PSA: Understanding map drop streaks

"

Shagsbeard wrote:

Players are frustrated because their expectations aren't matching reality.

Or formulated another way: People are frustrated because the mapping reality in PoE sucks.

I don't think that peoples' intuitions on randomness are so wrong as it is portrayed in math articles. I think it's more that people blame randomness as a scapegoat of last resort, and these fallacies of comprehension are actually mental acrobatics we go through to pin that blame on the scapegoat.

Almost everything in POE is generated with random processes, but it takes until map sustainment before many people start complaining there is some sort of hidden bias or stored seed to the RNG. After all the thousands, or perhaps millions, of random objects and occurances that we see in the game (to presage the scale of it: that's every item which is generated, damage roll ranges on every attack, mob and map layout, and so on), there's no problem with the RNG as long as it doesn't stop our progress. Its not until the RNG stops us that people start coming up with theories about how the RNG is broken. An aside: another common complaint is in regards to fusing orbs, which can also halt progress.

People have no problem understanding randomness throughout the game, perfectly accepting when 3 yellow items drop from one elite, while 0 drop from another elite. But change the words "yellow item" -> "map" and "elite" -> "map instance" and suddenly there are conspiracy theorists that irrationally make different conclusions about the same system. They don't misunderstand randomness; if they did they would have had problems with the first scenario of 3 yellow items. Instead, they are doing what they can to get the results they want, and have still failed. After they've done the obvious like investing currency in map crafting and clearing out every corner of the map instances they play, the observed results still might not match expectation. In that case, RNG is the scapegoat of last resort. Let the mental gymnastics begin.

It's easy to blame a black box over which we have no control. On a short-term basis, this isn't even incorrect- it's certainly possible to get a bad streak randomly! But when that scapegoat persists- when it stops being the short-term explanation and morphs into the catch-all for explaining the chasm between expectation and results- that's when the understanding of randomness vanishes. It's easier to do all that than it is to adjust expectations and accept that your internal model was wrong. Better to do the mental gymnastics- keeps that brain fit!

Anyway, my point is that people don't get confused about randomness because they don't understand it, instead people purposefully deceive themselves into getting confused about it. Showing the math would only help if people were confused for the first reason. Changing people's minds who are confused for the second reason is more about persuasion and charisma than it is about mathematics. And the lesson here is not either of those things, the lesson is:
Preventing progress on the basis of random chance is something that some players will not accept.

I disagree, Polaris. I mean, I think you've written a decent piece on why some players don't want to understand, and will actively avoid seeking the truth. But there's a difference between not wanting to understand but you do, and not wanting to understand when you don't. In the former instance, I can imagine someone wishing for the bliss of ignorance, but suggesting that large numbers of people repress what they know is just weird.

I've played more than enough poker to know that people will always look for patterns and claim the game is rigged or blame the card dealer for their misfortunes and failures no matter how true the RNG in real or online poker is.

"

Xavderion wrote:

I've played more than enough poker to know that people will always look for patterns and claim the game is rigged or blame the card dealer for their misfortunes and failures no matter how true the RNG in real or online poker is.

At least in terms of online poker people could have legitimate reason for concern. The website would have something to gain by using underhanded tactics.

GGG has absolutely nothing to gain by giving out false information about how maps drop. It doesn't make any sense for people to think something else is going on behind the scenes.

"

TheAnuhart wrote:

"

Qarl wrote:

"

Vhlad wrote:

The thing is I don't see a normal (Gaussian) distribution of maps. It's binary, feast or famine.

The streakiness is too extreme for there to be a static global % map drop success scaled by map quantity.

No, it isn't.

Streakiness in random distributions happens.

Just come out and say the only factor to map drops is the mods on the map and that there is no other (and far more determining) factor such as a varying seed.

Or don't.

This.

Because this is a pretty deciding factor: If there is a map seed which gets amplified by quantity % then quantity would make the whole process more streaky.

If there is no seed quantity should not change the streakiness or even flatten it a bit.

And no matter which statistical approach is right, the decising factor should always be how it feels to players. Heavy streaks can be very demotivating. Imo it's better to rig the RNG a bit so that players get a better experience and actually get the feeling that all that curreny spent to roll those tasty mods actually matters.

