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Ratio of 5* to total amount of pulls


salinea
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1 minute ago, Silith13 said:

I'm easily past 60 pulls and got only a single 5*

Ouch, that's tough. 

I haven't been really recording stats, but mine has also been something like 65-75 pulls, with four 5* total. So... about 5,33 ~ 6,15% of 5*.

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From my rough math, you've got a roughly 1 in 4 chance of getting at least one 5* in any given set of five.

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Out of my 51 characters, 3 of them are natural 5* (~5.8%). This doesn't take into account the fact that I've sent some duplicate characters home and that my 51 characters includes some free units. Overall, I'm probably right around the expected value of 6%.

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(0.94^4*0.06)*5=0.234

So yeah 1 in 4 is about right. 23.4% chance.

With a 2.9% chance for 2 5*.
0.2% for 3 5*.
0.006% chance to get 4 5*
aaaand 0.00008% chance for a full 5* pull.

Realistically that's a total of 26.1% chance a 5* is included.

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16 Full Draws = 80 Pulls
7 Five-Star Characters
$40 Investments

Ratio: 0.088 or 8.8%
Characters: Marth, Cain*, Ryoma*, Seliph, Chrom* || Camilla || Ephraim // * = Non-Focus
* * * * *

Out of those 7 characters, only 3 have favorable Boons and Banes (Ryoma, Ephraim, Cain). 2 have decent natures but can be improved (Camilla, Marth) while the last 2 are just merging fodder (Chrom, Seliph).

Given that the baseline ratio is about 6% (3% for a 5* Focus, 3% for non-Focus 5*), I am a bit above average. Still, I want more 5* characters...

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tbh too many merges and I've lost count. (consults screenshots of all but the first of my summons) 
 

Spoiler

 

My first two pulls were all 3*, except for 4* Cecilia

  • Selena
  • F!Corrin
  • Azama
  • Raigh
  • Setsuna 
  • Nino
  • M!Robin
  • Draug
  • Tiki (Adult)
  • 4* Cecilia

For pulls, I currently sit at;

6/70 @ 5* = 8.6%

24/70 @ 4* = 34.3%

40/70 @ 3* = 57.1%

 

Not bad if I do say so myself. Still a f2p.... considering that I'm considered "too disabled" to work... :(

 

 

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49 minutes ago, Silith13 said:

(0.94^4*0.06)*5=0.234

So yeah 1 in 4 is about right. 23.4% chance.

With a 2.9% chance for 2 5*.
0.2% for 3 5*.
0.006% chance to get 4 5*
aaaand 0.00008% chance for a full 5* pull.

Realistically that's a total of 26.1% chance a 5* is included.

Oh thanks! I was wondering what the chances where (for a batch of 5), but too bad at math to make the calculation myself.

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1 hour ago, Silith13 said:

(0.94^4*0.06)*5=0.234

So yeah 1 in 4 is about right. 23.4% chance.

With a 2.9% chance for 2 5*.
0.2% for 3 5*.
0.006% chance to get 4 5*
aaaand 0.00008% chance for a full 5* pull.

Realistically that's a total of 26.1% chance a 5* is included.

The easier way to figure is

  • 1-(1-0.06)^5=0.266

for a 26.6% chance of "at least one" 5-star.

For the record, with the failure bonus:

  • 1-(1-0.065)^5=28.5%
  • 1-(1-0.07)^5=30.4%
  • 1-(1-0.075)^5=32.3%
  • and so on.
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12 full pulls.

2 5* units (3.33%)
23 4* units (38.33%)

Looks like I'm literally pulling the banner ratio for 5*, and am slightly above the 4* rate. WTF.

 

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I've been keeping tabs and out of my 75 pulls/15 batches, I've obtained:

4 5-stars.(3 focus [1 colorless, 2 red], 1 non-focus [1 red]) [5.3%]

17 4-stars [22.7%]

The results get skewed by 3 unlucky batches of just 3-stars [20% of my batches -_-]. I stick to a focus until I get 5-stars which helped out a bit, but I may skip out on doing more of the Sibling Bonds focus after 2 eh batches.

