PSA: Understanding map drop streaks

So let's say, in a white map, the item drop table is called 5000 times. This is just an arbitrarily large number I pulled out my ass, but it'll do.

Now some GGG balancing guy decides that, for this map tier, they want you to average, um, let's say 100% increased quantity maps to sustain. So they make the chance of success 1/10000 per drop. That means a map with 100% increased quantity will have 10000 drops, and the average result would be 1 success.

And given a huge sample size, this is precisely what 100% quantity would average to. Seems completely reasonable so far, amirite?

However, let's look at a small sample size. The smallest, actually. Here's a breakdown of how likely it is to have a particular number of "successes" in the situation described, in a single map...
0 successes: 36.79% (.9999^10000)
1 success: 36.79% (.9999^9999*.0001*10000)
2 successes: 18.39% (.9999^9998*.0001^2*10000*9999/2)
3 successes: 6.13% (.9999^9997*.0001^3*10000*9999*9998/6)
4 successes: 1.53% (.9999^9996*.0001^4*10000*9999*9998*9997/24)
5+ successes: 0.37%

Now, just for contrast, let's do the math for a single 20% quantity map:
0 successes: 54.88% (.9999^6000)
1 success: 32.93% (.9999^5999*.0001*6000)
2 successes: 9.88% (.9999^5998*.0001^2*6000*5999/2)
3 successes: 1.98% (.9999^5997*.0001^3*6000*5999*5998/6)
4 successes: 0.30% (.9999^5996*.0001^4*6000*5999*5998*5997/24)
5+ successes: 0.03%

This is the part which surprises people. But it's nevertheless true. Even if you're rolling your maps well enough to sustain them on average, you should expect to get no return a full 36% of the time. That's over one third!

This is also why there is a myth that quantity does not effect map drops. This is false when looking at a large sample size, but given the situation I described, a single 20% map will have more successes than a 100% quality map 21% of the time, and the same number of successes 35% of the time. The higher quality map will do better 44% of the time, but with a small sample size it might seem that the two types of maps are merely "trading wins."

The high and low quantity maps also have about the same odds for a single successful drop (37% vs 33%). So if players are focusing on "reasonable" returns, merely chaining one map into another, quantity will still incorrectly appear not to matter.

Instead, the major advantage of higher quantity maps is their streaking potential. Running high quantity greatly improves your odds of "high RNG" instances of multiple successful map drops in a single map. This will still occur a minority of the time, but almost never occur on improperly rolled maps. These streaks are were you recoop on your investment and ensure map sustainment.

So in conclusion, lower your expectations for results from a single map, build a larger map pool, expect mediocre results a majority of the time, and open your heart and your currency wallet to RNGesus so that, with His blessing, He may decide to let it rain.

EDIT: BONUS SECTION
For you overachievers, here's what 140% quantity would look like.
0 successes: 30.12% (.9999^12000)
1 success: 36.14% (.9999^11999*.0001*12000)
2 successes: 21.69% (.9999^11998*.0001^2*12000*11999/2)
3 successes: 8.67%
(.9999^11997*.0001^3*12000*11999*11998/6)
4 successes: 2.60% (.9999^11996*.0001^4*12000*11999*11998*11997/24)
5+ successes: 0.78%

Also, when you go on a map drop streak, the first thing you're supposed to do is start a forum post with the title "Did they stealth buff map drops?". And then when you go on a map drop lull, you post another with the title "Did they stealth nerf map drops?"

At least that's how it's been done in the past.

Hopefully not anymore.

Good post, by the way.

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ScrotieMcB wrote:

Hopefully not anymore.

You may be overly optimistic.

EDIT: Holy shit, this may be the first time a thread has ever been moved from Feedback INTO GD. Unfortunately, support, this would actually belong in Gameplay Help and Discussion.

Only thing I disagree with is your presumption that they thought this out rather than pulled some number out of the hat and are using the ends to justify their means. They've got the data on sustainability, and they seem to be happy enough with it. But to think that they "designed" it to do this isn't realistic. They guessed. We got the results.

"

"

ScrotieMcB wrote:

Hopefully not anymore.

You may be overly optimistic.

EDIT: Holy shit, this may be the first time a thread has ever been moved from Feedback INTO GD. Unfortunately, support, this would actually belong in Gameplay Help and Discussion.

I posted this in Feedback by mistake and requested the move to GD as I originally intended. But Gameplay Discussion would be okay I guess.

This being true doesn't change the human response part of the equation. Which is why I still hold firm that while it's ok to rng gate the most exclusive endgame content it's not ok for the majority of a character's endgame phase.

People are still going to expect a proportionate output to their perceived input and if they get boned 'enough' times then the cumulative negative experiences appear to outweigh the good even if as you have shown that's not literally true.

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Shagsbeard wrote:

Only thing I disagree with is your presumption that they thought this out rather than pulled some number out of the hat and are using the ends to justify their means. They've got the data on sustainability, and they seem to be happy enough with it. But to think that they "designed" it to do this isn't realistic. They guessed. We got the results.

Maybe? You might be right but I'm not confident you are. My point is that even if GGG selected map drop rates with the most logical Spock-esque perfection, the RNG results would still have people looking at small sample sizes and saying it's fucked.

The problem is that frustrated players don't provide large sample sizes...they just leave the game lol. I think the game SHOULD be balanced to medium to small-medium sample sizes...because human emotions > statistics when it comes to player retention. i.e. when it feels bad or is not fun...people leave and that's bad for everyone :[

Also I need to post this

Because this much science should not exclude the orb that IS the embodiment of science. :D

Noice math post, mate!