Super Stats Score for LS Hunter

[Quantalex]

I made a scoring system based on physicals only for human Hunter. This scoring system uses accumulated points converted from positioning in frequency of receiving a certain stat. Each homeland has about 700-2000 stat sample pool.

1-4 (points) * 3 (weight)
-----------
19 Str: Kandor(12) > Two Rivers(9) > Borderlands/Shienar(6) > Saldaea/Arafel(3)
19 Dex: Arafel(12) > Kandor(9) > Borderlands/Saldaea(6) > Shienar(3)
19 Con: Two Rivers(12) > Saldaea(9) > Borderlands/Shienar(6) > Kandor/Arafel(3)

1-4 * 2
-----------
18 Str: Borderlands/Saldaea(8) > Kandor(6) > Two Rivers/Shienar(4) > Arafel(2)
18 Dex: Borderlands(8) > Kandor/Saldaea(6) > Shienar/Arafel(4)
18 Con: Two Rivers(8) > Kandor(6) > Borderlands/Saldaea(4) > Shienar/Arafel(2)

1-4
-----------
17 Str: Kandor(4) > Two Rivers(3) > Borderlands/Shienar(2) > Saldaea/Arafel(1)
17 Dex: Borderlands/Shienar(4) > Saldaea/Arafel(3) > Kandor(2) > Two Rivers(1)
17 Con: Borderlands(4) > Shienar/Kandor/Arafel(3) > Saldaea(2) > Two Rivers(1)


Total Points
-----------
1st >> Kandor: 51
2nd >> Borderlands: 48
3rd >> Saldaea: 42
4th >> Two Rivers: 38
5th >> Shienar: 34
6th >> Arafel: 33


So this ranks Kandor as the best homeland to stat a super-statted human hunter, which I define as two 19's, and one 18. It ranks pretty high for most things other than 19 con, so it has the best chance of a 19 19 18 hunter, but not as great for a 18 19 19 or 19 18 19, which Borderlands or Saldaea would be better fit for.

[Quantalex]

Of course, this all means nothing without data. Therefore, behold the data:

Code: Select all

+-------------+------+------+------+-------+----------+----------+----------+
| Borderlands | Str  | Dex  | Con  | Total | Str %    | Dex %    | Con %    |
+-------------+------+------+------+-------+----------+----------+----------+
|          19 |  175 |   35 |   31 |  2158 | 8.1094%  | 1.6219%  | 1.4365%  |
|          18 |  376 |  157 |  148 |  2158 | 17.4235% | 7.2753%  | 6.8582%  |
|          17 |  323 |  376 |  381 |  2158 | 14.9676% | 17.4235% | 17.6552% |
+-------------+------+------+------+-------+----------+----------+----------+
+-------------+------+------+------+-------+----------+----------+----------+
| Saldaea     | Str  | Dex  | Con  | Total | Str %    | Dex %    | Con %    |
+-------------+------+------+------+-------+----------+----------+----------+
|          19 |  122 |   24 |   29 |  1620 | 7.5309%  | 1.4815%  | 1.7901%  |
|          18 |  285 |  100 |  111 |  1620 | 17.5926% | 6.1728%  | 6.8519%  |
|          17 |  234 |  268 |  259 |  1620 | 14.4444% | 16.5432% | 15.9877% |
+-------------+------+------+------+-------+----------+----------+----------+
+-------------+------+------+------+-------+----------+----------+----------+
| Shienar     | Str  | Dex  | Con  | Total | Str %    | Dex %    | Con %    |
+-------------+------+------+------+-------+----------+----------+----------+
|          19 |   67 |    7 |   12 |   835 | 8.0240%  | 0.8383%  | 1.4371%  |
|          18 |  136 |   49 |   54 |   835 | 16.2874% | 5.8683%  | 6.4671%  |
|          17 |  125 |  144 |  139 |   835 | 14.9701% | 17.2455% | 16.6467% |
+-------------+------+------+------+-------+----------+----------+----------+
+-------------+------+------+------+-------+----------+----------+----------+
| Kandor      | Str  | Dex  | Con  | Total | Str %    | Dex %    | Con %    |
+-------------+------+------+------+-------+----------+----------+----------+
|          19 |  139 |   30 |   19 |  1467 | 9.4751%  | 2.0450%  | 1.2952%  |
|          18 |  247 |   93 |  106 |  1467 | 16.8371% | 6.3395%  | 7.2256%  |
|          17 |  205 |  216 |  240 |  1467 | 13.9741% | 14.7239% | 16.3599% |
+-------------+------+------+------+-------+----------+----------+----------+
+-------------+------+------+------+-------+----------+---------+----------+
| TwoRivers   | Str  | Dex  | Con  | Total | Str %    | Dex %   | Con %    |
+-------------+------+------+------+-------+----------+---------+----------+
|          19 |  241 |    0 |  213 |  2776 | 8.6816%  | 0.0000% | 7.6729%  |
|          18 |  454 |    0 |  436 |  2776 | 16.3545% | 0.0000% | 15.7061% |
|          17 |  351 |  236 |  399 |  2776 | 12.6441% | 8.5014% | 14.3732% |
+-------------+------+------+------+-------+----------+---------+----------+
+-------------+------+------+------+-------+----------+----------+----------+
| Arafel      | Str  | Dex  | Con  | Total | Str %    | Dex %    | Con %    |
+-------------+------+------+------+-------+----------+----------+----------+
|          19 |   59 |   16 |    8 |   782 | 7.5448%  | 2.0460%  | 1.0230%  |
|          18 |  120 |   46 |   52 |   782 | 15.3453% | 5.8824%  | 6.6496%  |
|          17 |  132 |  126 |  127 |   782 | 16.8798% | 16.1125% | 16.2404% |
+-------------+------+------+------+-------+----------+----------+----------+

