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Drop Rate Discussion: Failure rate for rare item drops
http://exiledkingdoms.com/forum/viewtopic.php?f=4&t=10279
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Author:  VDX_360 [ Wed Mar 22, 2017 10:12 am ]
Post subject:  Drop Rate Discussion: Failure rate for rare item drops

***For Clarity, 1% and 3% Item Drop Rates are used as examples. I do not know what the real Item Drop Rates are for rare items in the game****

The statistical oddities of Item Drop Rates are a frequent topic of discussion on this forum (typically in the form of frustration at not getting an item). So, I figured it might be a good idea to put the reality of failure in context. If for no other reason to be able to reference the chart in future discussions.

Basically, the rarer the drop, the more likely a lot of players won't get an item when simple math says they should expect to get it. For example, an easy Drop rate of 50% works out to be every other attempt. So easy math says kill two monsters and get one item. In contrast, the more exact statistics says 1 out of 64 players will have to kill six monsters to get the item and 1 out 128 will have to kill seven monsters to the item. Overall, only a few players will to kill just a few more monsters to get the item. Not really noticeable in real game play.

But the same can't be said for rare drops, such as 1% and 3% Item Drop Rates, which are widely used Item Drop Rates for rare drops in games. For clarity, I don't know what Exiled Kingdom uses as a rare drop rate, this is just an example.

At 3% Item Drop Rate, roughly a quarter of players (22%) will not get an item after 50 attempts and 5% will still not have gotten it after 100 attempts. Thus, if a hundred players tried to get the item, three lucky players will get the item of their first try (roughly), and five frustrated ones will be still trying to get the item 100 attempts later. Pretty sizable difference, pretty decent size crowd of players. The good news is that almost 2/3 of all players (63%) will have gotten at least one after 100 tries as 26% of players will have gotten more than 1, those lucky heroes.

At 1% Item Drop Rate, almost two-thirds (61%) will not get an item after 50 attempts and more than a third (37%) will not get after 100 attempts. In fact, while not listed in the chart below, about one-seventh of players (13.4%) will still not have gotten it after 200 attempts. So if 100 players were trying to get an item with a 1% drop rate, one very lucky player gets the item on his or her first try, and 13 players will be still trying 200 attempts later. Huge difference in effort, sizable crowd.

For re-cap, the rarer the item drop, the more likely there will be a notable number of players who have to make herculean efforts to get the item, if they ever do. It's just the reality of random chance.

For a quick reference, below are the Binomial Probability charts for 1% and 3% Item Drop Rates with 1, 10, 20, 50, and 100 attempts. The most useful lines are in gold, which are the chances of not getting the item (None) and the total chances of getting at least one of the item (1 or More). See the notes about the numbers.

Notes:
Given:
1) Item Drop Rates are fixed, i.e. same chance of success each time.
2) Item drops have only two outcomes i.e. item dropped or it did not drop.
3) Each attempt at an Item Drop is independent, i.e. no Gambler's Due (or fallacy)
Therefore, Item Drops are a Binomial Distribution (Statistic nerds, cheer!)

"Just one" means "exactly one", which is why the odds of getting 1 or more is higher than getting Just One as it's possible to get an item more than once in each group of attempts (i.e. try 10 times and hey, you might get the item a few times).

The 3% drop rate at 20x and 50x are both 34% due to slight rounding and the 50x is high enough where it becomes more statistically likely to have multiple successes (think flipping a penny, the more you flip, the more unlikely its going to come up heads only once).

Attachments:
EK_2017_Mar_Item_Drop_Rates_Chart_1_3_percent.jpg
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Author:  MikeB [ Thu Mar 23, 2017 9:37 pm ]
Post subject:  Re: Drop Rate Discussion: Failure rate for rare item drops

Very nice post. Perhaps a bit lengthy, but it puts some things into perspective for the "unlucky ones" among the players who constantly wonder whether there is some bug which prevents them from getting the rare drop they are desperately grinding for.

