Another FEH channel on the 14th: Post Talk

[dragonlordsd]

4 minutes ago, Galactaray said:

I agree with your statement that GHBs are great but during the recent datamine a new BHB was found in the files. Presumably will be released tomorrow titled BHB T&H. The map seems to be based off Cheve in Fates and I deduce that it's probably Takumi and Hinata. 

We'll find out tomorrow for sure when the daily reset rolls about.

Must've missed that. Good catch.

Still, BHBs have always been (to me at least) a poor substitute for GHBs. Even when the characters were bad, it still was fun to get an exclusive character that way. Orbs just don't give the same thrill.

[Shiki]

My late thoughts about this.

Spoiler

Summon Banner:
- cool to see even more Sacred Stones presentation. Joshua was one of the more titular characters that were missing from the game while Lute was strangely popular (it's the memes, right? It's the memes).
- I saved up 40 Orbs and with the new update, we get around ~20 more + Tempest Trial rewards. I wanted to save them up but ... Mia happened. Well, I'm dead.
- The community managed to get the oldest FE meme in form of Dorcas into the game. Not sure how I feel about this. Japan memed Arden and we got him as well. Does that mean if everyone memes enough we can potentially get anything in the game?
- They all have a BST. Well, I suppose this is the new standard. Maybe they will take a long look back to handout the same treatment to other characters?
- While they all have their Prf weapons, I'm still waiting for Poleaxe/Halberd or Firesweep Axe.

Rebalancing:
- Yes, about time Staff gets some love. However it still requires one to have/sacrifice Genny to have acceptable offense and most of them don't even have stats that are 'good' for that kind of assignment (Elise has 32/32). But with the stronger bonus effects they might become stronger than Dagger.
- Speaking of Daggers; nothing for them. RIP.
- Glimmer is the big winner of the cooldown change. Damn it! I sent all that Glimmer fodder away. The rest is still pretty terrible though. I guess Noontime has somewhere its use, I suppose?

Weapon Refinery:
- They actually did it right ... well somewhat. It's good that not all weapons are eligible for forging. Brave Weapon are already plenty strong and there is no need to buff them with added endurance and extra attack. Same for Gem Weapons and Raven Tomes which pretty much hard counter the color, they are effective against (the latter with TA).
I'm not a fan that Slaying Weapons are forgeable though. Effective weaponry and Silver weapons really needed that to stand out from the their competition but now that Slaying Weapons are always better than both (except Armor stuff for highest Arena Tier) this is kinda disappointing.
Personal weapons are also upgradeable which is well deserved for them after what happened with Ayra.
- Good that only a select amount of Legendaries are forgeable. Still want to see Binding Blade, Eckesachs, Regal Blade, Sieglinde, Cymbeline, Brynhildr and Parthia on that list. Falchion could also need a boost on its renewal effect because it's just a 16 MT stick in any other scenario outside TT.
- YES. Killing and Armor weapons can be upgraded to their better versions. This is the best thing announced in the stream. Now nobody needs to pray that you pull that 1 character from the pool so you can give someone else a +3 Atk boost.
- Double Yes on outdated legendaries.
Seliph and Julia are really appreciating this since their parents made them utterly obselete. The former will still be not that good but he isn't useless anymore.
Eliwood is statwise still worse than Roy who trades the Res lead for better Spd (which is more important for an offensive cavalier).
Linde is now Delthea with more Spd but less Res. Not sure how I feel about this.
Curious how Merric will turn out now. Dark Excalibur mitigates his bad base Atk.

New Story:
- Cool I guess. Don't play Feh for the story and probably never will.
- Even though the new character Fjorm is in the 8% banner Blue is easily the worst color to pull from that banner. B!Caeda is not amazing and S!Xander smells really bad. At least we're getting her free but all those whales who want to have her at +10 ... good luck.
Colorless is absurd with B!Cordelia and B!Lyn, Genny is going to be at least an acceptable consolation prize with the new changes.
Green is also pretty good with the best flier mage and Hector for DC fodder. Deirdre is the least exciting but still not bad for fodder sake (Spd Ploy). 
Red is ... okay if you still need a decent Red unit. Otherwise it is an easy pass.

 

[Ice Dragon]

4 hours ago, DehNutCase said:

Yeah, they're not necessarily the *best* characters, but that's why you raise up lower rarity characters that are optimized to fill those holes. (I mostly promote for skill fodder, but even despite that I'm pretty sure my lower rarity characters promoted to 5*s outnumber my natural 5*s.)

I have no idea how this is relevant at all.

You originally said that "the problem with being infantry is that fliers and cavalry are better as a whole". The problem is not that the player cannot fill their 28-unit team with units, but that they cannot fill their 28-unit team with fliers and cavalry. This means that it will be necessary to fill some of those slots with infantry units.

 

4 hours ago, DehNutCase said:

Honestly, it'd be stranger if a F2P or small Minnow that's been playing for a while didn't have every single 4* unit they cared about.

A minnow friend of mine who has been playing since a week after launch pulled his first Tharja last week.

Making 75 pulls of red (300 orbs at 4 orbs per pull) gives you only about an 85% chance of pulling any particular 4-star red character. So no, 1000 orbs is not enough to statistically have one copy of every 4-star character in the game.

 

4 hours ago, DehNutCase said:

I mean, Swift Sparrow is kind of the definition of a mediocre middle of the road skill.

That's only vaguely relevant to the argument and actually makes it more strange that the skill is restricted to 5-star exclusive characters for so long and not less.

