5* Pull Rates & Capping Futility
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helix72
Posts: 992 Critical Contributor
***EDITED MATH AND EXAMPLES TO CORRECT CURRENT 5* PULL RATE TO 15%***
I've seen a few discussions suggesting the developers should institute a cap on how many non5* pulls you can get in a row before guaranteeing a 5*.
But if they simply add a cap, then the effective pull rate goes up. Today, the pull rate is 15%. So, in 20 pulls you will on average get 3.00 5*s (ignore BH for the moment). If they said, "okay, if you go 19 pulls in a row without a 5* the 20th pull is a guaranteed 5*" then the effective pull rate actually increases to 15.6%. Now, every 20 pulls you'd be expected to get 3.12 5*s. Maybe this is one of the reasons they haven't done it.
So my question to the community: would you be willing to accept a lower pull rate in exchange for a cap that keeps the effective pull rate the same?
For example, the below are all within 0.1%0.2% on an effective pull rate basis:
Current: 15% pull rate, no cap
Proposal 1: 9.4% pull rate, cap at 9 (10th draw guaranteed if 0 for last 9)
Proposal 2: 13.2% pull rate, cap at 14 (15th draw guaranteed if 0 for last 14)
Proposal 3: 14.3% pull rate, cap at 19 (20th draw guaranteed if 0 for last 19)
The lower the cap, the lower the pull rate needs to be and thus the more likely you are to hit the cap. At the extreme, the pull rate could be 0% with a cap of 6.
One other side that might make this never happen: any cap reduces randomness. The randomness is part of what psychologists call random rate reinforcement which is what keeps us playing and earning and pulling and playing and earning and pulling and playing and earning and pulling...
So giving us a cap might actually be counter to a good business model, which relies on an active player base. The question then is, which is higher: players who give up and stop playing because it is too random, or players who get bored and stop playing because it is not random enough? But I digress. Focus on the original proposal! Pull rates and caps: what's your ideal?
I've seen a few discussions suggesting the developers should institute a cap on how many non5* pulls you can get in a row before guaranteeing a 5*.
But if they simply add a cap, then the effective pull rate goes up. Today, the pull rate is 15%. So, in 20 pulls you will on average get 3.00 5*s (ignore BH for the moment). If they said, "okay, if you go 19 pulls in a row without a 5* the 20th pull is a guaranteed 5*" then the effective pull rate actually increases to 15.6%. Now, every 20 pulls you'd be expected to get 3.12 5*s. Maybe this is one of the reasons they haven't done it.
So my question to the community: would you be willing to accept a lower pull rate in exchange for a cap that keeps the effective pull rate the same?
For example, the below are all within 0.1%0.2% on an effective pull rate basis:
Current: 15% pull rate, no cap
Proposal 1: 9.4% pull rate, cap at 9 (10th draw guaranteed if 0 for last 9)
Proposal 2: 13.2% pull rate, cap at 14 (15th draw guaranteed if 0 for last 14)
Proposal 3: 14.3% pull rate, cap at 19 (20th draw guaranteed if 0 for last 19)
The lower the cap, the lower the pull rate needs to be and thus the more likely you are to hit the cap. At the extreme, the pull rate could be 0% with a cap of 6.
One other side that might make this never happen: any cap reduces randomness. The randomness is part of what psychologists call random rate reinforcement which is what keeps us playing and earning and pulling and playing and earning and pulling and playing and earning and pulling...
So giving us a cap might actually be counter to a good business model, which relies on an active player base. The question then is, which is higher: players who give up and stop playing because it is too random, or players who get bored and stop playing because it is not random enough? But I digress. Focus on the original proposal! Pull rates and caps: what's your ideal?
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Comments

Apologies to @helix72! I misinterpreted what you were suggesting. Yes, a cap (aka streak breaker) like you're suggesting is a good idea as it keeps the average (effective) pull rate at 15% but reduces the variance (randomness).
As for which value, I think having the cap at 14 (15th draw guaranteed if 0 for last 14) sounds like a good compromise between reducing some of the randomness but still keeping it fun.0 
The pull rate is 15%. It is not exactly 1 in 7, that is an approximation. That is if you choose to belive the ingame and forum (and discord) info on it.
My personal pulls, since I started keeping track 15 months ago is ~13.57% (169/1245). For what it's worth, I was probably slightly above average before that point, but can't be sure. Also, my bonus hero rate on 5* is way above average. I had 710 before starting records, and had 13 since. So that helped remove the sting of below average pulls. But one of my alliancemates can count the total number of his bonus 5's to date with one hand...
I'd be ok with adjusting the overall odds (all taken into account  base odds, streak breaks, bonus odds) if it meant we do have some type of streak breaker. Doesn't have to be a hard break after X misses, though that's probably the easiest way for all players to see it "working".
1 
I want the better long term odds. Whichever gets me that is what I want. I couldn't care less about streaks. I've pulled twenty in a row without a 5. I've pulled six and gotten 4 of them.
