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Let's Take a Look at Droprates


Nerevar
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What is your opinion of droprates?  

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Alright, so to start off; I don't mind how rare things are on this server, even if the drop rates are a little steep in practicality.

However I've seen people in chat complain about drop rates, so I decided to write up a basic program coded so that it will spit out data based on what a normal expected value is based on our current drop rate percentages that we can see in the Monster Droptables interface: 

droptableInterface.png.5c02d82ef6728be0b90ec86555898128.png fig1. Monster Droptables Interface

 

I did this out of boredom and some interest in what I may find in the results. The only thing that I believe will be proved here is that the percentages shown to us aren't correct drop rate percentages to what is actually happening behind the scenes. 

This little program of mine takes in:

  • A desired droprate as a percentage (same way as is shown to us in the droptable interface; for readability and understanding)
  • An amount of items to be dropped at that percentage.

The program will show us, after executing its iterations:

  • Our desired droprate
  • The amount of items we wanted to gain that had this droprate
  • The TOTAL number of 'kills' it required to reach that number of items gained
  • And the Average number of kills it took to acquire each item

 

The Aim
Considering this post, I believe it would be a nice change if EITHER: the drop rates advertised in the Monster Droptables interface were changed to show us what we should actually expect it to be, OR if the drop rates behind the scenes were tweaked a little to actually respect the values we are shown. OR a middle ground of both; seeing as just changing the drop rates would be a massive buff to all items coming into the game, which isn't ideal. And I don't have a massive problem with the current drop rates, although it is misleading for those of us who look at the % shown in the droptables interface.

 

Acknowledgements

The monster I decided to test the data against is the Celestial Fox. This is because the most kills on any creature that I have in-game, is on the Celestial Fox. This provides me with the largest in-game data set available to me immediately. Of course it's not the largest data set so the data may or may not be 100% correct and may skew closer or further from what the absolute correct values are behind the scenes. But with 1.7k kills on the foxes, it's the best I could get as of right now without reaching out to anybody for additional data.
CelestialFoxCollectionLog.png.00e80e7272004d10008285a6632c5d5b.pngfig2. My Celestial Fox collection log

These simulations are run to find how close I have gotten to what an expected droprate may be. For example, if something has a droprate of 20%, 20% of 1 is 0.2. 1 divided by 0.2 gives us a result of 5. Therefore we can assume that in a perfect world we may get a drop of that something every 5 kills. The statistical Confidence Interval of ACTUALLY gaining a drop will be different though because each kill is a different/unique event that prior kills do not have anything to do with. Therefore in reality we may get a drop earlier than the expected value, or beyond the expected value. IT'S STILL ALL RNG.

Also, because I don't know how any drop rate code for the server actually works, I have disregarded any bonus applied to drop rates. I.e the gamemode bonus, or any equipment drop rate bonuses.

I feel we can all have some confidence in the statement that the droprates indicated are not correct, as some of us have seen others go many kills dry without a drop. That being said, I'm not going to be calculating the Confidence Interval at any point in this at any range (e.g. a 90% CI, 99% CI etc) to find out the number of kills expected to ALMOST be guaranteed a drop. That number at a 95%+ CI, I would expect to be ridiculously high that most people won't reach upon getting their first drop anyway.

I have selected items from the droptable of Celestial Fox that are able to be tracked in the collection log, and they share a unique drop rate %. For example, I am not testing anything against the drop rate of the Featherfall bow, as the Featherfall bow and the Dragon platebody both share a drop rate of 2.2%. Because we have no idea how the system for dropping items works properly, I will use values that are as confined as possible.
With that being states, I simulated the drop rate of the Celestial Staff - a "3.3%" drop, the Dark celestial scimitar - a "4.0%" drop, and combined the Frost fire key, and chest as they share a drop rate of "15%" and both of those items are tracked in the collection log, so I know how many I have received from Celestial Foxes.

 

The Simulations

Let's start with the rarest drop I simulated (simmed) with a unique drop rate, so there were no uncounted for conflicting drops:

The Celestial Staff Sims

With a drop rate of 3.3%, we can expect the numbers to tell us that we may get one every 30.3 kills from: 1 / 0.033 = 30.303.

celeStaffSims.png.0e17a98ec92f83c1ce5ed3cb17079bac.pngfig3. Output from 5 different simulations, each aiming to receive the number of drops I have received in-game.

This is the output that I got after simulating the number of drops that I have received over my entire killcount of 1.7k with a real 3.3% drop rate.
The overall average number of kills it took me to get a Celestial Staff according to these sims, comes to: 34.1 kills per staff.
Calculating my real average, to get 8 staffs over 1728 kills it took me: 216 kills per staff.

Seeing as my sample of only 8 staffs received is a low sample size, I simmed what receiving 1000 staffs may look like:
celeStaffLargeSim.png.dfbb1c3d196ac181515879218cea7d0f.pngfig4. Output from a single simulated larger sample size of 1000 staff drops.
We can see that after 1000 staffs were dropped, 30,327 Celestial Foxes would have been killed giving us a staff every 30.327 kills. Very close to the calculated 30.303 kills per staff.

