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FYI: Estimating time to expected value with some math... (handy shaded table included)

Jhereg

Jhereg

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Feng Huan SecretAznMan Zho
Hi everyone. After the many times I've seen the comment "Keep Shooting" or "I can't believe my returns are so bad" or "Look I have 100%+ TT return after 2000 kills so efficiency/looter doesn't matter and I hacked the system", I thought it was time to produce some quantitative data on evaluating your return % and, more importantly, how much confidence you can have that the TT% you have is near your expected value.

Many thanks to @miathan for access to his pytropia suite (https://github.com/opentropia/pytropia), along with his multiplier distribution data that he collected of a large number of loot samples. I was able to use his multiplier distribution, and run a large number of simulated hunts over different number of kills per hunt, to generate the table below.

One caveat: This distribution represents the generally most common loot distribution for mobs in game, but there is at least one other distribution for larger mobs, where the minimum multiplier is larger...so if you are using this on larger mobs, this may not be full reflective of the actual probabilities and will underestimate your chance to achieve expected %...

How to understand the table
Each column is hunts with a certain number of loot events (i.e. number of mobs killed). I've normalized a player's expected value, or EV (what their expected tt% will be after an infinite number of kills) to 100%. So whatever your expected loot return % should be (whether it is 90% or 99%), in this table, it is represented by 100%.

The leftmost column represents a threshold for observed return %, as a percentage of EV... This represents what percentage of your EV you want to achieve. The table shows the percent chance of achieving that performance or better.

As an example, if you want to know what the probability is of achieving 95% of your EV or better after 1000 kills, the table shows that you have a 56% chance of achieving that, versus after 10k kills, you would be at 83%. To flip that around, after 1000 kills, you have a almost 50/50 chance to be worse than 95% of your expected value versus better, while at 10000 kills, you have a 3 out of 20 chance of being worse than 95% of your expected value.
If you expect your long term expected tt% to be 98%, then you would have to multiply that 98% by the 95% here to get your real TT% threshold that you are evaluating for...

Hopefully this is useful, and again, thank you @miathan for all of your help and data gathering :). He is the real MVP here.

Updated with a couple more columns...

WnWCWGS.png
 
Last edited:
Updated with a couple more columns...
 
Thanks to both you @Jhereg and @miathan for the contribution! Greatly apreciated compiled data!
 
its interesting thing
the more we hunt the less a chance to break even vs TT

its not surprising, but now we have some numbers

thanks for the work
 
I take it you rely on the assumption that looting instances are independent and identically distributed draws from the multiplier distribution; otherwise I think you'd need more sophisticated machinery like an order-m Markov chain to model this. Lots of players believe their returns decrease following a large HOF in a non-I.I.D. fashion. Do you have any data to warrant the I.I.D. assumption?
 
TheOneOmega said:
I take it you rely on the assumption that looting instances are independent and identically distributed draws from the multiplier distribution; otherwise I think you'd need more sophisticated machinery like an order-m Markov chain to model this. Lots of players believe their returns decrease following a large HOF in a non-I.I.D. fashion. Do you have any data to warrant the I.I.D. assumption?
Click to expand...
The many times that MA has stated that there's no personal loot pool, i.e. no mechanism for 'kickbacks'. So I do assume all loot events are independent based on this.

If miathan wants to chime in , I believe he has not seen anything to suggest otherwise as well in his tracking.
 
Very interesting post, cheers for time and patience to make it.
 
So the answer is..?

200,000?

Unless a hunter has tracked over at least 200,000 kills, they have no right to complain about their returns because, as they say: "You need a larger sample size"

Well I'll be damned. How long would that take? I'm level 50, have I even killed 200,000 yet?

Well, a bit of math could help, so if it takes me 12 seconds to kill 1 mob, then it would take me 666.67 hours to kill 200,000 :eek:

Really!? You need to hunt for 667 hours to have a level of confidence near 100% over your 97% returns??? That seems crazy to me...
 
I understand the pretty colors, good job.
 
This is very cool, I am not a hunter but I respect the effort..
 
Legends said:
So the answer is..?

200,000?
Click to expand...

There is no answer. The answer is and always has been "the more loot instances, the closer you are going to get to your EV"

What this does is give a bit of perspective. It does for instance show that despite my trying times with loot recently, it could have been significantly worse.
 