[Vaximillian]

4 hours ago, Galactaray said:

Presumably will be released tomorrow titled BHB T&H. The map seems to be based off Cheve in Fates and I deduce that it's probably Takumi and Hinata. 

According to the datamine…

…it’s Takumi and Hinoka:

[bethany81707]

25 minutes ago, Ice Dragon said:

A minnow friend of mine who has been playing since a week after launch pulled his first Tharja last week.

 

I'm still waiting on three 4* characters from launch, all of different characters, and one of whom is an important fodder (Roy).

Were you doing the math remembering to account for the 3-4* rate swap, @DehNutCase?

[thecrimsonflash]

4 hours ago, DehNutCase said:

Honestly, it'd be stranger if a F2P or small Minnow that's been playing for a while didn't have every single 4* unit they cared about.

only last month, I was able to pull my first camilla, and that was after amelia made me spend every orb I had on two 5* boeys and camilla was the savage blow fodder that I was wanting to have around.

[mcsilas]

A thought just occurred to me with the healer buffs...

Maybe they were waiting for that to buff the healers in the Camus/Xander infernal maps and make the maps more challenging

[DehNutCase]

1 hour ago, Ice Dragon said:

I have no idea how this is relevant at all.

You originally said that "the problem with being infantry is that fliers and cavalry are better as a whole". The problem is not that the player cannot fill their 28-unit team with units, but that they cannot fill their 28-unit team with fliers and cavalry. This means that it will be necessary to fill some of those slots with infantry units.

The problem with melee infantry is what I meant. That is, even after cavalry and fliers are accounted for, Neph still has to fight through bows and mages. (Bow Infantry and Mage Infantry are still better than Melee Infantry.)

1 hour ago, Ice Dragon said:

A minnow friend of mine who has been playing since a week after launch pulled his first Tharja last week.

Making 75 pulls of red (300 orbs at 4 orbs per pull) gives you only about an 85% chance of pulling any particular 4-star red character. So no, 1000 orbs is not enough to statistically have one copy of every 4-star character in the game.

And he cared about Tharja? (If I cared about a 4* unit enough, I'd be preferentially pulling focus units sharing that unit's color.)

 

And 85% is damn good, since it takes literally infinite pulls to hit 100% chance of getting a particular unit. Like, it takes 4 coin flips to have a 93% chance of getting at least one heads, and three flips only gives 87.5%, but I'm not going to argue that it'd take 3 flips to get a head just because you need to flip 3 times to get almost 90% odds. (You need to flip 50% more than usual to get a near 90% chance)

 

And coins heads or coin tails have very high starting odds, let's take a fair dice (6 sided) and the chance of rolling a '1':

1 - (5/6)^17 = 0.95492675589. It needs 17 rolls to reach 95% odds.

1 - (5/6)^11 = 0.86541201425. It needs 11 rolls to reach 86% odds. (You need to roll almost twice normal to get less than 90% odds).

 

But are you seriously going to argue it takes 11 or 17 rolls to roll a damn 1 on a dice?

 

This is literally how gacha games get people, the expected number of pulls to get a unit (2 flips to get a head, or 6 rolls to get a '1') is not the number of times you need to roll to have a good shot at getting a particular unit.

A particular unit. If you're dealing with all units in aggregate the times you get short changed by RNG and the times you get blessed starts to even out, meaning getting a full set of units is far closer to the 2 flips for a coin or 6 rolls for a dice rather than the hugely inflated number of pulls to have like 95% chance of pulling a given unit.

1 hour ago, Ice Dragon said:

That's only vaguely relevant to the argument and actually makes it more strange that the skill is restricted to 5-star exclusive characters for so long and not less.

Yeah. (I have a tendency to just ramble on.)

 

Edit:

1 hour ago, bethany81707 said:

I'm still waiting on three 4* characters from launch, all of different characters, and one of whom is an important fodder (Roy).

Were you doing the math remembering to account for the 3-4* rate swap, @DehNutCase?

I didn't do any math. (All my numbers are backed by bullshit)

 

Like, I know how to setup the equation for it, but, if you've noticed, I've half-assed both the orbs required and the orbs we get per month.

 

Mind, missing a few characters is normal, if you look at my example above, expecting to get 100%, or even 90% odds is how gacha games make a killing, because the average number of rolls needed to get a certain unit and the number of rolls needed to get a 95% or even 85% chance of getting a certain unit is very different.

Like, the first is straight up 1/.03 (assuming 3% odds).

But the second is 1 - (.97)^x = odds, where x is the number of pulls.

If you want good odds x skyrockets.

 

Double Edit:

The worse the base chance, 50% for coin flip, 17% for dice roll, 3% for my example unit (3% is actually way too high), or about 1% or even .5% on large banners for a particular focus, the bigger x is compared to y, where odds = 1 - (1 - base chance)^x and y = 1/(base chance).

 

This is why the Ayra banner was actually very player friendly, and the people asking for huge ass banners with everyone on it is ruining everything for everyone.

 

Triple Edit:

@thecrimsonflash @bethany81707 But yeah, I misspoke when I said it's weirder to not have all the unit one cares about. What I really meant was that, past 1000 orbs (or however many it actually is), you'll have exceeded the expected number of pulls needed to get a full set of 4* units. Actually getting every single 4* means passing the odds = 1 (1 - base chance) ^ x check, which is... uncomfortable, to say the least, because every single unit needs to pass that check.

