falkao
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- Marc falkao Falk
This thread will give basic insights into mining loot and here is a summary of what we were able to identify so far.
I have first to say thanks to Steffel and Noodles for providing their data and to make it public. This is not a matter of course. I have seen many Avas hiding their data or not willing to share.
The set consists first of 7360 drops with MF105 + MA104, 1998 of them had a find. This corresponds to a find rate of 27.1%. If you have followed the loot analysis thread, you'll know that the inverse of the find rate gives the mean waiting time for the next drop. This leads to 3.68 drops until a find. This can be depicted as follows.
fig.1: Wait in drops until find.
[br]Click to enlarge[/br]
Using an exponential distribution I can estimated the waiting time which leads again to 3.68. So the set fits to perfectly random waiting times.
Adding also Noodles data we have a total of n = 3925 finds, 78.9% of them are enmatter and 21.1% ore finds. Since taxation is evident in lower loot classes, the amp effect is multiplicative and the difference between enamtter and ore is known, all finds have been standardized using the following equation:
Loot Std = Loot /(1-Tax)/Amp/c,
where c is a correction factor, c=1 for enmatter, c=2 ore
For the find rate there are several possibilities. The estimated 95% confidence interval ranges from 26.1% to 28.2% and hence values between 26% and 28% do look reasonable. However, we do have no data about a skill or equipment related find rate and hence we're not sure if this find rate can be considered as universally valid.
There is a small difference in median loot (about 10 PEC) between Steffel and Noodles data, but not different between ore and enmatter (p = 0.027 and p = .152 respectively). Since Steffel was mining only 4 different enmatter types, the difference might also be related to rounding and having a large dataset we're able to detect small differences that might not be relevant.
tab. 1: Finds according to miners. n = 3925, values in PED, p=.027 Mann-Whitney U-test.
There is however an exception between enmatters. Melchi Water seems to have a lower mean loot, whereas Alicenies Liquid has a higher one.
Fig. 2: Mean loot according to miner and resource type
[br]Click to enlarge[/br]
[br]Click to enlarge[/br]
Loots distribution is depicted in the next fig 3.
[br]Click to enlarge[/br]
Please note the log scale on mining loot (log base 3 was used as explained later on). As one can clearly see, loot is split up in so called loot classes, i.e. loot is more frequent in those classes and between classes there are gaps.
As you may have noticed, there are sometimes observations between classes in the gaps. Those observations are most probably related to rounding/truncation as a consequence of res TT or taxation. Therefore I do consider them as noise.
To get a more or less noise free signal I used a kernel estimator to derive class limits. Here is an example
Fig. 4: Noise identification using a kernel density estimator, showing class C1 and C2
[br]Click to enlarge[/br]
Every datapoint below the visually identified noise level (.117 in the figure) gets eliminated. Here C1 in a higher resolution:
[br]Click to enlarge[/br]
Loot class limits are derived from the denoised signal and means per class can be calculated. The denoising has the further advantage, that we get a more general representation not so bound on the observed data.
The most interesting find about those class means is, that they are closely related to the class number as shown in the next fig.
Fig. 5: Log Loot class means per class number
[br]Click to enlarge[/br]
I used a log scale (ln) so that the correlation is better visible. The real correlation has an exponential form. Fitting such a model to the observed data results in the following equation
Mean class loot = .215*exp(1.099*class)
This formula can be reexpressed as
Mean class loot = .215*exp(1.099)^class = .215*3^class
There is nothing natural behind this formula and since a human being invented it, I’m rather sure that the real one might look like this
Loot model
Mean class loot = .22*3^class (PED) or .21*3^class (PED).
All this would lead to the following loot table assuming loot = .22*3^class PED:
Table 2: Loot classes, for ore use a multiplier of 2
All values are expressed in PED
obs.mean = observed mean
w.mean = weighted mean
cum w.mean = cum. weighted mean
rr = return rate, assuming a find rate of 27% and the below explained costs.
Class 0 and classes above 6 are only given for completeness and are not observed in the data.
My first assumption about class 1.66 was that it comes from rounding, but that didn't prove to be correct. Class 2.66 looks also artificial but the gap from about 1 PED can't be explained in another way, therefore I kept it in the model.
Overall return rate till class 6 should be close to 95% assuming a cost of .528 PED per drop including finder and driller decay. Till class 5 (globals) you should get 88% back, till C4 (minis) 81%. Below that (normal loot) only about 71%.
Limitations:
Results are not validated using an independent dataset and hence the model might overfit the data.
As depicted in the next figure, using bootstrapping, the observed mean loot is 1.94 PED ranging from 1.79 to 2.18 PED (95% confidence interval using bootstrapping with 100k samples). This would lead to a return rate from 90.5% to 110%. Hence the estimated 95% from the model lies within those ranges.
fig.6: Kernel density of mean loot using bootstrapping
[br]Click to enlarge[/br]
Some applications of the loot model.
