BL Keys + Zone Completion

[Illconceived Was Na.9781]

Wall of text: my numbers show that we cannot reject the hypothesis that the true rate is around 24% of getting a key drop from each and every map. None of the examples of bad luck are so horrid that we have to consider more complicated mechanics, as the OP and others have suggested.

 

Or in simpler terms: the OP (and others) are just unlucky, in some cases really really really unlucky and nothing more.

 

****

**Gory details**

 

>! > You are talking about mathematical expectations.

>! No, I'm not talking about "expectations." Expected results are just barely helpful in determining whether someone's results are typical or not. If the true odds are 25%, then anyone getting 8-12 out of 25 (from world completion) doesn't have to look further; that's close to the mathematical expectation of 10.

>!

>! The OP (among others) know that their results are far below expectations. The question is therefore: can their results be explained by bad luck? Or do we have to consider the possibility that we have misunderstood the mechanics involved?

>!

>! > However, considering that 1) rolls for keys are independent and 2) sample sizes are statistically small,

>! We don't know for certain that (1) is true. It's a reasonable assumption, because that's how the rest of the game works and it's how ANet has explained how all drops work. So (see below), I include it as a baseline for the purpose of testing.

>!

>! (2) depends on the context. The wiki data is over 600 map completions, which is sufficient to determine a drop rate **if** the other assumptions are accurate, especially the one that assumes that players are accurately tracking & posting **all** of their results.

>!

>! > it’s quite normal to have ‘long’ periods of no keys.

>! Yes & no. Yes, people should expect streaks of bad luck; no one has expressed any doubts about that. The question that concerns us is just how long a bad streak needs to be before we can consider it abnormal.

>!

>! My calculations are set up to help put numbers on that.

>!

>! Several things complicate the conversation:

>! * Humans are traditionally bad at tracking results and recognizing the importance of using all data, not just the good or bad streaks.

>! * We have very, very bad intuition about probability. We tend to assume that "expected results" are normal, and feel disappointed when we get even just under average (which is quite normal), tend to ignore just over average (hey, we're due for a little more), discount lucky streaks, and over emphasize unlucky ones.

>! * The law of large numbers makes things more confusing. It's statistically improbable, for example, that you or I will win the MegaMillions lottery in the US: 1 in about 300 million chances. However, there's an over 30% chance that _someone_ will win (considering 370 million tickets were sold).

>!

>! Here are the assumptions I've made in my calculations:

>! (a) Chance of a key is independent of any previous map results

>! (b) Chance of a key dropping can be estimated by a single number

>! © Chance of a key dropping from completing any specific map is identical to that of any other.

>! (d) Data provided by individuals is accurate

>!

>! (a) is consistent with the rest of the game and it's how ANet explains their drop tables, so I'm confident it's a reasonable assumption. (b) is a fair assumption for a binary result (either key or transmutation), also given the mechanics we do know about.

>!

>! © is a reasonable assumption except we have no particular reason to believe it to be true. It could be that each map has different odds, or that it's different for LS3 & LS4 maps or L80 maps generally. Our odds-determining samples don't account for map or map level, so we can't directly refute the idea. That's good enough for me, though, based on Occam's Razor: the simpler explanation sufficiently explains the data.

>!

>! (d) is **not** accurate. We know in fact that most people are unable to collect good data. (I don't blame them; it's hard to do it at all, let alone be rigorously accurate. And worse: it takes time away from playing.) Additionally, over the years, we've spotted all sorts of issues with data posted to the wiki. The good news is the wiki gurus have added tools to the wiki to improve the consistency of data entry. The bad news: that doesn't ensure accurate record keeping.

>!

>! However, sometimes the wiki is the only data we do have in bulk & from diverse sources. It's probably not good enough to find the "true" rate in this case. Nevertheless, I think it gets us in the right ball park.

 

 

[Illconceived Was Na.9781]

> @"Konig Des Todes.2086" said:

> I once managed to get 8 keys in a row when I was doing S3/PoF/S4 mapping on alts, then got a string of ~5 t. charges in a row. So yeah, not improbable but pretty lucky.

Assuming a 24% rate...

* 8 keys of 8 in a row: 0.0011%

* 5 transmutes in a row: 76% chance

* [8, 9, 10, 11, 12, or 13 keys from 13 maps](https://www.wolframalpha.com/input/?i=24%25+chance+of+success,+13+trials,+at+least+8+successes): 0.4%

 

Pretty lucky indeed. Gz :)

(I'm guessing you to bupkus from the chests, since you didn't mention anything special, so un-gz on that :( )

 

 

> I'd be most inclined to trust the wiki's data so far, and say it's about 25% chance to get a BLKey from mapping.

The posted numbers are consistent with this possibility.

 

> It's possible that higher level maps have a slightly higher chance to drop though (since afaik, nobody's been counting the level of zones and what they drop, just how many zones, aside from cities),

Yeah we don't have the data to determine that directly.

 

> but that's really just pure hypothesizing there. But if that does hold some weight (and would explain @"Illconceived Was Na.9781" 's statements of seeing people say 20, 25, and 30% chances) if you did high level maps like me, then multiple keys in a row would be a lot more likely to occur.

 

For what it's worth:

* Of my 300+ map completions, I have over 200 from L80 maps and over 100 from sub-80 maps. My key rates are 34% and 31% respectively.

* If I restrict to "under L70" (so ruling out Orr & Frostgorge), it drops to 27%.

* Restricting to just LS maps (not HoT nor PoF): 40%, whereas just Core (not even DT or SW): 30%

 

Which is a lot of text that basically says: I've been extremely luck in LS maps and just luckier-than-average in Core maps. It's not enough to reject the idea that the rate is identical across all maps.