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A recalibration of the convolution integral.
Posted By: skrumgaer at 6:32 PM, Friday December 26, 2008 EST
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
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
Replies 1 - 4 of 4
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kevin143 wrote
at 4:20 AM, Sunday December 28, 2008 EST I don't understand what the list is supposed to be.
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skrumgaer wrote
at 10:20 AM, Sunday December 28, 2008 EST The list, which was also the top 100, was the database from which I did my calculations. The convolution integral is a fancy name for the estimate of what your PPG would be based on now many firsts, seconds, etc. you had and if you played only at the zero level tables. For example, if you had 50% first places and 50% second places, your CI would be 0.50x60 + 0.50x42 = 51.0. The CI could have a max of +120 and a min of -120, but as we see from the data, the very best players are unlikely to have a CI more than +40.
The guts-per-game (GPG) is the ratio of a player's PPG and his CI and is an indicator of the level of table that he plays at. The average GPG of the top 100 is approximately 5, which indicates that they spend most of their time at the 500 level tables for which the buyin is 5 times that of the zero level tables. The GPG is also the buyin per game; multiply the GPG by the number of games to get the estimated total buyin. |
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the full monte wrote
at 12:04 PM, Sunday December 28, 2008 EST hey skrum, a naive suggestion (feel free to show me my bad assumptions)...
the CI is based on how a below-average person will fare on a 0-level table. is there any way to include some formula that roughly estimates what table levels they have played at for the month, and then have a series of CIs for each table level? ex.: shadolin this month has probably played 0 games at 0-level tables, probably a handful on 100-level, a lot at 500-level, a lot at 2000-level, and a handful at 5000-level. then convolve his percentages (i guess you would have to use his total percentages, which would introduce error, instead of percentages limited to each table level, which dont exist)... convolve those total percentages with the proper estimated fraction of games played at each table level. on second thought maybe this isnt such a hot idea. you would have to figure out how to derive a reasonable CI for each table level, and who knows how you would sample the kdice population for that. anyways, again, thanks for all the great stat-massaging! |
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skrumgaer wrote
at 2:06 PM, Sunday December 28, 2008 EST full monte:
The convolution integral can be calculated exactly for the 0 and 100 level tables since there is no dom. But even with an exact computation, there is still some scatter because the PPG is rounded off to integers. So the PPG/CI ratio can have error, and it can have division by zero error. So I set any GPG of less than 1.0 to 1.0. With the top 100 players, the convolution appears to involve mostly the 500 tables, as you suggested with the case of shadolin. So if I fit it for the 500 level tables, it will be a little off for the lower level tables (unlike well-tempered piano tuning which leaves all the keys a little, but equally, out of tune). Since most people are interested in the stats of the better players, it is better to have a convolution that is more nearly accurate for the better player. If Ryan were to provide total buyin or buyin per game *cough cough* then I could calculate CI exactly. |