More. Just more.2 
First, I believe the real pull rate is 15%, which is 1 out of 6.66666. For the sake of some player's math skills, they simply labeled it ~1:7. Second, how did you calculate that limiting 4* streaks to 13 would increase the 5* rate by 1.8%? The odds of getting 13 x 4* covers in a row are 12.09% (which is 1 out of 8.27). So, a streak of 13 x 4* covers is supposed to happen once every 107.5 pulls (13 x 8.27 = 107.5). If we got an extra 5* cover every 107.5 pulls, that's an increase of 0.93%, making the overall odds 15.93%. Add in 5*BH odds, which are 0.75% (5% x 15%) and the overall odds would be 16.68%.I do believe a 4*streak limit would be good for player morale and not break MPQ economics at the same time. Do they realize how much work it takes just to get 1 LT or 25 CP? Then after an entire week of working at your parttime MPQ job, you open a small batch of Latest Legends, getting just 1 x 5* cover. Sometimes, you don't even want that 5* character, but if you do want it, then that's just 1 out of 13 covers you need to collect. But since distribution is random, it may take 15  18 covers to complete the character. Then before you complete the character, they move out of Latest into Classics.I hope Demiurge realizes how demoralizing this situation is. It's possible to work hard in this game and not get "rewarded" with completing 5* characters. I know many players can complete every 5* that comes along, but there are many players who cannot. If a player has a deep roster of 4* champs, but no 5* champs, something went wrong.1

bbigler said:If a player has a deep roster of 4* champs, but no 5* champs, something went wrong.2

I think a big part of it is understanding that streaks will break. I just went a 30 Latest legend streak with no 5*. Thanks to these forums and players who understand these things much better than I do, I know things will change if you keep going. Even though it has been frustrating.
Without that though, well, it could easily look like there is something seriously screwy going on and the temptation to quit would be high.0 
This sort of system would be sort of how Fire Emblem does theirs: You get a base pull rate for 5*s, then for each character you pull that *isn't* one, that rate goes up for the next pull. It's effective in giving users a definite stopping point saying "YOU WILL GET A 5* NOW", but it has similar drawbacks and complaints:
 I have a 96% chance of pulling a 5 and didn't! Rigged!
 I had a 25, 30, 35, 40% chance of pulling and I didn't! That's more than 100% Rigged!
 I pulled a 5 after 10 pulls and I pulled a freakin' XYZ? XYZ is junk! They rig their desired 5* rates!
I'm not saying their system is better or worse than a purely statistical system, as that's subjective. Just that it doesn't necessarily solve the desired perception problems; It replaces them with others.10 
But adding some sort of rolling guarantee would be regarded as an improvement almost universally, no matter the fringe complainers. Not doing something because someone is bound to complain isn't a reason to not do something. It's not like it stops the release of a character every 2 weeks.
6 
I don't see the proof that higher pull rates = lower sales.
where iz the maths that says if you gave the players a higher percentage chance of pulling a 5*(i vote 20%) AND every tenth LT you open is guaranteed to be a 5* AND the BH rates were doubled AND you created a Classic Token(CT) that would somehow diminish revenue?Borstock said:More. Just more.
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Sometimes it can seem like things aren’t right , I had a run of a few months getting next to no 5*s from the special stores spending over 1000 CP on each.
But then it started to even out and then you get things like this release where I pulled 5 5*s from 15 pulls which is way above the 15% and 3 5*s from the legendary store from 10 pulls
so although it gets really frustrating at times im quite happy with the percentages .
Id rather see different stores so that you can try for specific characters , I don’t have any champed 5*s yet and the big hitters are all in the classic store which is extremely diluted0 
I really hoped that this sort of Pity Timer would be added to at least the Bonus Heroes system. A separate count for each * tier, that ticks up and increases the odds every time a player 'fails' their RNG Bonus Hero roll.0

justsing said:No, a reduced pull rate in exchange for an assured minimum rate is not worth it in the long run imo.
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jamesh said:justsing said:No, a reduced pull rate in exchange for an assured minimum rate is not worth it in the long run imo.
0 
Just for purposes of illustration on that:
Take a 15% pull rate for 5s. So chances of you pulling 2 in a row is ~2.2%, or ~1:50. So, say a drop cap were introduced and it was worked out that for the same chance it would be 8% drop rate and raises enough per pull that statistically you'll get the same number of 5s over time. We'll say 3% per pull. Well, that means that you now have a ~0.6% chance to pull 2 in a row, or ~1:166. So way lower chance of getting that lucky streak. AND it means that for the first 3 pulls, you have a *lesser* chance of getting a 5 than at current in exchange for getting more down the line.
Again, I can't say which one's better. Some people will subjectively say that getting a 5 every 30 pulls max is better even if it means that a few pulls are largely wasted to "prime the pump" with a lower base rate. Others will say that the higher rate is better because no pulls are wasted at a low rate and it grants a better chance at that 2 for 2 jackpot.3 
@bbigler I've shared the sheet, and left it at 1/7 and 13 so you can see where the original results came from. It's easy to update the sheet to use 15% or any other amount and put any cap you want. As for the math, I believe the problem as presented is each group of pulls is not independent and the order in which you get the 5* matters.
