04]
| | | |--leaf "pityu"
| | | `--leaf "Shondven"
| | `--[dendrogram w/ 2 branches and 2 members at h = 0.049]
| | |--leaf "chaiNblade"
| | `--leaf "maurum"
| `--[dendrogram w/ 2 branches and 8 members at h = 0.201]
| |--[dendrogram w/ 2 branches and 5 members at h = 0.155]
| | |--leaf "matt 1234"
| | `--[dendrogram w/ 2 branches and 4 members at h = 0.11]
| | |--[dendrogram w/ 2 branches and 2 members at h = 0.0436]
| | | |--leaf "PsykomanT"
| | | `--leaf "IhlieDaily"
| | `--[dendrogram w/ 2 branches and 2 members at h = 0.0557]
| | |--leaf "GreGGWar"
| | `--leaf "ZOUILLE95850"
| `--[dendrogram w/ 2 branches and 3 members at h = 0.172]
| |--leaf "timmm"
| `--[dendrogram w/ 2 branches and 2 members at h = 0.107]
| |--leaf "Friedz"
| `--leaf "itrecal"
`--[dendrogram w/ 2 branches and 53 members at h = 0.998]
|--[dendrogram w/ 2 branches and 45 members at h = 0.59]
| |--[dendrogram w/ 2 branches and 13 members at h = 0.329]
| | |--[dendrogram w/ 2 branches and 7 members at h = 0.152]
| | | |--[dendrogram w/ 2 branches and 4 members at h = 0.0777]
| | | | |--[dendrogram w/ 2 branches and 2 members at h = 0.0412]
| | | | | |--leaf "Orlafede"
| | | | | `--leaf "miki00"
| | | | `--[dendrogram w/ 2 branches and 2 members at h = 0.051]
| | | | |--leaf "aurian7"
| | | | `--leaf "MudDobber"
| | | `--[dendrogram w/ 2 branches and 3 members at h = 0.109]
| | | |--leaf "Albert C"
| | | `--[dendrogram w/ 2 branches and 2 members at h = 0.0787]
| | | |--leaf "hatty"
| | | `--leaf "PJDev"
| | `--[dendrogram w/ 2 branches and 6 members at h = 0.160]
| | |--[dendrogram w/ 2 branches and 4 members at h = 0.102]
| | | |--[dendrogram w/ 2 branches and 2 members at h = 0.064]
| | | | |--leaf "topare"
| | | | `--leaf "The Chode"
| | | `--[dendrogram w/ 2 branches and 2 members at h = 0.0781]
| | | |--leaf "cwwyatt"
| | | `--leaf "goJoin.com"
| | `--[dendrogram w/ 2 branches and 2 members at h = 0.111]
| | |--leaf "Big Jumblies"
| | `--leaf "Revilo"
| `--[dendrogram w/ 2 branches and 32 members at h = 0.415]
| |--[dendrogram w/ 2 branches and 16 members at h = 0.239]
| | |--[dendrogram w/ 2 branches and 3 members at h = 0.0864]
| | | |--leaf "Tunzy"
| | | `--[dendrogram w/ 2 branches and 2 members at h = 0.0574]
| | | |--leaf "janLOL"
| | | `--leaf "rodelo"
| | `--[dendrogram w/ 2 branches and 13 members at h = 0.175]
| | |--[dendrogram w/ 2 branches and 9 members at h = 0.107]
| | | |--[dendrogram w/ 2 branches and 4 members at h = 0.0864]
| | | | |--leaf "Egle"
| | | | `--[dendrogram w/ 2 branches and 3 members at h = 0.0533]
| | | | |--leaf "riesi1904"
| | | | `--[dendrogram w/ 2 branches and 2 members at h = 0.0332]
| | | | |--leaf "idnera"
| | | | `--leaf "Matt Braun"
| | | `--[dendrogram w/ 2 branches and 5 members at h = 0.0911]
| | | |--[dendrogram w/ 2 branches and 3 members at h = 0.0432]
| | | | |--leaf "ma1achi"
| | | | `--[dendrogram w/ 2 branches and 2 members at h = 0.04]
| | | | |--leaf "Who am I ?"
| | | | `--leaf "mrmot"
| | | `--[dendrogram w/ 2 branches and 2 members at h = 0.0566]
| | | |--leaf "potato27"
| | | `--leaf "bsn"
| | `--[dendrogram w/ 2 branches and 4 members at h = 0.145]
| | |--leaf "baloo"
| | `--[dendrogram w/ 2 branches and 3 members at h = 0.0432]
| | |--leaf "Mitsi the cat"
| | `--[dendrogram w/ 2 branches and 2 members at h = 0.04]
| | |--leaf "jbw"
| | `--leaf "nyos"
| `--[dendrogram w/ 2 branches and 16 members at h = 0.279]
| |--[dendrogram w/ 2 branches and 10 members at h = 0.171]
| | |--[dendrogram w/ 2 branches and 3 members at h = 0.0867]
| | | |--leaf "last place"
| | | `--[dendrogram w/ 2 branches and 2 members at h = 0.06]
| | | |--leaf "fatboy98"
| | | `--leaf "gereffi"
| | `--[dendrogram w/ 2 branches and 7 members at h = 0.0942]
| | |--[dendrogram w/ 2 branches and 4 members at h = 0.0525]
| | | |--[dendrogram w/ 2 branches and 2 members at h = 0.03]
| | | | |--leaf "Leek Step"
| | | | `--leaf "Takadade"
| | | `--[dendrogram w/ 2 branches and 2 members at h = 0.0361]
| | | |--leaf "Pat Whalen"
| | | `--leaf "1HAPPYBOY"
| | `--[dendrogram w/ 2 branches and 3 members at h = 0.0653]
| | |--leaf "shadolin"
| | `--[dendrogram w/ 2 branches and 2 members at h = 0.0436]
| | |--leaf "habit1"
| | `--leaf "Mr.-T"
| `--[dendrogram w/ 2 branches and 6 members at h = 0.255]
| |--[dendrogram w/ 2 branches and 2 members at h = 0.052]
| | |--leaf "MadHat_Sam"
| | `--leaf "eeeekekekeke"
| `--[dendrogram w/ 2 branches and 4 members at h = 0.135]
| |--[dendrogram w/ 2 branches and 2 members at h = 0.04]
| | |--leaf "Easy A"
| | `--leaf "Art54"
| `--[dendrogram w/ 2 branches and 2 members at h = 0.0707]
| |--leaf "ACG"
| `--leaf "Vinter"
`--[dendrogram w/ 2 branches and 8 members at h = 0.735]
|--[dendrogram w/ 2 branches and 2 members at h = 0.396]
| |--leaf "smumustang"
| `--leaf "Zete02"
`--[dendrogram w/ 2 branches and 6 members at h = 0.401]
|--[dendrogram w/ 2 branches and 3 members at h = 0.159]
| |--leaf "moondust"
| `--[dendrogram w/ 2 branches and 2 members at h = 0.107]
| |--leaf "ropat"
| `--leaf "arwesome"
`--[dendrogram w/ 2 branches and 3 members at h = 0.268]
|--leaf "yay"
`--[dendrogram w/ 2 branches and 2 members at h = 0.0927]
|--leaf "gawron"
`--leaf "ImagoDei"