[Pallaeon]

Not sure what happened to the statdb but there was a community project that had several orders of magnitude more data points than this. It pretty much conclusively established that blands, arafel, shienar, kandor, and saldaea stat the same across all classes.

[Guest]

Not sure what happened to the statdb but there was a community project that had several orders of magnitude more data points than this. It pretty much conclusively established that blands, arafel, shienar, kandor, and saldaea stat the same across all classes.

Yeah I was looking for that for a while. Though, I cany imagine with percentages that the results would deter much at all between a rate of 2000 and a rate of 200000 samples. Bar no changes are made to the homelands and the data remains honest.

[Thuvia]

For the various Borderlands-type homelands, each stat rolls a range of 9, which can be achieved with a 2d5 (fairly easily ruled out), 4d3, or 8d2. The latter two showed only small differences in my simulations, especially when combined with the other mechanics in statting, but if each homeland has some mix of the two different rolls for their different stats you might see some variation between the homelands.

As far as percentages go, the results, or rather their statistical interpretation, could indeed change with more samples. Taking your data, and simplifying by assuming that each stat is independent of the others (which is not quite true), you can calculate confidence intervals about the sample means for various confidence levels. A larger sample size would have the effect of narrowing the confidence intervals for a given CL.

For your Str=19 data, for instance, a 99.5% CL shows no statistical difference between the 5 homelands. At 90% CL, Kandor does seem to stick out. I haven't examined the data for the other stats, but similar observations are likely. I can't say offhand what the "correct" confidence level for something like this would be, but given the complexity of statting mechanics a larger sample size is always a good thing.

90% CL

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90% CL  Blands  Saldaea  Shienar  Kandor  Arafel
x        175     122      67       139     59
n       2158    1620     835      1467    782

p       8.11    7.53     8.02     9.48    7.54
Low CI -0.95   -1.05    -1.49    -1.23   -1.50
High CI 1.03    1.17     1.72     1.35    1.74
					
Lower   7.16    6.48     6.53     8.24    6.05
Upper   9.14    8.70     9.74    10.83    9.28

95% CL

Code: Select all

95% CL  Blands  Saldaea  Shienar  Kandor  Arafel
x        175     122      67       139     59
n       2158    1620     835      1467    782

p       8.11    7.53     8.02     9.48    7.54
Low CI -1.12   -1.24    -1.75    -1.45   -1.75
High CI 1.23	 1.39	  2.05	  1.61	 2.08
					
Lower   6.99    6.29     6.27     8.02    5.79
Upper   9.34    8.93    10.08    11.09    9.62

99% CL

Code: Select all

99% CL  Blands  Saldaea  Shienar  Kandor  Arafel
x        175     122      67       139     59
n       2158    1620     835      1467    782

p       8.11    7.53     8.02     9.48    7.54
Low CI -1.44   -1.59    -2.24    -1.87   -2.23
High CI 1.63    1.85     2.73     2.14    2.76
					
Lower   6.67    5.94     5.79     7.61    5.31
Upper   9.74    9.38    10.75    11.61   10.31

99.5% CL

Code: Select all

99.5% CL Blands  Saldaea  Shienar  Kandor  Arafel
x         175     122      67       139     59
n        2158    1620     835      1467    782

p        8.11    7.53     8.02     9.48    7.54
Low CI  -1.56   -1.72    -2.41    -2.02   -2.38
High CI  1.78    2.02     2.99     2.34    3.01

Lower    6.55    5.81     5.61     7.45    5.16
Upper    9.89    9.55    11.01    11.81   10.55

[Quantalex]

For your Str=19 data, for instance, a 99.5% CL shows no statistical difference between the 5 homelands. At 90% CL, Kandor does seem to stick out. I haven't examined the data for the other stats, but similar observations are likely. I can't say offhand what the "correct" confidence level for something like this would be, but given the complexity of statting mechanics a larger sample size is always a good thing.

Yeah, you were right. Kandor str and dex rolls were on average pretty high for the first 1K. By 2K, its pretty much the same as the others.

I guess the main problem with statting is the insanely high chance of a statsum of below 75. There's just not enough points to go around.

