Treasure Hunter Testing

[Motenten]

Here's the grouping data for those parses:

TH0:
       Dropped  0 items   785 times ( 78.34 %)
       Dropped  1 items   189 times ( 18.86 %)
       Dropped  2 items    23 times (  2.30 %)
       Dropped  3 items     5 times (  0.50 %)


    Number of times each group of items dropped.

      785 [ 78.34 %] -- Nothing
      101 [ 10.08 %] -- tuft of dhalmel hair
       68 [  6.79 %] -- slice of dhalmel meat
       12 [  1.20 %] -- giant femur
        8 [  0.80 %] -- slice of dhalmel meat, slice of dhalmel meat
        7 [  0.70 %] -- dhalmel hide
        6 [  0.60 %] -- slice of dhalmel meat, tuft of dhalmel hair
        4 [  0.40 %] -- giant femur, slice of dhalmel meat
        3 [  0.30 %] -- giant femur, tuft of dhalmel hair
        2 [  0.20 %] -- giant femur, slice of dhalmel meat, tuft of dhalmel hair
        1 [  0.10 %] -- dhalmel hide, sprig of papaka grass
        1 [  0.10 %] -- sprig of papaka grass
        1 [  0.10 %] -- dhalmel hide, dhalmel hide
        1 [  0.10 %] -- slice of dhalmel meat, slice of dhalmel meat, tuft of dhalmel hair
        1 [  0.10 %] -- dhalmel hide, sprig of papaka grass, tuft of dhalmel hair
        1 [  0.10 %] -- giant femur, slice of dhalmel meat, slice of dhalmel meat

TH1:
       Dropped  0 items   598 times ( 59.80 %)
       Dropped  1 items   272 times ( 27.20 %)
       Dropped  2 items   101 times ( 10.10 %)
       Dropped  3 items    29 times (  2.90 %)


    Number of times each group of items dropped.

      598 [ 59.80 %] -- Nothing
      143 [ 14.30 %] -- slice of dhalmel meat
      101 [ 10.10 %] -- tuft of dhalmel hair
       57 [  5.70 %] -- slice of dhalmel meat, slice of dhalmel meat
       22 [  2.20 %] -- giant femur, slice of dhalmel meat
       18 [  1.80 %] -- slice of dhalmel meat, tuft of dhalmel hair
       17 [  1.70 %] -- slice of dhalmel meat, slice of dhalmel meat, tuft of dhalmel hair
       12 [  1.20 %] -- dhalmel hide
       12 [  1.20 %] -- giant femur
        6 [  0.60 %] -- giant femur, slice of dhalmel meat, slice of dhalmel meat
        4 [  0.40 %] -- sprig of papaka grass
        3 [  0.30 %] -- giant femur, slice of dhalmel meat, tuft of dhalmel hair
        2 [  0.20 %] -- dhalmel hide, slice of dhalmel meat
        1 [  0.10 %] -- dhalmel hide, sprig of papaka grass
        1 [  0.10 %] -- dhalmel hide, giant femur, slice of dhalmel meat
        1 [  0.10 %] -- giant femur, slice of dhalmel meat, sprig of papaka grass
        1 [  0.10 %] -- dhalmel hide, dhalmel hide, dhalmel hide
        1 [  0.10 %] -- giant femur, tuft of dhalmel hair

TH2:
       Dropped  0 items    97 times ( 48.50 %)
       Dropped  1 items    66 times ( 33.00 %)
       Dropped  2 items    26 times ( 13.00 %)
       Dropped  3 items     7 times (  3.50 %)
       Dropped  4 items     4 times (  2.00 %)

    Number of times each group of items dropped.

       97 [ 48.50 %] -- Nothing
       41 [ 20.50 %] -- slice of dhalmel meat
       21 [ 10.50 %] -- tuft of dhalmel hair
       14 [  7.00 %] -- slice of dhalmel meat, slice of dhalmel meat
        6 [  3.00 %] -- slice of dhalmel meat, tuft of dhalmel hair
        4 [  2.00 %] -- giant femur, slice of dhalmel meat
        4 [  2.00 %] -- giant femur, slice of dhalmel meat, slice of dhalmel meat, tuft of dhalmel hair
        3 [  1.50 %] -- slice of dhalmel meat, slice of dhalmel meat, tuft of dhalmel hair
        2 [  1.00 %] -- giant femur, tuft of dhalmel hair
        2 [  1.00 %] -- dhalmel hide
        2 [  1.00 %] -- giant femur
        1 [  0.50 %] -- dhalmel hide, slice of dhalmel meat, tuft of dhalmel hair
        1 [  0.50 %] -- dhalmel hide, dhalmel hide, sprig of papaka grass
        1 [  0.50 %] -- giant femur, slice of dhalmel meat, tuft of dhalmel hair
        1 [  0.50 %] -- dhalmel hide, dhalmel hide, slice of dhalmel meat

I got a maximum of 4 drops with TH2. Given the probabilities of the highest dropping items (24% for each meat, 19% for hair, 7% for femur), the best chance of getting a 5-item drop pool assuming all drops are fully independant is 0.018%, or 1 in 5500. Since I only killed 200 in TH2, and 1000 in the others, it is not at all surprising that I didn't see that many at once.