For the second year in a row, fiero600 takes the top TAPL spot. The new TAZD further indicates that fiero600 is unmatched in kdice history for player strength.

Here are the final standings, showing player name, games played, percentagle profile, TAPL, and TAZD.


fiero600 1984 24% 23% 15% 13% 9% 6% 8% 9306 23713
Vermont 1415 19% 21% 18% 14% 11% 8% 7% 4987 15079
montecarlo 2181 20% 18% 16% 12% 10% 8% 11% 4008 14056
pityu 1500 20% 19% 16% 14% 12% 9% 8% 3407 12255
jpc4p 1425 20% 19% 16% 12% 11% 10% 11% 2532 10376
nuflis 826 25% 15% 13% 13% 8% 9% 13% 3811 10255
mr Kreuzfeld 1251 20% 19% 15% 13% 10% 10% 10% 2554 10111
AMO 2889 20% 15% 11% 12% 11% 11% 13% 2325 9227
yellowfin 2487 19% 16% 14% 13% 12% 11% 13% 1513 8891
rrroll 1240 20% 19% 12% 13% 11% 10% 12% 2218 8686
zzaazz 1486 17% 15% 16% 16% 13% 11% 7% 1972 8332
SprintTx 1540 16% 17% 16% 11% 10% 12% 10% 1855 8142
captainLAGER 2743 20% 14% 11% 11% 12% 13% 15% 2074 7644
Shevar 2777 19% 13% 13% 13% 12% 13% 12% 1486 7551
moondust 1276 16% 17% 17% 14% 11% 10% 12% 1435 7422
MadHat_Sam 1880 19% 16% 13% 10% 9% 13% 18% 2634 7335
potato27 4669 16% 16% 12% 11% 12% 14% 16% 1531 6689
Johnson213 4122 15% 16% 14% 13% 11% 12% 18% 1432 6513
skrumgaer 2393 11% 11% 16% 20% 16% 14% 9% 3074 6646
aphex732 2006 17% 17% 13% 12% 12% 13% 14% 959 6508
wishbone 1211 19% 16% 14% 11% 13% 12% 13% 1109 6295
mss 1411 14% 14% 17% 16% 14% 11% 10% 1115 5808
olliejjc16 2216 12% 16% 15% 13% 10% 11% 15% 1174 5359
Tymbrwulf 1137 16% 17% 15% 13% 13% 14% 12% 506 4928
OldElvis 696 14% 16% 15% 18% 14% 13% 8% 1236 4793
kdicefreak 679 15% 17% 14% 17% 12% 11% 11% 762 4259
detenmile 1435 16% 14% 13% 11% 12% 14% 16% 483 3068
BreakYoSelfFool* 861 16% 14% 12% 15% 14% 12% 12% 358 3055
MadWilly 757 17% 13% 11% 13% 16% 15% 11% 608 2521