If I may, I would like to put the core of this into some graphics (which is easier to grasp than pure numbers) and place it in a separate section of the Wiki. Something like "Interesting facts about game mechanics" or so...

Author:  MikeB [ Fri Mar 24, 2017 6:56 am ]
Post subject:  Re: Drop Rate Discussion: Failure rate for rare item drops

@David: Can you give us a hint what the lowest drop rates actually are in the game right now? Nothing specific, just if it's indeed in the few percentage range or even sub-percentage (which would be really mean :D).

Author:  VDX_360 [ Sun Mar 26, 2017 6:39 pm ]
Post subject:  Re: Drop Rate Discussion: Failure rate for rare item drops

MikeB wrote:
Very nice post. Perhaps a bit lengthy,

Yeah, I was trying to find a way to explain the concept without being too wordy. Perhaps, if I get the real drop rate for certain key items I can create a chart with accurate values and a more concise intro.

Author:  VDX_360 [ Sun Mar 26, 2017 6:54 pm ]
Post subject:  Re: Drop Rate Discussion: Failure rate for rare item drops

Another useful chart might a similar success/fail chart for collection quests such as Turning the Scales. Given the item drop rate for fire drake scales, whats the odds of collecting five drake scales by killing 5, 10, 15, 20 drakes? Does not include finding scales in chests. That's a quest that sometimes gets cited as bugged because it takes a few more tries than expected.

The goal of such charts is to help put into visual concept realistic success and failure rates for grind sessions.

Author:  MikeB [ Sun Mar 26, 2017 7:43 pm ]
Post subject:  Re: Drop Rate Discussion: Failure rate for rare item drops

VDX_360 wrote:
Another useful chart might a similar success/fail chart for collection quests such as Turning the Scales. Given the item drop rate for fire drake scales, whats the odds of collecting five drake scales by killing 5, 10, 15, 20 drakes? Does not include finding scales in chests. That's a quest that sometimes gets cited as bugged because it takes a few more tries than expected.

In principle a good idea, but I wouldn't put too much hope in getting exact drop rates. David stated once that he doesn't want to share them publicly (to have the freedom of adjusting them without creating too much stir). That's why I just asked for some order of magnitude.

Author:  VDX_360 [ Sun Mar 26, 2017 7:45 pm ]
Post subject:  Re: Drop Rate Discussion: Failure rate for rare item drops

And that makes sense.

Author:  DavidBVal [ Tue Mar 28, 2017 6:47 pm ]
Post subject:  Re: Drop Rate Discussion: Failure rate for rare item drops

MikeB wrote:
@David: Can you give us a hint what the lowest drop rates actually are in the game right now? Nothing specific, just if it's indeed in the few percentage range or even sub-percentage (which would be really mean :D).


It is not easy to answer that.

The system base is 1-100%, and items have drop chances in that range, some rare drops have a 2-5%, uncommon ones up to 25%. But a given loot table begins checking drop rate from the top of the table and then works its way down. However there is also the number of max items dropped (1-4) affected by various things, so once it's reached no other drops will be generated. Which means some items at the bottom of a long drop table with many high % drops above it might drop very rarely. The rarest drop ever is probably Ancient Tolassian Tome on the dragon drop table; it is a 1% but in reality it's more like a 0.3%

Author:  MikeB [ Fri May 26, 2017 1:16 pm ]
Post subject:  Re: Drop Rate Discussion: Failure rate for rare item drops

I tried to put the spirit of this thread into a Wiki article in our new Game Mechanics section. Just to let you know. Check it out. :)

Author:  VDX_360 [ Sat May 27, 2017 4:19 am ]
Post subject:  Re: Drop Rate Discussion: Failure rate for rare item drops

I like!

For RARE drops, I like viewing the problem from chance of failure rather than chance of success as it tends to show how much a failed hunt is really the expected outcome--But that's a nerdy point.

I also like high lighting that if there's a 100 Rare Drop Items form different quests and different monsters you're likely to get ONE of them in an average game, just might not be the one you want.

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