Loot simulation
We can use the mining loot model to simulate loot. With this we'll get a feeling about the distribution of return or return rate. For simplicity we've used the return rate.
The following setup was used:
1) run length 1k drops, 10k runs
2) run length 10k drops, 10k runs
3) run length 100k drops, 10k runs
fig.7: Simulated return rate of mining runs
[br]Click to enlarge[/br]
The different runs can come from different avas or the same ava, counting every run separately.
What we can observe is, that all run types do lead to the same expected mean but do have a different variance. Runs with a short run length (less drops) do spread more. This is a consequence of having a right tailed loot distribution.
Furthermore, when runs do come from different avas, then there will be avas that do profit, about 40% with 1k drops and 20% with 10k drops. If all avas do 100k drops, then there are still differences between them but they are smaller and all close to expected mean return rate.
So what does all that imply? Is it possible to profit when doing short runs? Yes and no. Due to the loot distribution that MA is using, those that play only for limited time and hence doing a lower number of drops, do have a 40% chance to profit from loot only.
(Hence we will have 40% noobs that are telling how able miners they are.) If those go on, their return rate will become lower and converge to the expected mean return. The contrary is also true. If those that were unlucky continue mining, then they will higher their return rate.
Why are sizes missing when using amps?
Loot is based on loot classes with respective weights. Hence when looting, first a class is drawn, amp is applied and tax detracted. This loot value is then expressed as size. Since sizes have fixed limits, it might happen when amped that some sizes are missing.
Here an example of loot class limits with amp 4, values in PED and using a res with TT = .01 as reference:
Size Tiny II goes from .32 to .99 PED (according to wiki). Since the first loot class starts at 2 PED size II can't be observed. Similarly, size III ranging from 1 to 1.99 PED can only be observed when taxed. However, the frequency of a size 3 will increase for higher TT res, due to rounding.
Here the same tab as before but with a .96 TT res.
As one can see, limits are slightly different. This is a consequence of rounding.
If we go on we will discover that also size 12 (35-49.99) and size 17 (303-449) will be missing.
I have first to say thanks to Steffel and Noodles for providing their data and to make it public. This is not a matter of course. I have seen many Avas hiding their data or not willing to share.
The set consists first of 7360 drops with MF105 + MA104, 1998 of them had a find. This corresponds to a find rate of 27.1%. If you have followed the loot analysis thread, you'll know that the inverse of the find rate gives the mean waiting time for the next drop. This leads to 3.68 drops until a find. This can be depicted as follows.
fig.1: Wait in drops until find.
[br]Click to enlarge[/br]Using an exponential distribution I can estimated the waiting time which leads again to 3.68. So the set fits to perfectly random waiting times.
Adding also Noodles data we have a total of n = 3925 finds, 78.9% of them are enmatter and 21.1% ore finds. Since taxation is evident in lower loot classes, the amp effect is multiplicative and the difference between enamtter and ore is known, all finds have been standardized using the following equation:
Loot Std = Loot /(1-Tax)/Amp/c,
where c is a correction factor, c=1 for enmatter, c=2 ore
For the find rate there are several possibilities. The estimated 95% confidence interval ranges from 26.1% to 28.2% and hence values between 26% and 28% do look reasonable. However, we do have no data about a skill or equipment related find rate and hence we're not sure if this find rate can be considered as universally valid.
There is a small difference in median loot (about 10 PEC) between Steffel and Noodles data, but not different between ore and enmatter (p = 0.027 and p = .152 respectively). Since Steffel was mining only 4 different enmatter types, the difference might also be related to rounding and having a large dataset we're able to detect small differences that might not be relevant.
tab. 1: Finds according to miners. n = 3925, values in PED, p=.027 Mann-Whitney U-test.
There is however an exception between enmatters. Melchi Water seems to have a lower mean loot, whereas Alicenies Liquid has a higher one.
Fig. 2: Mean loot according to miner and resource type
[br]Click to enlarge[/br]
[br]Click to enlarge[/br]Loots distribution is depicted in the next fig 3.
[br]Click to enlarge[/br]Please note the log scale on mining loot (log base 3 was used as explained later on). As one can clearly see, loot is split up in so called loot classes, i.e. loot is more frequent in those classes and between classes there are gaps.
As you may have noticed, there are sometimes observations between classes in the gaps. Those observations are most probably related to rounding/truncation as a consequence of res TT or taxation. Therefore I do consider them as noise.
To get a more or less noise free signal I used a kernel estimator to derive class limits. Here is an example
Fig. 4: Noise identification using a kernel density estimator, showing class C1 and C2
[br]Click to enlarge[/br]Every datapoint below the visually identified noise level (.117 in the figure) gets eliminated. Here C1 in a higher resolution:
[br]Click to enlarge[/br]Loot class limits are derived from the denoised signal and means per class can be calculated. The denoising has the further advantage, that we get a more general representation not so bound on the observed data.