Yes, even at odds = 50% a lot of them (half, actually), would be expected to pass that check, but even at odds = 99% you 1 or 2 should slip through (because we have more than 100 units), and x gets crazy with odds that high.

Edited November 16, 2017 by DehNutCase

[Ice Dragon]

10 minutes ago, DehNutCase said:

And he cared about Tharja? (If I cared about a 4* unit enough, I'd be preferentially pulling focus units sharing that unit's color.)

Yes. Because Raudhrblade happens to be a thing. And actually, up until about a month ago, the only red tome user he had managed to pulled at all was Raigh.

 

12 minutes ago, DehNutCase said:

And 85% is damn good, since it takes literally infinite pulls to hit 100% chance of getting a particular unit. Like, it takes 4 coin flips to have a 93% chance of getting at least one heads, and three flips only gives 87.5%, but I'm not going to argue that it'd take 3 flips to get a head just because you need to flip 3 times to get almost 90% odds. (You need to flip 50% more than usual to get a near 90% chance)

85% is shit if you're trying to make sweeping generalizations like you are. It means somewhere between 1 out of 6 and 1 out of 7 people who have pulled red 75 times still does not have [insert 4-star red unit here]. That's literally the odds on Russian roulette.

I personally find 95% (19 in 20) to be "a safe bet" when speaking probability for any binary outcome.

[DehNutCase]

24 minutes ago, Ice Dragon said:

Yes. Because Raudhrblade happens to be a thing. And actually, up until about a month ago, the only red tome user he had managed to pulled at all was Raigh.

...Unless his box is full of red units I find that unlikely. Edit: Or rather, unless his box is literally filled with 5* red foci I'm not pitying him, since that's kind of a natural consequence of simply not pulling a lot of red orbs.

24 minutes ago, Ice Dragon said:

85% is shit if you're trying to make sweeping generalizations like you are. It means somewhere between 1 out of 6 and 1 out of 7 people who have pulled red 75 times still does not have [insert 4-star red unit here]. That's literally the odds on Russian roulette.

I personally find 95% (19 in 20) to be "a safe bet" when speaking probability for any binary outcome.

If you say so. The higher odds you establish odds at, where odds = 1 - (1 - base chance)^x, the higher x needs to be.

 

And 51% is already enough for it to be more likely to have a particular unit than not.

 

95% is 5% wrong, just like 51% is 49% wrong, personally I'm fine with simply reaching y pulls/rolls/coin flips, where y = 1 / base chance.

But, let's say we're on a heafty, 6 unit focus, with the unit you want being at .5% odds.

 

The number of rolls needed to reach odds = .95 = 1 - (1 - .01)^x has x = 298 rolls. That's more than a thousand orbs to reach your 'safe bet,' and one out of twenty people will suffer through that.

 

Me, on the other hand, I'm fine with 1 / .01 = 100 rolls, which is basically a third as much. Yeah, my odds are only odds = 1 - (1 - .01)^100 = 63.3%, but asking for 'safe bets' kills you in gacha games.

Like, there's one guy out of 100 who hits the odds = .99 barrier, which has x = 458 rolls. Four hundred and fifty eight rolls, not orbs. That's almost two thousand orbs.

 

And, honestly? No one really cares about those people. 1 out of 100 or even 1 out of 20 is not a large fraction of people, most people get their focus early enough (100 rolls is already over 60% odds, you really only need like 70 rolls to hit 50/50) that the few whales utterly wrecked by how gacha games work doesn't actually do anything to the player base, because, for them, they got their units in a reasonable time.

 

85% is shit for making sweeping generalizations? 15% is even worse, 10% is even worse, 5%, which is [edit: the fraction of people which need] your 'safe odds,' is out numbered 19 to 1.

Edited November 16, 2017 by DehNutCase

[Ice Dragon]

46 minutes ago, DehNutCase said:

...Unless his box is full of red units I find that unlikely. Edit: Or rather, unless his box is literally filled with 5* red foci I'm not pitying him, since that's kind of a natural consequence of simply not pulling a lot of red orbs.

I honestly have no idea what the hell you're talking about anymore. You're clearly contradicting yourself.

 

46 minutes ago, DehNutCase said:

85% is shit for making sweeping generalizations? 15% is even worse, 10% is even worse, 5%, which is [edit: the fraction of people which need] your 'safe odds,' is out numbered 19 to 1.

Like really, what the hell are you even talking about?

"You should have a Tharja by now" when the player only has an 85% chance of having a Tharja by now is clearly worse than when the player has a 95% chance of having a Tharja by now. A 19 in 20 chance of the statement "you should have a Tharja by now" is clearly safer odds than a 6 in 7 chance.

Edited November 16, 2017 by Ice Dragon

[DehNutCase]

2 minutes ago, Ice Dragon said:

I honestly have no idea what the hell you're talking about anymore. You're clearly contradicting yourself.

Sorry, I misworded that badly. What I meant was that: Unless he has a box full of red units [I find it hard to believe he actually wanted Tharja], not that unless he had a box full of red units, [I find it hard to believe he didn't get Tharja.]

3 minutes ago, Ice Dragon said:

Like really, what the hell are you even talking about?

"You should have a Tharja by now" when the player only has an 85% chance of having a Tharja by now is clearly worse than when the player has a 95% chance of having a Tharja by now. A 19 in 20 chance of the statement "you should have a Tharja by now" is clearly safer odds than a 6 in 7 chance.