Code: Select all

Borderlands 80+:     12/3384 = 0.354%
Borderlands 75-79:  513/3384 = 15.159%
Borderlands 70-74: 2858/3384 = 84.456%

Kandor 80+:           6/3333 = 0.180%
Kandor 75-79:       464/3333 = 13.921%
Kandor 70-74:      2863/3333 = 85.598%

Saldaea 80+:         12/1620 = 0.740%
Saldaea 75-79:      222/1620 = 13.703%
Saldaea 70-74:     1386/1620 = 85.555%

85% of your stats will be terrible
13% will be decent
0.3% will have the chance of being amazing

If you get the 0.3% 80+ statsum, you can end up with just high mentals.

[sauin]

Quick question, while your data for the probability of getting a 19 in a certain stat is useful, do you also have the conditional probabilities of getting multiple 19s and is it linear?

i.e. Given the set of all data where a character's STR is 19, does the probability distribution of all characters with 19 DEX in that set remain constant?
Failing that, could I get access to the raw data?

[Quantalex]

Quick question, while your data for the probability of getting a 19 in a certain stat is useful, do you also have the conditional probabilities of getting multiple 19s and is it linear?

i.e. Given the set of all data where a character's STR is 19, does the probability distribution of all characters with 19 DEX in that set remain constant?
Failing that, could I get access to the raw data?

Chances of 2x 19's

Two Rivers: 16/3002 (0.532%) or 1 match every 187 stats

Code: Select all

+----------+----------+----------+----------+----------+
| stat_str | stat_int | stat_wil | stat_dex | stat_con |
+----------+----------+----------+----------+----------+
|       19 |       10 |       11 |       13 |       19 |
|       19 |        9 |       12 |       16 |       19 |
|       19 |       12 |       14 |       15 |       19 |
|       19 |       12 |       14 |       13 |       19 |
|       19 |       13 |       14 |       15 |       19 |
|       19 |       13 |       14 |       11 |       19 |
|       19 |        9 |       13 |       16 |       19 |
|       19 |       15 |       12 |       13 |       19 |
|       19 |       15 |       13 |       13 |       19 |
|       19 |       14 |       17 |       13 |       19 |
|       19 |       10 |       14 |       13 |       19 |
|       19 |       10 |       16 |       14 |       19 |
|       19 |       13 |       12 |       16 |       19 |
|       19 |       12 |       16 |       17 |       19 |
|       19 |        9 |       12 |       11 |       19 |
|       19 |       14 |       15 |       15 |       19 |
+----------+----------+----------+----------+----------+

Borderlands: 5/4290 (0.116%) or 1 match every 858 stats

Code: Select all

+----------+----------+----------+----------+----------+
| stat_str | stat_int | stat_wil | stat_dex | stat_con |
+----------+----------+----------+----------+----------+
|       19 |       11 |       13 |       19 |       16 |
|       19 |       12 |       12 |       16 |       19 |
|       19 |       10 |       11 |       15 |       19 |
|       19 |       11 |       12 |       15 |       19 |
|       19 |       14 |       10 |       13 |       19 |
+----------+----------+----------+----------+----------+

Kandor: 4/3080 (0.129%) or 1 match every 770 stats

Code: Select all

+----------+----------+----------+----------+----------+
| stat_str | stat_int | stat_wil | stat_dex | stat_con |
+----------+----------+----------+----------+----------+
|       19 |       13 |       12 |       15 |       19 |
|       16 |       10 |       13 |       19 |       19 |
|       19 |       14 |       11 |       19 |       15 |
|       13 |       10 |       13 |       19 |       19 |
+----------+----------+----------+----------+----------+

Saldaea: 4/1620 (0.246%) or 1 match every 495 stats

Code: Select all

+----------+----------+----------+----------+----------+
| stat_str | stat_int | stat_wil | stat_dex | stat_con |
+----------+----------+----------+----------+----------+
|       19 |       11 |       13 |       19 |       16 |
|       19 |       15 |        9 |       19 |       15 |
|       19 |       12 |       12 |       19 |       15 |
|       19 |       13 |       12 |       15 |       19 |
+----------+----------+----------+----------+----------+

Arafel: 1/807 (0.123%)

Code: Select all

+----------+----------+----------+----------+----------+
| stat_str | stat_int | stat_wil | stat_dex | stat_con |
+----------+----------+----------+----------+----------+
|       19 |       12 |       14 |       19 |       17 |
+----------+----------+----------+----------+----------+

Shienar: 0/835


For double 9's mentals, two 19's and an 18 you need a minimum statsum of 74.
Bumping the mentals to double 11's yields a minimum statsum of 78.

As far as the raw data goes, well.. I had a bunch, but not anymore. Saw a couple entries with an empty homeland, decided to delete them, ended up deleting everything just now.

Code: Select all

mysql> delete from wotmud.stats WHERE char_homeland="" or char_homeland=0;
Query OK, 15719 rows affected, 15710 warnings (0.12 sec)

Magical.