How to analyze loot

[falkao]

Originally Posted by kalanen

In your another excellent thread I suggested "seed value" from where loot is modified to hunter's final reward, to be 5pecs * stamina. That's because somewhere around y 200px was very dense dark area of lines with very little spread. Other "slots": *0.5, *0.25, *2 and *4 had clear limits too but spread was higher.

I'm atm waiting for some more data and reanalyzing what I have so far. I have to check your 5pecs assumptions on stamina (HP = 10 * stamina if I'm right?). I do get atm someting between 2 and 5Pec on HP.

[kalanen]

Originally Posted by falkao

I'm atm waiting for some more data and reanalyzing what I have so far. I have to check your 5pecs assumptions on stamina (HP = 10 * stamina if I'm right?). I do get atm someting between 2 and 5Pec on HP.

Loot of 3rd/4rd slot (which is above cost of kill with practically any weapon with no skills) has been very rare. The point is, that around stamina * 5pecs loots had least spread around it. So (im not a meth boy as you can see) I gathered that has to be some sort of seed, root or whatever.

If loots around 210 pecs had upper limit of 220 and lower limit of 200 pecs, loots around 1 ped had limits of 75 pecs to 130 pecs or so.

Nowadays loots around 1/2 and 1/4 of "cost of kill" are the most common. Peeps shoot. Peeps get loot. Peeps come home with 50% or less return. The effect of maxed sib weaponry neutralized. Less skills. Good work. Eco means shit.

[Acronoid]

I very much enjoy this thread, you have no Idea

Keep up the good work

[falkao]

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

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

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.

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.

[sempul]

wow my head hurts. but on a plus side great job, i think like i said my head hurts

[falkao]

Originally Posted by sempul

wow my head hurts. but on a plus side great job, i think like i said my head hurts

mine too . I'm sure there are not much persons that will understand the details of what I have posted. Not to offend anybody, but this was one of my trickiest tasks so far.

However, the main message is. We can judge the return rate and it seems that for mobs with HP >1000 it is over 77%. This can be achieved by a normal player. For classes C4 and C5 you'll need a lot of luck or you play for ages. Nevertheless, you'll get only 7% more.

So for the invested peds you'll get 77% back. Assume a markup of 120%, which is reasonable, then you'll end up to nearly break even (92%) plus you've got skills that you can sell.


Please note, these are results for 1000-5000 HP mob. I don't have enough data for mob <1000 atm. Furthermore I'm sure, that p for C1-C3 are higher in lower hp mobs with regard to higher ones. This might also explain why high HP mobs do global more often and might also explain why Jimmy's insane test.

[Noodles]

I'm soon ready to help with puny mob data. Killed over 700 sabakumas (young-old) in search of my shogun gloves. Still have gnome arms to go, so many more are going to have to bite the dust.

Here's the teaser:
Tentative conclusion about no loots: Somewhere between 55% and 60%.

I'll have some time to work with/post the data in one or two weeks.

[falkao]

Originally Posted by Noodles

I'm soon ready to help with puny mob data. Killed over 700 sabakumas (young-old) in search of my shogun gloves. Still have gnome arms to go, so many more are going to have to bite the dust.

Here's the teaser:
Tentative conclusion about no loots: Somewhere between 55% and 60%.

I'll have some time to work with/post the data in one or two weeks.

that sounds great. I have a set of 300 and 40 HP mob from which I was able to derive C2. Unfortunately to conclude something for C4 upwards I'll need a quite large sample (500 loots without no loots).

[falkao]

I've added the validation to my previous post.

Now it's up to you.

Furthermore I want to ask if there is a need to show how to derive a model like the one mentioned. It will be more complicated than what is already stated, so I'm afraid, although showing what I did, only a minority might understand.

All what is left now is some lower hp mob data. What I need to know are the p's for C2-C4.

Furthermore, It would be interesting to see if there are changes over time. I guess MA is constantly tweaking the system. So it might happen that one p or shift or shape gets larger or smaller.

Nevertheless, I found my answers already, so from my point of view we can close the thread.

[falkao]

here some figures from simulated data using the above mentioned model:

fig. 1 Simulated ambu loot in PED


Click to enlarge

Please don't be afraid about the strange fig. 1. But this is what we have in EU. Loot for Ambu y will be lower than 5 PED in 97% of cases. As already explained return rate is rather ok. If you play for some time it should be over 70%. Btw, roulette would have something near 90%, horse betting about 75% and lottery about 50%.

fig. 2 Simulated Ambu Globals. The same data as in fig1 but truncated at 50 PED. Furthermore the x-axes is shifted by 50 PED, therefore 0 = 50 PED.


Click to enlarge

Simulation was done with 100k kills. In 2.5% of cases loot would be in class3 and above and about 50% of them will be over 50 PED and hence a global. So in total I have in the global data about 1280 cases. What can be clearly seen is the rounding in the observed data and the rather good fit of the model. Furthermore, you need quite some kills to get an impression of loot as seen in the following fig. with n= 1000 simulated kills.

Fig. 3 Ambu globals for a total of 1000 kills


Click to enlarge

Personal comments. MA’s loot system is ok for me. The return rate is acceptable. However, a system like that will lead to whining and will give you an impression of gambling. On the other site there is the kick to global and this might be a nice surprise as we see in the global threads.
So it’s up to you how to deal with it.