Jhereg said:
The many times that MA has stated that there's no personal loot pool, i.e. no mechanism for 'kickbacks'. So I do assume all loot events are independent based on this.

If miathan wants to chime in , I believe he has not seen anything to suggest otherwise as well in his tracking.
Click to expand...
It depends how ma define personal loot pool tbh. I can tell you now their is kick backs. Yes it could be law large numbers but this data I assume is playing safe so would somewhat follow law large numbers especially if your hunting same ped per kill mob.

Stuff i have seen theirs alot more going on under the hood then law large numbers.
 
Wouldn't it also mean that if you were to start off with profit while hunting, the loot would decrease over time ?
 
R4tt3xx said:
Wouldn't it also mean that if you were to start off with profit while hunting, the loot would decrease over time ?
Click to expand...
It isn't that your loot decreases over time. It is just that your expected average return % in the long term is lower than that momentary profit you make, so in the long term you are most likely to trend towards that average....
 
TheOneOmega said:
I take it you rely on the assumption that looting instances are independent and identically distributed draws from the multiplier distribution; otherwise I think you'd need more sophisticated machinery like an order-m Markov chain to model this. Lots of players believe their returns decrease following a large HOF in a non-I.I.D. fashion. Do you have any data to warrant the I.I.D. assumption?
Click to expand...
Yes, the model is based on the assumption that loot events are 100% independent. Like Zho said this assumption is based on both official statements about no loot pool and analysis of loot.

I probably have data on over 1M individual loot events, cost and loot. I analyzed a few 100K of them to build the model.
It's still not enough data to build an accurate model for the very rare multis (1000x to 2000x) but I think it's pretty close.
I have tried to find patterns in the data, like "payback HoFs" and "payback of HoF". Haven't managed to find any.
That doesn't mean they don't exist, just means that they aren't obvious.
Personally I have no reason to believe they exist either, it would be a complicated system and risk introduce bugs or unintended features that could be exploited. is just not worth it when you could just set a a simple probabilistic model that is easy to reason about and easy to implement.

Payback HoFs, or other things people say the observe, can easily be explained by the human nature of finding patters in randomness.
You can even try this by running the model I implemented.
Just look at this payback hof at the end of a 10K kills grind:

index.php

index.php


(above is a simulation of 80% Eff, 60 Looter, killling 10000 5 PED/kill mobs)
 
miathan said:
(above is a simulation of 80% Eff, 60 Looter, killling 10000 5 PED/kill mobs)
Click to expand...
How do I change the simulation numbers? I was trying to show on stream last night until I remember I have no clue how python works XD
 
Honestly both are correct, three years if you've never learned a programming language before, three days if you have.
 
Legends said:
So the answer is..?

200,000?

Unless a hunter has tracked over at least 200,000 kills, they have no right to complain about their returns because, as they say: "You need a larger sample size"

Well I'll be damned. How long would that take? I'm level 50, have I even killed 200,000 yet?

Well, a bit of math could help, so if it takes me 12 seconds to kill 1 mob, then it would take me 666.67 hours to kill 200,000 :eek:

Really!? You need to hunt for 667 hours to have a level of confidence near 100% over your 97% returns??? That seems crazy to me...
Click to expand...
200k kills is like a month, no biggie
 
I like how as customer we just take it we have to grind for that long.

"Oh you want me to bend over MA. Sure how low do you want me to go"?
 
Art Jennifer said:
I like how as customer we just take it we have to grind for that long.

"Oh you want me to bend over MA. Sure how low do you want me to go"?
Click to expand...
You don’t have to do anything. I think your missing the point of this data
 
Legends said:
So the answer is..?

200,000?

Unless a hunter has tracked over at least 200,000 kills, they have no right to complain about their returns because, as they say: "You need a larger sample size"

Well I'll be damned. How long would that take? I'm level 50, have I even killed 200,000 yet?

Well, a bit of math could help, so if it takes me 12 seconds to kill 1 mob, then it would take me 666.67 hours to kill 200,000 :eek:

Really!? You need to hunt for 667 hours to have a level of confidence near 100% over your 97% returns??? That seems crazy to me...
Click to expand...

Kill 200k Puny with a big ass rocket launcher can be done fairly fast :D
 
Currently 30k kill on very small mob and having 87% return, had big loose on avg hp mob before that, once i do 100k kill i will post my result. I believe "payback" take more than kill count, ammount of peds must be a factor.
 
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