The odds of a femur/meat/meat/hair drop (the only 4-drop combo) given the above probabilities is 0.17%. I 'should' have seen such a combo only once in 570 kills, but instead got 4 in 200. 0.17% is actually outside the confidence interval for 4/200, so there's certainly more to be considered.


Given possible drops of:
dhalmel meat (x2)
dhalmel hide (x3)
dhalmel hair
giant femur
papaka grass

A total of 8 items, which should be perfectly fine within the known limits of the game.

Combinations of items include:
femur/meat/meat/hair -- femur, meats and hair are all independant
hide/hide/grass -- grass is independant of at least 2 of the hide drops
hide/grass/hair -- hair is independant of at least one of the hide drops as well as grass
hide/femur/meat -- one hide is independant of femur and at least one of the meat drops
femur/meat/grass -- grass is independant of femur and at least one of the meats
hide/hide/meat -- at least one of the meats is independant of two hides


Even assuming some of the items can share drop slots, at best you're getting the third hide shared with the femur, the grass, the hair or the second meat. Such a limited combination seems rather pointless. I could maybe see the third hide being shared with the hair since the hair is a new drop for those mobs compared to previous dhalmels, but since the hides aren't part of the main analysis comparison here due to their relatively low drop rate it wouldn't matter much.


Reviewing the meat distributions:

TH0 data:
100 total
90 instance (kills with at least 1 meat)
10 2x drops

Raw drop rate: 100/1002 = 10%
Drop rate of total/(kills*slots) = 100/2004 = 5.0% (4.1%-6.0%)
Unique drop rate = 90/1002 = 9.0% (7.4%-10.9%)
Ratio of double to instance: 10/90 = 11.1% (6%-19.4%)


TH1 data:
350 total
270 instance
80 2x drops

Raw drop rate: 350/1000 = 35%
Drop rate of total/(kills*slots) = 350/2000 = 17.5% (15.9%-19.2%)
Unique drop rate = 270/1000 = 27.0% (24.3%-29.8%)
Ratio of double to instance: 80/270 = 29.7% (24.5%-35.3%)


TH2 data:
96 total
75 instance
21 2x drop

Raw drop rate: 96/200 = 48%
Drop rate of total/(kills*slots) = 96/400 = 24% (20%-28%)
Unique drop rate = 75/200 = 37.5% (31.1%-41.4%)
Ratio of double to instance: 21/75 = 28% (19%-39%)



You'll note that in each instance, the rate of double drops is higher than it should be if they were fully independent (compare double-to-instance ratio with total-per-kill*shot ratio). Margin of error for TH0 and TH1 also don't overlap between the two measures. TH2 overlaps, but 2x drop ratio is mostly higher than nominal drop rate.


Suppose we assume that the second meat can only drop if the first meat drops. That is, they are not two independent slots, but one independent slot and one dependent slot.

The drop rate on the independent slot can be determined by the number of unique kills where that item appeared (unique-drop-rate ratio). In this case, that gives 9%, 27% and 37.5% for TH0/1/2, respectively.

In that case, the odds of the second drop appear to always be within the margin of error of the unique drop rate ratio.

Implication: this is where multiple rolls come in. EG: Chance of main drop is 10%. If successful, you can make another roll on the second slot, but still with the 10% chance. This works for the (roughly) 9% TH0, 27% TH1 and 36% TH2 for the above data.

Expected overall drop rate given those rough guesstimates:
TH0: 9% + (9%*9%) = 9.8% (actual: 10%)
TH1: 27% + (27%*27%) = 34.3% (actual: 35%)
TH2: 36% + (36%*36%) = 49.0% (actual: 48%)


It's impossible to figure out if it works the same on the hide drops due to how few sample points there are (I suspect that they have a higher base chance of a second drop; it would be reasonable to have a minimum 10% chance on the second roll), however the above scale makes me rather confident that that is in fact how the multi-drop system works.