I did spend the last days (better weeks) on an approximation for overall loot. My main interest was to estimate loot pay out (return rate).
First of all, it is not possible to derive a single loot formula. Loot is rather handmade (
MA). As I mentioned before, I was using several mixture distributions to model loot. Base characteristic is still an exponential distribution, that gets shifted and truncated. To make things short, I was rather successfully to model parts of the loot distribution with a GP model (Generalized Pareto distribution). From those models I was able to identify parameters that are related to the dmg done (HP). Here is what I have atm for mob > 1000 HP:
Loot classes for loot in PEC valid for mobs with HP >1000
Code:
Class p m1 s (k = .25) m2 truncation
C0 1.0000 HP/20
C1(§) .97500 HP*.08 .05
C2(*) HP*2/3
C3 .00375 HP HP/(1-k) 500
C4 .02119 2*HP 2*HP/(1-k) 1000 .001
C5(#) .00005 HP*150
C6(#) .00001 HP*1500
Class denotes the loot classes that I was able to identify. Classes are distinct and separated by gaps. Not all gaps are given here. For simplicity, I didn’t state the ones within C1. C0 is min loot you will get. The given values are empty corrected. Further C1 is normal loot, C2 are peddlers, C3 are globals, C4 hofs and C5, C6 ATH’s.
p is the probability that the given class gets triggered. The given probabilities are not very precise yet, therefore I used the lower limit and they might change when I have more data.
m1 and m2 are location and s is a scale parameter.
For some classes loot get’s truncated, i.e. loot is limited. The given probability is P(loot > x), this implies that you can’t observe loot higher then x for the given probability.
(§) s for class 1 is HP/10. Since there is truncation it must be corrected to .08.
(*) Class C2 is not present in mobs with HP >1000. (#) Classes 5 and 6 are preliminary and not validated yet. Furthermore I’m not sure if C4 to C6 are present in mobs with HP <1000.
(#) class C4 and C5 are preliminary and not very precise yet. Those events are rare and therefore a lot of data is needed, data that I don’t have atm.
To calc mean loot, get mobs HP, calc m1, s, m2 as given, sum them up and multiply by p.
Example Ambu Young with 1010 HP. Due to regain I set dmg done to 1010*1,1 = 1111 HP
Code:
Class P m1 s m2 mean Loot
C0 100% 55.55 55.55
C1 97.5% 88.9 86.68
C3 0.38% 1111 1481.3 500 11.60
C4 2.12% 2222 2962.7 1000 108.23
C5 0.005% 166700 8.33
C6 0.001% 1666500 16.67
Class Class Loot Pec/HP Cum Pec/HP Cum Return rate
C0 55.55 0.050 0.050 15.2%
C1 111.10 0.078 0.128 38.8%
C3 3,092.33 0.010 0.138 42.0%
C4 6,184.67 0.118 0.256 77.7%
C5 166,650 0.008 0.264 80.0%
C6 1,666,500 0.015 0.279 84.5%
Total returned Pec/HP are .279. This corresponds to a return rate of about 85%, assuming a cost of .33 PEC per HP. This fits quite well to the picture we had so far. However, there is still space left, e.g. return rate might be eventually higher.
edit: To get a feeling of loot per class I added the column class loot. It is the expected loot per class without weight. So for ambu in C3 you can expect a mean loot of 31 PED.
With class C3 globals do start but mainly those close to 50-70 PED. So reaching class 3 doesn’t guarantee a reasonable return rate (42%). You need at least a higher global or HOF to get a return over 70%.
Edit: I did confuse PED with PEC for C5 and C6. Table is now updated. Furthermore, I did estimate p of C5 and C6 with a larger dataset. So the probabilities are slightly different now leading to a higher return rate.
Validation:
please note, to validate the model I used Starfinders loot data. If you apply my estimators directly to the global data then you'll get different results due to the truncation at 50 PED.
Code:
Validation (values in PED)
Samples from Jimmy, Kolobok and Woody
Mob n obs exp (C1-C6) exp (C1-C4)
Ambu Y 66 266 309 284
Formidon Y 192 321 335 308
Global data
Mob n obs exp (C1-C6)
Aurli Hunter 202 164 177
Aurli Devastator 376 166 161
Aurli Ravager 645 162 153
Aurli Strong 486 150 141
Aurli Soldier 299 124 115
Ambu Y 718 98 111
Hogglo Y 453 141 115
Not suited
Argonaut Y 487 86 78
Argonaut Hunter 402 170 96
Bery y 95 1.06 0.51
To calc loot I did assume a dmg done of HP*1.1 for all mobs. Since I have no information about effectively dmg done, I have to use this assumption that might lead to underestimation.
As you can see from the validation table the model works rather good for mobs with health > 1000. Mean error is about 4.4 PED.
For the validation of global data I had to estimate the proportion of loot >50 PED per class, since global data is truncated.
Sample size is rather large with global data. As you can see from normal hunting data, Jimmy reached in his test with a size of 66 kills class C4 slightly. Therefore his loot was lower than expected. The Formidon data has a better fit.
To show the flaws of the model I added some low health mob data. Argo Hunter and Bery y don't show a good fit. This is mainly related to the still missing C2 class.