The most interesting find about those class means is, that they are closely related to the class number as shown in the next fig.
Fig. 5: Log Loot class means per class number
[br]Click to enlarge[/br]I used a log scale (ln) so that the correlation is better visible. The real correlation has an exponential form. Fitting such a model to the observed data results in the following equation
Mean class loot = .215*exp(1.099*class)
This formula can be reexpressed as
Mean class loot = .215*exp(1.099)^class = .215*3^class
There is nothing natural behind this formula and since a human being invented it, I’m rather sure that the real one might look like this
Loot model
Mean class loot = .22*3^class (PED) or .21*3^class (PED).
All this would lead to the following loot table assuming loot = .22*3^class PED:
Table 2: Loot classes, for ore use a multiplier of 2
All values are expressed in PED
obs.mean = observed mean
w.mean = weighted mean
cum w.mean = cum. weighted mean
rr = return rate, assuming a find rate of 27% and the below explained costs.
Class 0 and classes above 6 are only given for completeness and are not observed in the data.
My first assumption about class 1.66 was that it comes from rounding, but that didn't prove to be correct. Class 2.66 looks also artificial but the gap from about 1 PED can't be explained in another way, therefore I kept it in the model.
Overall return rate till class 6 should be close to 95% assuming a cost of .528 PED per drop including finder and driller decay. Till class 5 (globals) you should get 88% back, till C4 (minis) 81%. Below that (normal loot) only about 71%.
Limitations:
Results are not validated using an independent dataset and hence the model might overfit the data.
As depicted in the next figure, using bootstrapping, the observed mean loot is 1.94 PED ranging from 1.79 to 2.18 PED (95% confidence interval using bootstrapping with 100k samples). This would lead to a return rate from 90.5% to 110%. Hence the estimated 95% from the model lies within those ranges.
fig.6: Kernel density of mean loot using bootstrapping
[br]Click to enlarge[/br]Some applications of the loot model.
Loot simulation
We can use the mining loot model to simulate loot. With this we'll get a feeling about the distribution of return or return rate. For simplicity we've used the return rate.
The following setup was used:
1) run length 1k drops, 10k runs
2) run length 10k drops, 10k runs
3) run length 100k drops, 10k runs
fig.7: Simulated return rate of mining runs
[br]Click to enlarge[/br]The different runs can come from different avas or the same ava, counting every run separately.
What we can observe is, that all run types do lead to the same expected mean but do have a different variance. Runs with a short run length (less drops) do spread more. This is a consequence of having a right tailed loot distribution.
Furthermore, when runs do come from different avas, then there will be avas that do profit, about 40% with 1k drops and 20% with 10k drops. If all avas do 100k drops, then there are still differences between them but they are smaller and all close to expected mean return rate.
So what does all that imply? Is it possible to profit when doing short runs? Yes and no. Due to the loot distribution that MA is using, those that play only for limited time and hence doing a lower number of drops, do have a 40% chance to profit from loot only.
(Hence we will have 40% noobs that are telling how able miners they are.) If those go on, their return rate will become lower and converge to the expected mean return. The contrary is also true. If those that were unlucky continue mining, then they will higher their return rate.
Why are sizes missing when using amps?
Loot is based on loot classes with respective weights. Hence when looting, first a class is drawn, amp is applied and tax detracted. This loot value is then expressed as size. Since sizes have fixed limits, it might happen when amped that some sizes are missing.
Here an example of loot class limits with amp 4, values in PED and using a res with TT = .01 as reference:
Code:
Class lower upper
1 2.0 3.3
1.66 5.0 5.9
2 5.9 9.9
2.66 15.3 17.4
3 17.8 29.7
4 53.5 89.1
...Size Tiny II goes from .32 to .99 PED (according to wiki). Since the first loot class starts at 2 PED size II can't be observed. Similarly, size III ranging from 1 to 1.99 PED can only be observed when taxed. However, the frequency of a size 3 will increase for higher TT res, due to rounding.
Here the same tab as before but with a .96 TT res.
Code:
Class lower upper
1 1.9 2.9
1.66 4.8 5.8
2 5.8 9.6
2.66 15.4 17.3
3 18.2 29.8
4 53.8 89.3
5 160.3 266.9
6 481.0 801.6
...As one can see, limits are slightly different. This is a consequence of rounding.
If we go on we will discover that also size 12 (35-49.99) and size 17 (303-449) will be missing.
Last edited:
so how is tax generated if not taken from the claims...two ideas: 1) mining aint taxed (although i remember one landowner once was ableto confirm a tower being on his land due toimmediate tax receipt) or 2) tax does not apply to the find but is taken from your expenditures, ala "expenses - tax => lootpool"...