Take the case where you get one 5* randomly in 13 pulls. If you got it on pull #1, the expected number of 5*s in the second set of 13 pulls goes up because you are guaranteed to get a 5* on either pull 14 or 15. But if you got it on pull 13, the cap got reset and the expected number of 5*s is less than in the first scenario.
Please feel free to play around, and let me know if I messed up the simulations:
https://docs.google.com/spreadsheets/d/1ZKhFnBxUqifirb68eHWOPv0Xr_rNoDR0sw1M8f9eNwU/edit?usp=sharing
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All I know is, it's the runs of 30+ pulls without a 5* when I start thinking  what am I doing with this game? why bother with this tinykitty when it can all be in vain because of rng? I realize how the odds work, and can see on my own example that 2030 runs without a 5* happen all the time. Still, that's how it feels to me. And those are not the trully horrible runs, people have had 50+ or 70+ run dry spells...
8 
IceIX said:Just for purposes of illustration on that:
Take a 15% pull rate for 5s. So chances of you pulling 2 in a row is ~2.2%, or ~1:50. So, say a drop cap were introduced and it was worked out that for the same chance it would be 8% drop rate and raises enough per pull that statistically you'll get the same number of 5s over time. We'll say 3% per pull. Well, that means that you now have a ~0.6% chance to pull 2 in a row, or ~1:166. So way lower chance of getting that lucky streak. AND it means that for the first 3 pulls, you have a *lesser* chance of getting a 5 than at current in exchange for getting more down the line.
Even at 15% it's not that easy to cover the latests 3 if RNG decides you're not covering that character.
(Fire Emblem uses a low rate because you only need 1 cover to unlock that character, we need 13 covers...)
I like the Fire Emblem Heroes system. From my experience, it's rather effective at actually allowing you to chase a character and get it eventually (their special vaults also run much longer which is super useful, in MPQ its like 5 days which is way too short).
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sinnerjfl said:IceIX said:Just for purposes of illustration on that:
Take a 15% pull rate for 5s. So chances of you pulling 2 in a row is ~2.2%, or ~1:50. So, say a drop cap were introduced and it was worked out that for the same chance it would be 8% drop rate and raises enough per pull that statistically you'll get the same number of 5s over time. We'll say 3% per pull. Well, that means that you now have a ~0.6% chance to pull 2 in a row, or ~1:166. So way lower chance of getting that lucky streak. AND it means that for the first 3 pulls, you have a *lesser* chance of getting a 5 than at current in exchange for getting more down the line.
Even at 15% it's not that easy to cover the latests 3 if RNG decides you're not covering that character.
(Fire Emblem uses a low rate because you only need 1 cover to unlock that character, we need 13 covers...)
I like the Fire Emblem Heroes system. From my experience, it's rather effective at actually allowing you to chase a character and get it eventually (their special vaults also run much longer which is super useful, in MPQ its like 5 days which is way too short).
Fire Emblem does actually need multiples of characters, since it requires sacrifice of a character to make a Skill Book. Given the sheer number of 5s over there too, chasing certain abilities can easily run you through hundreds of pulls with nothing but "junk" 3s and 4s and relatively useless (for that purpose) 5s in that hunt.0 
IceIX said:I'm not saying their system is better or worse than a purely statistical system, as that's subjective. Just that it doesn't necessarily solve the desired perception problems; It replaces them with others.How about a system that just guarantees the bonus pull rate?Since bonus heroes were introduced I have opened over 1,200 legends tokens and the 5* drop rate has been pretty much spot on at around 15% +/1 1% but my 5* bonus rate is about 1/2 of expected at 2.5%. Since the bonus system is the only real way to try to target specific characters this deficit is especially aggravating.
1 
Why even go with that complex a system that still leads to some players getting more 5* than others if they get a 'lucky' run. You should just go to a fixed system for everyone.Lets say you wanted to go with 1/7 odds for a 5*. You just randomize the numbers 17 endlessly. So the sequence would look something like: 45316721523746 and so on with a '1' representing a 5* and everything else a 4* (you then randomly roll for which 5* or 4* you got).The guarantees exactly 1/7 draw rates for everyone for 5* characters and means the *longest* streak you can go without a 5* is 12 draws.This also represents a perfectly fair system. I know the idea is that 15% averages out in the long run but I've seen lots of posts by players who track their rates that show they are getting say 13% in over say 2000 draws. Doesn't seem like much but that means they got 260 5* instead of 300. If another player was equally extra lucky and got 17% they'd have 80 extra 5* covers which is a lot of undeserved 'good' or 'bad' luck depending on which side you are on.IceIX, I wonder if you'd be allowed to post the 'luckiest' and 'unluckiest' 5* draw rates for say all the players who've made over 5000+ LT draws. You can't give player names but could you show the best and worst rates?KGB3
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