"You should have Tharja by now" is something I'll say at 50.1%, because I'll be right more often than not.

 

The problem is that what I'm saying is that 'You'll need less orbs than x to pull y' at a probability = odds.

Whereas you're countering with 'You'll need more orbs than x to pull y' at a probability = odds.

 

Even if what you're saying is the same as mine, that is, you'll need less orbs than x to pull y rather than you'll need more orbs, the % of people you catch isn't the raw 95% or whatever. It's 95% or whatever minus my percentage.

 

Like, let's say 60% of people get Ayra in 200 orbs, and 85% of them get her in 400 orbs.

 

When you say: "It takes less than 400 orbs to get Ayra" and I say "It takes less than 200 orbs to get Ayra" the number of people I'm right about is the 60%, whereas you're right about 85% - 60% = 25% of them. And, if you said "It'll take more than 400 orbs to get Ayra," the number of people you'll be right about would be 15% of them, because that's the % of people who won't get Ayra in that amount of orbs.

 

The reason the 60% goes to me and not you is because less than 200 orbs is a stronger statement than less than 400 orbs. Otherwise the statement 'It takes less than infinity orbs to get Ayra' would be more right than both of us, and that's not true, because the statement itself is a weaker one than 400 orbs or 200 orbs.

 

That is, for 60% of people, the statement of 'less than 200 orbs' is more true than 'less than 400 orbs' because my hypothesis, like yours, is correct, but mine is the stronger hypothesis. Like: 'The coin will land either heads or tails' is a weaker hypothesis than 'The coin will land heads.' So the coin landing heads up is stronger evidence for the 'The coin will land heads' hypothesis than the 'The coin will land either heads or tails' hypothesis.

 

Yeah, getting Ayra under 200 orbs is support both for the under 200, under 400, and under infinity hypotheses, but that doesn't support all three hypotheses to the same degree, if you get what I'm saying.

 

[Ice Dragon]

19 minutes ago, DehNutCase said:

Sorry, I misworded that badly. What I meant was that: Unless he has a box full of red units [I find it hard to believe he actually wanted Tharja], not that unless he had a box full of red units, [I find it hard to believe he didn't get Tharja.]

He wasn't ever specifically aiming for Tharja, but he pulls evenly across non-colorless colors and was lamenting his severe lack of red mages.

 

20 minutes ago, DehNutCase said:

"You should have Tharja by now" is something I'll say at 50.1%, because I'll be right more often than not.

"You should (statistically) be male" is a ludicrous statement to make even though you will be right for 50.05% of the humans on Earth.

"Less than 200 orbs" is indeed a stronger statement than "less than 400 orbs", but being right only 60% of the time instead of being right 85% of the time is statistically weak. 60% accuracy is less than 1 sigma, which is literally shit in any scientific area of study (except maybe psychology) and is actually almost literally as good as meaningless from a statistical perspective. 95% is 2 sigma, which is good enough accuracy for undergraduate (200-level) experimental physics (and that's actually my college background).

[DehNutCase]

14 minutes ago, Ice Dragon said:

"You should (statistically) be male" is a ludicrous statement to make even though you will be right for 50.05% of the humans on Earth.

"Less than 200 orbs" is indeed a stronger statement than "less than 400 orbs", but being right only 60% of the time instead of being right 85% of the time is statistically weak. 60% accuracy is less than 1 sigma, which is literally shit in any scientific area of study (except maybe psychology) and is actually almost literally as good as meaningless from a statistical perspective. 95% is 2 sigma, which is good enough accuracy for undergraduate (200-level) experimental physics (and that's actually my college background).

The fact the other option is 'you're either male or female,' is the problem here. Being right is pointless if it doesn't actually tell you anything. Just like how 'it'll take less than infinite orbs to get Ayra' is literally 100% correct, it's also meaningless because you can't use that statement to determine the correct course of action---how many orbs you'll want to budget for her.

My argument is that 'less than 400 orbs' is already toeing the line into meaningless territory because it's not, in fact, relevant for a large portion of the population. (Because 60% of those get it under 200 orbs.) And also because 95% is a damn arbitrary number, even if it's an arbitrary number science folks have gotten used to.

 

It's a trade-off between correctness and precision---the less precise you are, that is, the larger number of orbs you name, the more people to catch, but, in exchange, the number becomes less and less relevant, less and less userful, for anyone inside the category. To increase the number of orb's precision, that is, how useful it is, you have to limit the amount of people you apply the number to.

 

Mind, this is true no matter what particular number of orbs we choose. We already have enough information to completely compute the odds of getting a given unit given a certain number of orbs/pulls, we can just shove that into people's faces and let them determine what's the number of orbs that satisfies their need of correctness vs. precision. We're, essentially, arguing over what particular number of orbs we should arbitrarily choose to use as the 'you need this many orbs to pull someone.'

 

 

You're setting it as number of orbs = x * orbs per pull when .95 = 1 - (1 - odds per pull)^x

That is, when you have a 95% chance of getting the unit. (A number that, like you say, catches 95% of people while shoving 5% off a cliff, because 95% is statistically significant.)

 

I'm using a different equation. (It's just that it happens that .6 or thereabouts = 1 - (1 - odds per pull)^x.)

I use the number of 'expected orbs per Ayra.' That is, number of orbs = x * orbs per pull when x = 1 / (odds per pull).

It's just that odds happens to equal 60% or so when you plug the x into odds = 1 - (1 - odds per pull)^x equation.