*February omitted because of bad percentage data

In the beginning of the month I did a least-square error fit of the PPG and the calibration integral (which the PPG should be if it is based only on the percentage distribution of firsts, seconds, etc.) I found that the best fit was approximately 96% place and 4% dom.

Now, at the end of the month, with the average number of games much greater, I did another least-square fit for the top 100 and found that dom made hardly any contribution at all (about 99.9% place and 0.1% dom). So I will go back to using a place-only convolution integral, except for a 0.2 point add-in to reduce the likelihood of a division by zero error.

Here are the top 100 arranged by the new convolution integral. There are fewer spurious results (particularly annat) compared to my contemporaneous post with the old convolution integral.

Rank Player Games PPG CI GPG BUY-IN
5th MadHat_Sam 22 1028 39.3 26.2 34,530
94th Bald_Knob 6 321 27.4 11.7 4,224
65th riser 66 117 23.2 5.1 20,010
62nd murphyb2 60 49 21.7 2.3 8,140
51st pityu 124 53 17.6 3.0 22,421
7th yellowfin 40 377 17.5 21.6 51,795
90th savif 133 35 15.8 2.2 17,641
27th Spectear 75 34 15.1 2.2 10,104
99th Artful Nudger 181 27 14.9 1.8 19,725
78th fiero600 111 32 14.8 2.2 14,368
2nd dasfury 62 324 14.6 22.2 82,500
1st shadolin 346 156 14.1 11.0 228,954
49th kimmy382 174 15 13.1 1.1 11,913
63rd Henrik 241 31 13.0 2.4 34,595
92nd Hoosier84 35 52 12.7 4.1 8,598
21st Simmo3k 193 61 12.5 4.9 56,420
29th Michaeldeigratia 54 23 11.8 2.0 6,330
13th Zosod 131 106 11.7 9.1 71,500
28th cnkcnk 311 15 11.6 1.3 24,036
56th EliteEagle 134 42 11.6 3.6 29,154
19th ZIGIBOOM 294 51 11.3 4.5 79,386
3rd montecarlo 121 160 10.9 14.7 106,618
88th Si McC 152 25 10.8 2.3 21,145
46th lennyrunsred 259 31 10.7 2.9 45,136
42nd ffbsensei 70 102 10.5 9.7 40,903
43rd vicsf 70 60 10.4 5.8 24,308
55th hatty 200 30 10.2 2.9 35,141
52nd Canarioz 207 23 10.1 2.3 28,332
61st jetsjetsjets31 243 31 9.9 3.1 45,678
11th rugbyjoe 110 64 9.8 6.6 43,234
10th Shevar 155 126 9.4 13.5 125,190
26th Rowdyazell 166 57 9.3 6.1 61,243
33rd GreGGwar 242 53 9.1 5.9 85,026
32nd snmlmz 208 22 9.0 2.4 30,439
76th kevin143 89 20 8.8 2.3 12,132
17th jpc4p 71 30 8.5 3.5 15,046
93rd Citizen Cope 118 14 8.5 1.6 11,669
70th BUCKAC 287 20 8.4 2.4 41,144
53rd habit1 334 22 8.3 2.7 53,311
83rd darklordum 144 11 8.0 1.4 11,850
47th Fatman_x 184 14 8.0 1.8 19,423
15th beyazguvercinus 292 41 8.0 5.2 90,270
14th potato27 302 60 7.8 7.7 139,923
66th acmilanfan3 253 22 7.6 2.9 43,683
39th Carlisle 174 15 7.4 2.0 21,082
80th Ridgeback 294 24 7.3 3.3 57,844
64th stakaboo 285 22 7.2 3.0 52,105
79th Dice! 170 14 7.2 1.9 19,846
68th fcuku 88 15 7.2 2.1 11,066
96th Korovief 144 14 7.1 2.0 16,929
37th Ketchel 286 29 7.1 4.1 69,762
100th {A}Monkey SLayer 234 7 7.1 1.0 14,040
36th Iborra 373 12 6.9 1.7 38,950
97th joe2me 121 41 6.9 6.0 43,227
58th Klown 206 28 6.8 4.1 51,178
31st SilentSyllogism 378 31 6.7 4.6 104,707
50th imanema 595 13 6.7 1.9 69,264
34th Isidro L 203 36 6.6 5.4 66,051
71st g0d0t 391 17 6.5 2.6 61,217
67th ceban 94 15 6.3 2.4 13,360
86th MadWilly 196 28 6.1 4.6 53,585
12th KJ Sado 336 48 6.0 8.1 162,413
75th start1 121 19 5.8 3.3 23,642
4th Orlafede 174 50 5.8 8.6 89,498
74th finkebr 95 41 5.8 7.0 40,082
24th pumpyobrakes 113 5 5.8 1.0 6,780
38th Spokos 96 5 5.8 1.0 5,760
69th riccardo 435 17 5.7 3.0 77,740
60th Mitsi the cat 307 24 5.2 4.7 85,774
6th Thraxle 177 119 5.0 23.7 251,233
8th MikeMike83 327 74 4.9 15.1 296,605
30th Dark_lunatic_K 73 11 4.8 2.3 9,945
20th olliejjc16 276 47 4.5 10.5 173,980
72nd Caephus 122 14 4.2 3.4 24,609
9th moondust 81 11 4.1 2.7 12,897
82nd jethr0 243 0 4.0 1.0 14,580
85th Honyo 60 -21 3.7 1.0 3,600
89th masterDD 395 5 3.7 1.4 32,293
59th detenmile 87 41 3.5 11.8 61,431
95th BreakYoSelfFool 144 6 3.5 1.7 14,993
48th oilking 397 15 3.1 4.8 113,609
73rd >Username< 38 1 3.1 1.0 2,280
81st Äkäkäkäkä! 154 13 2.6 5.0 46,513
35th Antipathy 146 -2 2.6 1.0 8,760
22nd Kehoe 24 -15 2.5 1.0 1,440
45th Jitterbug 481 16 1.9 8.4 243,673
84th peter luftig 242 2 1.7 1.2 17,007
1974th skrumgaer 121 -10 1.3 1.0 7,260
18th smirkatroid 229 8 1.0 7.8 107,765
87th 6948312507 541 7 0.1 85.5 2,775,861
23rd lesplaydices 84 -33 -0.7 45.7 230,275
91st /wanted 177 13 -0.7 1.0 10,620
44th snoopdog 103 34 -1.0 1.0 6,180
57th StudiousGangster 147 -77 -2.5 31.0 273,847
16th bsn 286 -16 -2.8 5.8 99,516
41st El Destructor 95 12 -4.3 1.0 5,700
54th KDicer X 175 -4 -5.1 1.0 10,500
98th annat 6 -13 -5.2 2.5 894
40th Johnson213 116 -43 -6.7 6.4 44,470
77th Avarice 60 12 -12.6 1.0 3,600