I wanted to see what it would look like if I nuked the drop rate tenfold:
celeStaffNukedDR.png.f79cf96936b87877b1f82e84e17b86cd.pngfig5. Output from a single simulated larger sample size of 1000 staff drops at a nerfed drop rate by tenfold.
Over the time it took to get 1000 staffs at a horribly nuked drop rate, by tenfold; the results were a bit worse than my real average kills per staff. Compared to 34.1 kills per staff, my 216 kills per staff is still scarily close to 304.887 kills per staff by comparison. A bit over the top though.
(The drop rate shown in the output of this sim is still 3.3% and not 0.33% because the nuke to the drop rates were done in a part of the code of the program that didn't need to affect the output based on my input. I will show at the end of this)

 

The Dark Celestial Scimitar Sims

With a drop rate of 4.0%, we can expect the numbers to tell us that we may get one every 25 kills from: 1 / 0.04 = 25.

darkCeleScimSims.png.ff80d8549a4e501276b9899fca15d806.pngfig6. Output from 5 different simulations, each aiming to receive the number of drops I have received in-game.

The overall average kills per Scimitar received, according to these simulations come to: 33.033 kills per Scimitar.
Calculating my real average of 6 Scimitars over 1728 kills is: 288 kills per Scimitar.

Simming with a larger sample size:
darkCeleScimLargeSim.png.53a7e519ad4b9f3c72dd0ebed2b8bba7.pngfig7. Output from a single larger simulated sample size of 1000 Dark Celestial Scimitars.
The average shown here (25.204 kills per Scimitar) is, as expected, very close to the calculated drop rate of 25 kills per Scimitar.

What does the nuked drop rate data look like:
darkCeleScimNukedDR.png.e7eaded327b300b6e49f06e8f00036e6.pngfig8. Output from a single simulated larger sample size of 1000 Scimitar drops at a nerfed drop rate by tenfold.
253.36 kills per Scimitar is, again, scarily close to my real average of 288 kills per Scimitar.

The Frost Fire Chest & Key Sims

Even though the Chest and Key are different items, they share the same drop rate of 15.0% and they are both tracked in the collection log, so I could sim getting 76 drops of either a key or chest, rather than 44 of one, and 32 of the other, or a middle value. I also wanted to do it this way because a value of 76 (with a shared drop rate value of 15.0% giving me confidence in this) is my largest real sample from all my kills & loot.
We may expect a key or chest every 6.667 kills from 1 / 0.15 = 6.667.
chestKeySims.png.d1017533d84a3b8bc097750eaddf23d6.pngfig9. Output from 5 different simulations, each aiming to receive the number of drops I have received in-game.
Again, a combined average across all the sims here of 6.534 kills per Chest OR Key, close to the calculation of 6.667 kills per.

Do we need to see a larger simulated sample size? Here it is, for consistency.
chestKeyLargeSim.png.5163bae710a44390fa24e5e0f562edf2.pngfig10. Output from a single larger simulated sample size of 1000 Frost Fire Chests OR Keys.
A slight deviation below our sims from before, but still close at 6.454 kills per Chest OR Key.

What does the nuked drop rate look like comparing it to my actual average?
chestKeyNukedDR.png.e9d7befb9d80f0a0d055106906e2637b.pngfig11. Output from a single simulated larger sample size of 1000 Chest or Key drops at a nerfed drop rate by tenfold.
At the internally nuked drop rate we are only getting a Chest or Key every 62.873 kills.
My real average for a Chest or Key is 22.737.

Because this is such a large difference compared to the returned value from the simulation, my average only being almost a third of the simmed value, this leads me to assume that either:

  • The drop rates aren't as bad as these tenfold nuked drop rates in my simulation
  • Or that there is some drop table fuckery happening behind the scenes skewing drop table returns toward the more common drops, which would be why my average for a more common item is much better, in comparison to the simulated results and real averages of the somewhat more rare items.

I can understand the skewing of items being dropped in favour of more common items, as I have developed a game for uni that had drop tables and item rarity was involved. There is always a way to calculate and estimate your drop rates though with the correct math being done.

 

In case anyone wanted to see a snippet of what the nuked drop rate looked like compared to the normal drop rate in my code:
normalDRCode.png.243c447a869a4eb69674a4c7c9332528.pngnukedDRCode.png.0c3016575bef8d50271fe1cd4947e52d.png
 

If you read my entire post, good shit! And if anybody has any problems with my methods, feel free to correct me! 

Cheers for reading, don't take this post too seriously, I was bored and just wanted to see if I could sim some results and see what came out the other end (Yes, this probably took too much of my time, but I'm currently in lockdown, so whatever). Also it was an excuse to code a very basic program as I haven't coded in a while and needed to start getting back into it.

Cheers everyone!
- Nerevar

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Thank you for posting this, I was getting tired of being ridiculed ingame for calling it out. But having data to back it up helps a ton, so I appreciate the amount of work you put into this!

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  • 2 weeks later...

Heh...  voragoCL.png.ae3ded2df58f8194c019a50cc59ffa49.png 7 Tec pieces giving me an average over 2777 kills of 396.7 kills per piece. Guess I'm lucky there compared to the expected rate of 1/607. Over time that's mathematically guaranteed to smooth out over enough kills 😉

Never lucky for that pet tho lmao.

I could add a function to my program to simulate the amount of kills I've done and see if a simulation gets luckier than me.. But I won't, it probably would have gotten pet by now

 

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  • 3 weeks later...
3 hours ago, Iron Mizery said:

Very detailed suggestion backed with evidence and data-- good job!

Since this post Bennie added a more accurate droprate ratio in the drops interface giving us a better representation. Happy with that simple and quick addition of more detailed information ingame 🙂 Bennie's goated

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