 

My number is more precise, of course, because it catches less people. (I'm in favor of shoving more people off cliffs, in other words, but, in exchange, the people that I didn't shove off cliffs get more useful information.) We can call this effectively neutral factor, that is, neither a plus nor a minus. Like, I can be way more precise and say, you'll need between 75 - 125 orbs, and catch, say, the 50% smack dab in the middle of the bell curve (numbers are just for example), but, naturally, I shoved the 50% on the edges off cliffs in exchange for that exceeding precise range of 50 orbs.

 

The main advantage is that my number of orbs happens to use the 'average number of orbs,' that is, if we took the amount of orbs everyone spent to get Ayra, and divided it by the amount of Ayras that popped out, we'd get my number.

This means:

A, It can be experimentally verified.

B, It's not arbitrary

That is, the 66% or whatever odds is not something I just randomly say 'this is a good, significant number.' For getting heads in a coin flip x is two, because 1/.5. Giving us an odds of odds = 1 - (1 - .5)^2 = .75, for example, 75% Getting a 1 on a dice roll would be x = 1 / (.16666), for odds = 1 - (1 - 1/6) ^ x = 67%.

 

Why is the average useful? Because, surprisingly or not, gambles are less and less about sheer luck the more you do them, the orbs you waste from being unlucky as hell on one banner would be counteracted by the orbs you save from being full of luck another.

Even for one person, over a long enough time, the orbs needed to get all the units he care about approaches the sum of [# of copies he wants] * [average orbs needed per copy]. (That is, you sum up # * average orbs for every single unit he wants.)

The number you give can't be used for that equation because it wildly overestimates the # of orbs needed. (And, unfortunately, even then it doesn't catch everyone---you might've shoved less people off cliffs than I did, but you still shoved 5% off.)

 

This is why I used the 1k orbs (or whatever it actually is---I didn't actually calculate because, honestly, the precise number doesn't matter too much for our argument) value for the number of orbs which, after you've expended them, you should have a full set of 4* units. (Technically that isn't it, precisely, the number I gave is more specifically the number of orbs you need to spend, on average, to get one, particular, specific 4*. It's just that you'll usually have pulled every other 4*, on average, in the process of getting that specific 4*)

 

This is because the number that catches 100% of people will always be 'bring an infinite number of orbs, buddy,' which is bloody meaningless, and I don't see any particular difference between shoving 5% of people off cliffs and 15%, 20%, or whatever% of people off cliffs. (And the people who are getting shoved off cliffs won't see any particular difference either---no matter how high we set the bar, there'll always be some people we're shoving off cliffs, so we might as well use the more useful number.)

 

Even for experiments, .95 being statistically significant is merely a bar for getting published. Like, do you honestly think, for example, we only have F(gravity) = GM1M2/r^2 at 95% confidence? Heck no. We have like .999999999999999999 confidence in it because every single experiment that uses the gravitational constant and ends up working is another bit of evidence that our value of G is correct.

This is also why people do additional experiments if they find, for example, 1 flavor out of 20 flavors of jelly bean causes an arbitrary effect. 95% is 'good enough' yeah, but it's 'good enough' for being published, not 'good enough' for actually using. I'd much, much rather use our current value of G than a G we have 95% confidence in.

 

Obligatory xkcd link:

https://xkcd.com/882/

[bethany81707]

Do you two even know what you're trying to argue anymore? I think it was something about having or not having a certain 4*?

[DehNutCase]

37 minutes ago, bethany81707 said:

Do you two even know what you're trying to argue anymore? I think it was something about having or not having a certain 4*?

We argue for the sake of arguing, of course. (It works on our debate skills and Ice Dragon helps me see where I could improve---like my tendency to ramble on and on about irrelevant things.)

Edit: A lot of the argument is also helping me see where I stand on things. It turns gut feelings I have into things I've written out, something I can examine, something that I have the time between typing it up and clicking submit to think about, and then think about again when Ice responds.

And, when I actually agree with his counter-arguments---I change my mind. (Which is actually a secondary effect of arguing, despite what it might seem like. It does no good to be correct about one thing when your way of thinking is flawed---arguing is a way to improve the way you think as well as a way to know particular correct things.)

Edited November 16, 2017 by DehNutCase

[Clogon]

3 hours ago, Ice Dragon said:

"You should (statistically) be male" is a ludicrous statement to make even though you will be right for 50.05% of the humans on Earth.

Sorry to derail but WTF. When did this happen? Back in my day, there were more women then men... We need more male only wars to kill off our population especially the chinese (no racial hate just that they have the highest male to female ratio). :P In all seriousness though, this just blew my mind. I am dumbfounded enough to forget the entire reason why I came to this thread.

[Ice Dragon]

1 hour ago, DehNutCase said:

-snip-

Of note, the math comes out that if you use the average number, you'll always end up close to 1 sigma (actually a bit lower) (triple the average number gets you to 2 sigma) since this is a binomial distribution. Of course, by virtually every measure, 1 sigma (p > 0.32) is shit.

 

There is one inherent flaw with you saying that the average is useful: The average is only meaningful if you can conduct a large number of trials. This is how the law of large numbers works. When your data set isn't large enough, random variance takes over and the noise is the same magnitude as the signal, which is functionally indistinguishable from there being no signal at all.

When pulling from a gacha, the fact that you should, on average, have one copy of x for every n pulls only matters if you can pull some 5n or 10n times so that your signal (the number of copies of x) becomes noticeably larger than the noise of random chance. When you've only pulled n times (which gets you about a 63% chance of success), your signal is indistinguishable from random noise.