Beautiful math.

I dont know if anyone already mentioned, but i think if you add the possibilities for +1 and +2 drops it get even streakier. You have higher chances for 3 and 9 successes that way. So if you are working at a sustain, the chance for 0 successes will be even higher than 36%.

"

PolarisOrbit wrote:

People have no problem understanding randomness throughout the game, perfectly accepting when 3 yellow items drop from one elite, while 0 drop from another elite. But change the words "yellow item" -> "map" and "elite" -> "map instance" and suddenly there are conspiracy theorists that irrationally make different conclusions about the same system.

True.

However, there is an important difference. Get no yellow item drops, who cares. Get no map drops, you cannot play the game (or only play boring content which, to make matters worse, doesn't even have a chance to drop interesting content, because to play the really interesting content, you have to play the interesting content first....)

"

Sa_Re wrote:

And no matter which statistical approach is right, the decising factor should always be how it feels to players. Heavy streaks can be very demotivating. Imo it's better to rig the RNG a bit so that players get a better experience and actually get the feeling that all that curreny spent to roll those tasty mods actually matters.

+1

So I decided to run some numbers around the idea of running 100 maps, instead of just one.

As I predicted, steakiness went down considerably. With an "EV 1" situation of 100 drops per map and a 1% chance of success...
*over 99% chance of at least 77 successful map drops per 100 maps
*over 95% chance of at least 84 successful map drops per 100 maps
*over 80% chance of at least 91 successful map drops per 100 maps
However...
*47.3% chance of at least 100 successful map drops per 100 maps

Now if you're not opposed to trade, that level of quantity in your maprolling isn't a problem. If other people are doing the same, you'll spend a lot less currency buying maps IF you're a little unlucky, than you'd spend rolling all of your maps at much higher quantity.

Now, if you're really dedicated to long-term self-sustain without trading, you'd probably want to get about 25% more drops. This isn't 25% increased, it's 25% more, so if 60% increased quantity sustains a certain map tier, 100% increased would be 25% more (1.6*1.25=2).

With 25% more drops, the numbers change to a 98.8% chance of at least 100 successes in 100 maps.

The problem is: that's a lot of maps. Running the same quantity over just 20 maps gives a 81.6% chance of at least 20 good drops, which isn't terrible, but that's still almost a 1 in 5 you end up with less than you started.

Now, if you went 50% more drops, that'd be a lot better for the 20 maps - 96.5% of at least 20 successes in 20 maps. But if 60% quantity is the EV 1 situation, 50% more drops means a whopping 140% effective quantity, which is... well, it's a lot.

I guess the point is this: if you start a tier with a very small number of maps and you want to ensure sustainment, you're going to need to drop insane amounts of currency rolling those suckers or there is too great a risk you'll fizzle out. On the other hand, start with a large pool you can ensure sustainment with a much lower rolling cost per map.

So in the end, it all goes back to the classic map guide advice: take your time on each tier, establish a good map base before you start a new tier, and be careful with your currency management. Otherwise, you'll need to either go broke rolling your maps, or fizzle out (of, with a very small sample size, perhaps both).

Math is love, math is life.

Seriously, though: I agree with a lot being said and I agree with those who say something needs to change. I'm the typical player who plays a bit too much to be just casual (two 85s and one 79 in talisman) but not enough to count as non-casual...
That being said: T9 maps feel too easy most of the time. Sure, 2 or three bosses were hard but now, both my solochar and my partychar just storm through T9 maps. Me and my friends would love harder content but we just can't get the map drops. We had three T10 maps I think and none of them dropped anything higher than T9...

I am totally fine accepting that I will never have a lvl 100 char, seriously.
I am totally fine accepting that I will probably never beat uber atziri, seriously.
I am not fine that I can't progress because of RNG. If it was too hard for us, cool. But the fact that we've run about 50 T9 maps (fully chiseled/alched) and just can't progress is bad design.

(And screw anybody who telle me we should buy maps. We want to do it ourselves, you know... Buying maps would feel like paying somebody to kill uber for me, what's the point)

oh, and one more thing: if running a blue map with increased monster pack size really has a higher expected map drop than a rare map... then that's bad design too :P