How to analyze loot

[Legion]

Originally Posted by falkao

here some strange finding on mob dmg and mob health.

I used the following 500 HP mobs where I had enough data:

        n    Dmg    Loot    p (vs Aurli)
Argonaut Guard.    287    40    71        
Atrox Old    213    56    74    .001    
Aurli Weak    155    77    67        
Longu Old    66    69    74    .018

loot in the table is median loot. Dmg is the dmg the mob does. p is the p-Value compared to Aurli.

Kaplan Meier

Click to enlarge

Box-Plot

Click to enlarge

Interestingly Atrox with lower dmg loots better than Aurli. The team percentage is the same, 15% with Atrox and 16% with Aurli. So this time the difference can't be explained by a team effect.

I do not hunt Aurli's very often. So do they hit less often than Atrox, or do they always loot?
The difference is 7 PED, which is quite some (10%). I don't think this is a false positive finding, so there must be some kind of explanation.

I think the difference here is mainly just more risk = possible better reward but also bigger chance of loss.

[falkao]

Originally Posted by Legion

I think the difference here is mainly just more risk = possible better reward but also bigger chance of loss.

When I remember right, then Aurlis do loot quite often, more than Atrox. So they have a lower empty rate. Since they loot more often, loot should be lower to get the same mean from them. If this is the case, then this would be an indication that also global loot must be empty corrected before analysis, as we already know from normal loot.

[falkao]

added some comments in the Experimental section of main post.

[falkao]

Originally Posted by Kosh

--
The loot is certainly exponential or if rounded to be discrete, poisson with a small peak at the beginning of the scale. But I feel that by smoothing the function you miss the true distribution here, which is discrete that skips certain ranges altogether.

I found this one here that would be usefully when trying to model single loot values:

Mix Exp Poisson

With this approach every loot value is regarded as a single species independent form all other species. The frequency of one loot value is modeled as an poisson random variable with mean m. The means mi of the different loot values are then modeled by an exponential or mixture of exp distributions. They do the mixture only to achieve a better fit. So there is no interpretation given.

I'm not sure if this approach fits our situation, but for those that like discrete distributions this might be an interesting idea.

[Kosh]

When you say mean Mi, you mean that every loot is exponential with a different parameter (mean)?

If they all have the same mean, the sum of all loots in a hunt would be distributed Erlang with parameters (mean, number of mobs looted).

And again I say, I find the assumption of each loot being independent of the previous very problematic. I know that intuition plays tricks on you when it comes to probability but still. I can not think of a way to check this assumption though.

[Kosh]

Originally Posted by falkao

I found this one here that would be usefully when trying to model single loot values:

Mix Exp Poisson

With this approach every loot value is regarded as a single species independent form all other species. The frequency of one loot value is modeled as an poisson random variable with mean m. The means mi of the different loot values are then modeled by an exponential or mixture of exp distributions. They do the mixture only to achieve a better fit. So there is no interpretation given.

I'm not sure if this approach fits our situation, but for those that like discrete distributions this might be an interesting idea.

That is very interesting. So if we go by this we should try to divide the below global loot of a certain mob or HP into classes, then check the hypothesis that the classes distribute poisson, and inside every class is distributed exponential. This sounds worthwhile to check for mining too, in this case the classes are quite obvious.

[falkao]

Originally Posted by Kosh

That is very interesting. So if we go by this we should try to divide the below global loot of a certain mob or HP into classes, then check the hypothesis that the classes distribute poisson, and inside every class is distributed exponential. This sounds worthwhile to check for mining too, in this case the classes are quite obvious.

I guess it goes the other way around. From the observed data you build i classes. The count (number of loots) of each class is poisson distributed with mean mi (expected number of events during a specified time period). So every class can have it's own mean. The means mi itself are exponentially distributed or more generally follow a mixture of exp. distributions (hyper-exponential, phase-type dist).

In letting the counts of a single class being poisson distributed you model the observation time. This is not the case with my approach.

Counts within classes are iid from other classes, but since the mean do follow a mix exp you model indirectly a dependency.

[Noodles]

Originally Posted by Kosh

And again I say, I find the assumption of each loot being independent of the previous very problematic. I know that intuition plays tricks on you when it comes to probability but still. I can not think of a way to check this assumption though.

There are methods involving correlation analysis that could get at your concern. Not that I know much about the mathematics of these methods, but they do exist . . .

[falkao]

here some further testing on ambus with an exp mixture.

if I use a 2 phase model and assume truncation at 50 PED (so not a shift by 50) I get the following estimates. (I changed from MLE to EM estimation, but thats only for those that are interested how to estimate).

m2 =
p	m	pt	pe
0.05108	226.02	0.8015	0.01764
0.94892	37.912	0.2674	0.98235

p is the relative frequency of the respective exp dist within global loot. m is the respective mean, pt is the rel. freq. within the truncated observations as expected from the respective exp distribution and finally pe is the effective rel. freq without truncation.

With the 2 phase model we get one exp with mean 37.9 and a relative frequency within global loot of 95%. The second has mean 226 and a rel. freq of 5%. An exp dist. with mean 37.9 would have about 27% of all observations after the truncation point of 50 PED. For the second dist this is 80%.

So for every dist we have

pt_i * pe_i = p_i

this can be resolved to pe_i = p_i/pt_i * n
where n is a normalizing constant and is equal to sum(p_i/pt_i).

This gives the above depicted pe. So the real rel. frequency of the first dist. with mean 37.9 is 98% and that of the second with mean 226 is 2%.

So what does that mean?

If the assumption "that we observe truncated data" is right, then there are two loot distributions. The first has mean 37.9 PED and is triggered in 98% of cases. Only about 27% of the values from dist dist lead tio globals. The second has mean 226 and is triggered in about 2% of all loots. About 80% of the values from this dist. lead to globals. So it looks as we are able to estimate from global loot also one part of the non observable loot.

One further thing. It might be that MA sets an upper limit. With an exp distribution you would be able to generate an infinity high loot. Therfore I guess they truncate the propability at .001 or .0001. The respective multipliers would be abou 7 and 9. So maximally 259-333 PED would be generated by the first dist and 1582-2034 from the second.

Loot expectation for the m2 model is 41.23 PED

For a 3 phase model I get the following:

m3 =
p	m	pt	pe
0.65368	57.103	0.4166	0.17237
0.34144	16.164	0.0453	0.82706
0.00488	957.13	0.9491	0.00056

the 3 phase model fits quite better. However, I have some diffculties to understand the exp dist with mean 16. If this dist. existst, then there is so much in the global data, that we are able to extract it. Maybe this is the distribution for the pedders.

Loot expectation for the m3 model is 23.75 PED

[Noodles]

Originally Posted by falkao

One further thing. It might be that MA sets an upper limit. With an exp distribution you would be able to generate an infinity high loot. Therfore I guess they truncate the propability at .001 or .0001. The respective multipliers would be abou 7 and 9. So maximally 259-333 PED would be generated by the first dist and 1582-2034 from the second.

Fabulous work falkao. Didn't I just see a 10k+ ambu either yesterday or the day before? Is that in conflict with your truncation hypothesis? Or would the 10k+ ambu be a part of another distribution?

Wish I had more time to help with this. Hopefully this summer.