I'm working on doing some AI battles with KDice and was hoping to get some initial bots submitted as psuedo code algorithms. I'll name the bot after your kdice name and will have them battle each other. Eventually I can open up a kdice to write your own bot.

As a starting point, the current bots are dumb and run as follows:

findBattle(){
   for each enemy border region
      if my dice > enemy dice
         return enemy region
   return no region
}

Don't post your code here or others will take your good ideas! Ideally each bot is different. So email me first ([email protected]). I'll try to do a some battles on the test server and allow for some tweaking when they're done.

The December player stats appear not to have corrupted percentages. A glitch on the first day, where players stats were multiples of 100%, was fixed by Ryan. The glitch is automatically fixed for a player when that players plays at least one game after the fix.

The TAPL depends on accurate percentages stats. Weekly TAPL reports will resume when the top 100 players show enough game totals over 35 (Yate's Correction does not have to be used). Along with the TAPL, I will report on my new measure, the TAZD (Test Against Zero Datum).

I have also done some work on tweaking the Convolution Integral (CI). It measures a player's expected PPG according to what percentage firsts, seconds, etc. are in the player's profile and how many points each place is worth. The problem with the CI is that it does not pick up dom, so it is inaccurate for the 500 and 2000 level tables. I have been doing a least-square error analysis of the top 100 players' PPG's against a linear transformation of their CI's. Preliminary analysis suggests that the best linear fit of the CI is 96% place and 4% dom. The top 100 players' PPG's are roughly six times bigger than their CI's, which is consistent with the average level of table they play at being 600. Or you could say that the buy-in per game of the top 100 is roughly six times that of the buy-in at the zero level tables. The ratio of PPG to CI for a particular player can be used to measure that player's gutsiness, but gutsiness could be directly measured without having to calculate a CI if Ryan were to incorporate players' buy-ins into the stats *cough*.

The practical significance of the "96% place and 4% dom" is that 4th place would get 4% of the buy-in on average, instead of zero.