This is why my arbitrary threshold for meaningfully being able to say "you should have at least 1 occurrence of x" is at 2 sigma, or 95%. Heuristically, this can be (very loosely) interpreted as your signal being double the height of your noise.

This gives you a good balance of decent statistical significance with a small enough trial count to be meaningful. Smaller trial counts, like what you're using, sacrifice statistical significance to the point where random chance plays too large of a role, and larger trial counts are too large to be "powerful statements" that can be used as a heuristic. This can be easily seen with the egregious cases of "you should have Tharja by now after 1 pull (2.14% chance, 1 in 47 chance of success)", which is not only blatantly false, but also wholly dictated by random chance, and "you should have Tharja by now after 1,000 pulls (99.99999996% chance, 1 in 2.5 billion chance of failure)", which is at the level of "well no fucking shit, Sherlock". Neither of those statements are meaningful in any usable way.

 

1 hour ago, DehNutCase said:

Even for experiments, .95 being statistically significant is merely a bar for getting published. Like, do you honestly think, for example, we only have F(gravity) = GM1M2/r^2 at 95% confidence? Heck no. We have like .999999999999999999 confidence in it because every single experiment that uses the gravitational constant and ends up working is another bit of evidence that our value of G is correct.

Actually, this just shows you have no idea how this works.

You don't measure the gravitational constant by counting occurrences. That's inefficient and takes far too much data to lower the experimental uncertainty because the uncertainty in counting statistics is the square root of the count. E.g. to lower the uncertainty by a factor of 10, you need to perform 100 times more trials. For example, you can actually "measure" the value of pi by throwing toothpicks at a set of parallel lines, but it would take an order of 10^20 (100,000,000,000,000,000,000) toothpick throws just to get the first 10 digits. (According to Wikipedia, that many toothpicks would weigh about the same as enough food to feed the current population of the Earth for 2,000 years)

No, you measure the gravitational constant by measuring a quantity (distance, mass, etc.) to the highest possible precision your instruments allow you to. That precision then directly calculates to a precision for your derived value, in this case, the gravitational constant.

 

As for the xkcd comic, that's just poking fun at the media for jumping to dumb conclusions because they know nothing about how science works (and at scientists who blindly use the p > 0.05 heuristic without knowing what it means).

That's entirely different from what we're discussing. In clinical trials, the experimenters are doing the analogue of obtaining results, then using the results to determine the "success" rate, whereas in the case in our discussion, we know the success rate and are attempting to determine at what point can we can sufficiently correctly predict the results.

 

2 minutes ago, Clogon said:

Sorry to derail but WTF. When did this happen? Back in my day, there were more women then men... We need more male only wars to kill off our population especially the chinese (no racial hate just that they have the highest male to female ratio). :P In all seriousness though, this just blew my mind. I am dumbfounded enough to forget the entire reason why I came to this thread.

Google tells me that the current ratio of males to females on Earth is 101:100.

The problem with China is their current one-child policy, which heavily favors keeping a male child due to males having genetic predisposition to being better farmhands (more muscle mass, namely). Enough so that the government hands out subsidies to families that have a female child.

[Clogon]

I remember now:

Assuming Ice Shield is just an Aegis that adds reduced damage to the next attack, Fjorm with Shield Pulse can survive and KO an fully buffed +10 Blade S!Camilla with ATK boon+Seal that is next to a Goad Flier ally with Spur ATK 3 seal.

Edit:

I feel like wanting a -Res/+HP to maximize this special. You gain more EHP and deal more damage on return.

Edited November 16, 2017 by Clogon

[DehNutCase]

1 minute ago, Ice Dragon said:

Actually, this just shows you have no idea how this works.

You don't measure the gravitational constant by counting occurrences. That's inefficient and takes far too much data to lower the experimental uncertainty because the uncertainty in counting statistics is the square root of the count. E.g. to lower the uncertainty by a factor of 10, you need to perform 100 times more trials. For example, you can actually "measure" the value of pi by throwing toothpicks at a set of parallel lines, but it would take an order of 10^20 (100,000,000,000,000,000,000) toothpick throws just to get the first 10 digits. (According to Wikipedia, that many toothpicks would weigh about the same as enough food to feed the current population of the Earth for 2,000 years)

No, you measure the gravitational constant by measuring a quantity (distance, mass, etc.) to the highest possible precision your instruments allow you to. That precision then directly calculates to a precision for your derived value, in this case, the gravitational constant.

I guess I mispoke a bit---but yes, you're right that one very precise measurement in better than tons of bad ones. (Similar to how odds = 1 - (1 - base odds)^x has a very small x if base odds is high. You need a ton less x to have good odds if base odds is high. Coin flip vs. Dice roll has coin at a 50% increase over average against dice roll being almost an 100% increase over average to get about 90% odds.)

What I should've said was that the fact that the force of gravity was equal to F(grav) = GM1M2/r^2 is very certain because everything that uses the equation is testing the equation. And, if G was wrong, or M1*M2 were wrong, or weakening as the square of the distance were wrong, there's many opportunities to notice.

 

The repeated tests is an increase in certainty, not precision, is what I mean. Precision is 'you'll get it under x orbs,' certainty is the amount of people that it applies to (say, about 60% for 200).

 

12 minutes ago, Ice Dragon said:

Of note, the math comes out that if you use the average number, you'll always end up close to 1 sigma (actually a bit lower) (triple the average number gets you to 2 sigma) since this is a binomial distribution. Of course, by virtually every measure, 1 sigma (p > 0.32) is shit.

Not by the value of majority rules. p > .32 catches 64% of people. (If we're going by 1 sigma above and below the average.)

13 minutes ago, Ice Dragon said:

There is one inherent flaw with you saying that the average is useful: The average is only meaningful if you can conduct a large number of trials. This is how the law of large numbers works. When your data set isn't large enough, random variance takes over and the noise is the same magnitude as the signal, which is functionally indistinguishable from there being no signal at all.

When pulling from a gacha, the fact that you should, on average, have one copy of x for every n pulls only matters if you can pull some 5n or 10n times so that your signal (the number of copies of x) becomes noticeably larger than the noise of random chance. When you've only pulled n times (which gets you about a 63% chance of success), your signal is indistinguishable from random noise.

This is why my arbitrary threshold for meaningfully being able to say "you should have at least 1 occurrence of x" is at 2 sigma, or 95%. Heuristically, this can be (very loosely) interpreted as your signal being double the height of your noise.

This gives you a good balance of decent statistical significance with a small enough trial count to be meaningful. Smaller trial counts, like what you're using, sacrifice statistical significance to the point where random chance plays too large of a role, and larger trial counts are too large to be "powerful statements" that can be used as a heuristic. This can be easily seen with the egregious cases of "you should have Tharja by now after 1 pull (2.14% chance, 1 in 47 chance of success)", which is not only blatantly false, but also wholly dictated by random chance, and "you should have Tharja by now after 1,000 pulls (99.99999996% chance, 1 in 2.5 billion chance of failure)", which is at the level of "well no fucking shit, Sherlock". Neither of those statements are meaningful in any usable way.

There are two ways to reach a large number of trials: Each person can do tons of trials, or a ton of people can do trials.

Pulling from gacha---and giving advice to people pulling from gachas---satisfy both of these conditions.

If a person keeps playing this game, they'll obviously spend orbs on new banners. This is the tons of trials part. And, if we were to give advice to large numbers of people in aggregate, then they're a ton of people doing trials. (Hell, pulling for all 4*s in aggregate is also an example, because you're more or less conducting a separate trial for each individual unit---yeah, there'll be a ton of outliers, units that just won't come, but the majority would come in around the average because that's kind of how math works.)

 

There's going to a large (in absolute terms) number of people who do not approach any precise orb count---your 95% has 5% people screwed, my 60% or so has 40% screwed.

There's even another problem that comes in where stacking too many orbs is just as bad as having too few orbs. Why? Because orbs you saved for later is orbs you can't spend now. Every orb saved during, say, Brave Heroes was an orb that wasn't spent on B!Ike, B!Lyn, etc.

Basically, what I'm saying is that it's not necessary, not even a good idea, to assume that you need give expected orb counts for 95% odds to pull a unit. 95% odds is the kind of high reliability numbers you saved for units you really like rather than any given unit. Hell, this is evident if one simply imagines that everyone wants every unit at 95% odds. You know what will happen? They'll always only spend until they have 400 or so orbs left (whatever gets 95% odds) for the next unit they like, meaning they're basically sitting on 400 orbs worth of unused resource.

The difference between the guy sitting on 400 orbs and the guy who's comfortable going down to 0? The guy who's at 0 will have 400 more orbs invested in his units, forever. Because their orb acquisition rate is the same.

 

If you tried to save resources like that in any RTS game you'd get utterly wrecked. Yeah, if you save 400 minerals you can build a emergency 2 tanks or 8 marines (Starcraft) to fight off a rush, while keeping the option open to expand with it as well. (Assuming time is free for producing units here). But the guy who fast expanded, and the guy who built 8 marines immediate to come wreck your shit, got everything 400 minerals earlier than you did. If he fast expanded it means his income spiked 400 minerals before you did, meaning he'll have that income difference for the x seconds before you got your expansion up (while keeping your stockpile). If the guy built 8 marines it means his units have been out and about doing things for longer than your marines---defender advantage comes from shorter reinforcement paths, meaning less time to get to the front lines, but the time you saved with defender advantage is negated by the time the other guy saved by not having a stockpile.

 

Any guide that gives 'this is the amount of orbs you'll need to spend' is an implicit recommendation to have that many orbs on hand to pull this unit. In other words, anything that gives a 'expected orbs to pull' number is a recommendation in spending resources efficiently. And efficiency means as low as a stockpile as possible while not missing anything important. (In SC:BW, or a normal game of it, it means spending as much as possible on expansions and gathering more resources, and spending just enough that the other guy doesn't kill you.) In this game it means having enough orbs to reasonably use up your pity %. Because the last couple orbs you spend on a banner is more valuable than the first couple, thanks to pity rate. (This doesn't mean you should stockpile enough to force the 14% full pity break or whatever it is. Any efficiency you gain from having that many on hand is lost again because you're keeping that many orbs doing nothing. Honestly, always going down to 0 orbs on a banner isn't even a bad plan. It takes a long time for the efficiency of never having high pity rates before the banner rotates out to catchup to the fact that the guy hoarding orbs for getting pity-breakers is hundreds of orbs less invested in units at any given time.)

 

Even regular FE is like that. Holding stat boosters until the end game meant that the stat booster did literally nothing the whole game. (Part of many, many reasons why Jeigans are good, they're always around to recieve and use boosters thanks to their good availability and base stats. It's not putting boosters to use if your stats are still too low to fight, after all.)

[Hawk King]

9 hours ago, Ice Dragon said:

The problem with China is their current one-child policy, which heavily favors keeping a male child due to males having genetic predisposition to being better farmhands (more muscle mass, namely). Enough so that the government hands out subsidies to families that have a female child.

I'm sure you are aware, but China has recently dropped their one-child policy within the last year.

Since you guys are talking about the odds of pulling certain characters and stuff. I have noticed that certain characters are extremely common pulls during some of my summon sessions. Like, I will go hundreds of pulls without getting Lon'qu for instance and then all of a sudden I will get like 5 out of 10 red summons being a 3* or 4* Lon'qu. Recently for me it was Arthur, When pulling greens for Amelia I got Arthur on all 3 green orbs of a summoning session and 4 straight overall. Also I have gotten multiple non-focus 5* unit within the same day of doing summoning sessions.

My sample size isn't the largest so since you have done many more massive summoning sessions, have you noticed that the odds of pulling certain non-focus units change from day to day?

[XRay]

55 minutes ago, Hawk King said:

Since you guys are talking about the odds of pulling certain characters and stuff. I have noticed that certain characters are extremely common pulls during some of my summon sessions. Like, I will go hundreds of pulls without getting Lon'qu for instance and then all of a sudden I will get like 5 out of 10 red summons being a 3* or 4* Lon'qu. Recently for me it was Arthur, When pulling greens for Amelia I got Arthur on all 3 green orbs of a summoning session and 4 straight overall. Also I have gotten multiple non-focus 5* unit within the same day of doing summoning sessions.

My sample size isn't the largest so since you have done many more massive summoning sessions, have you noticed that the odds of pulling certain non-focus units change from day to day?

I do not think the odds change for a unit in a banner outside of the percentage changes.

For example, this is most likely NOT a random sample for coin flips:
hththhtthhthtthhththhtthhttthhhhtthhthtthhtthtthttthhhthththtthhhtthhhthhthththhthhhhtthththhhththhhtthhththth

This is much more likely to be random:
hththhhththhhhhhhhttthhththhtttttttttttttthhththhhtthhththtthhhttttthhhhtttttthhhhththhttthhhhhhtthhthttthhhhhttttt

Getting heads or tales many times in row is pretty common. Getting Lon'qu or Arthur in quick succession after a dry spell is little more complicated to illustrate since there are so many more options than just heads or tails, but hopefully you get the idea.

[Ice Dragon]

8 hours ago, DehNutCase said:

Pulling from gacha---and giving advice to people pulling from gachas---satisfy both of these conditions.

We are neither pulling from a gacha or giving advice to people pulling from gachas here. We are determining at what point is it safe to say that you probably should have gotten a copy of a character, i.e. at what point can we safely assume you have access to the resources the character has. This, by definition, is necessarily a single trial, which means the average value is utterly meaningless.

Furthermore, by "safe to say", we don't mean that we will be right more often than we are wrong. It's not safe to say that a D20 will land greater than 8 because you cannot depend on a D20 to land greater than 8. You can, however, depend on the fact that, for a single roll of the die, you will at least probably not roll a 1.

You can use the average to determine when it's safe to say that a player has gotten 10 copies of a character (because that's running the trial 10 times), but you cannot use the average to determine when it's safe to say that a player has gotten their first copy of a character. If you do the math, you'll see that to reach a particular threshold (say, 95%) for a certain number of required successes (say, 10 copies of a character), the larger the number of required successes, the closer the number of attempts needed to reach the threshold tends closer and closer to the average. But when the number of required successes is small (like 1), you need to make more attempts to hit the threshold because of the effect of random variance.

 

Your entire spiel about resource management is irrelevant. We are not trying to give advice on how many orbs to stockpile. We are trying to determine the point at which an assumption ("you have x character") can be considered a valid assumption based on the number of orbs already spent.

 

 

Also, as a side note, I know exactly how StarCraft resource management works. That happened to be my game of choice back in college while Fire Emblem was being released on systems that I didn't have (and emulation for those systems was not yet up to scratch).

[Okigen]

Am I the only one not hyped with the hero fest banner? I thought I could whale for a +10 this time but the chance is pretty slim given they have 3 heroes each color now. 

[Clogon]

4 hours ago, Hawk King said:

Since you guys are talking about the odds of pulling certain characters and stuff. I have noticed that certain characters are extremely common pulls during some of my summon sessions. Like, I will go hundreds of pulls without getting Lon'qu for instance and then all of a sudden I will get like 5 out of 10 red summons being a 3* or 4* Lon'qu.

Welcome to the world of true random distribution. Most people think that a random distribution will be spread over all possible outcomes and fail to realize this is only true over an infinite number of draws. As you would expect, most people hate true random since you are either super lucky or unlucky with little inbetween until you get into an extremely massive sample size.

 

Some games (like Dota) implement something call pseudo-random. Where they force the average and eliminate outliers. This makes the game a bit more predictable.

21 minutes ago, Okigen said:

Am I the only one not hyped with the hero fest banner? I thought I could whale for a +10 this time but the chance is pretty slim given they have 3 heroes each color now. 

This is not a hero fest so it is understandable that it doesn't have the same rates. But I agree that it will be quite difficult to +10 things... Makes me sad too.

Edited November 16, 2017 by Clogon