Edited by Silent Mercenary
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Looks like I'm around the following
Total Pulls:  60
Five Star:     5   -   8.3%
Four Star:   22   - 36.7%
Three Star: 33   -   55%

According to their estimates my pulls match up fairly well.  I pulled a five star in my last set so its likely I'll have another dry set or two which will likely drop my fire star average down some.  Likewise half of my 5 star were featured heroes (Lyn and Eirika).  
 

5 hours ago, Sire said:

Out of those 7 characters, only 3 have favorable Boons and Banes (Ryoma, Ephraim, Cain). 2 have decent natures but can be improved (Camilla, Marth) while the last 2 are just merging fodder (Chrom, Seliph).

I love and hate Boons and Banes in this game.  I love encountering enemies with interesting boons and banes, but I detest having really detrimental banes on my own draws.  -Attack on Brave/Dire users is unbearable.  Likewise many melee characters with -Def are really painful to use.  Speed is weird too in that a +Speed on someone slow as molasses can be infuriating.  One who always gets double attacked... still shall be doubled <faceplant>

Edited by Katrisa
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I got 2 Marths out of.... let's see... 36 units pulled? (7 full summoning sessions + 1 single summon) It might actually be more than that but that's all I have records of. Yeah, it's not the best. x___x at least I've gotten some characters I liked though.... 

What really sucks is that one of them was a second 3* Robin on top of the first one I got with a crappy bane (Def+/Speed-) ; but I sent the second one home without thinking to check either's boon/bane ;;; he could have been leagues better for all I know.... ;; I tihnk I didn't know about boon/bane at the time, but still.......

Edited by BANRYU
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11 hours ago, Ice Dragon said:

The easier way to figure is

  • 1-(1-0.06)^5=0.266

for a 26.6% chance of "at least one" 5-star.

For the record, with the failure bonus:

  • 1-(1-0.065)^5=28.5%
  • 1-(1-0.07)^5=30.4%
  • 1-(1-0.075)^5=32.3%
  • and so on.

I like to think I'm pretty good at math but this doesn't seem to make much sense to me. Like the end results are pretty close but this cannot be the exact numbers.

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All the pulls I did were out of doing 20 orb summons

Overall stats

Pulls: 6 pulls doing full 20 orb summons. So I summon 30 characters so far
5*:   3 5* out of 30  10%
4*  11 4* out of 30  37%
3*  16 3* out of 30  53%

Individial
Pull 1:  2 5*, 1 4*, 2 3* Focus Set: Legendary Heroes(This was rerolled group)
Pull 2:          2 4*, 3 3* Focus Set: Deep Devotion
Pull 3:          2 4*, 3 3* Focus Set: Deep Devotion
Pull 4:          3 4*, 2 3* Focus Set: Deep Devotion
Pull 5:          1 4*, 4 3* Focus Set: Deep Devotion
Pull 6:  1 5*, 2 4*, 2 3* Focus Set: Deep Devotion

So with my stats I have basically 1/10 chance of getting a 5* at the moment and in case anyone is wondering.  I'm saving 143 free orbs until their is a new summon focus I want.

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5 hours ago, Silith13 said:

I like to think I'm pretty good at math but this doesn't seem to make much sense to me. Like the end results are pretty close but this cannot be the exact numbers.

Given n attempts,

P(at least one success) = 1 - P(zero successes) = 1 - (P(failure) ^ n) = 1 - (1 - P(success)) ^ n.

Since P(success) is 0.06 = 6% at the base success rate and n is 5 for a full round of pulls, P(at least one success) = 1 - (1 - 0.06) ^ 5 = 0.266.

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What I did was (Chance of failure^numbers of failure*Chance of success^number of success)*number of different ways this can occur. I repeat this for 1 through 5 successes.

(0.94^4*0.06)*5=0.234224688

(0.94^3*0.06^2)*10=0.029901024

(0.94^2*0.06^3)*10=0.001908576

(0.94*0.06^4)*5=0.000060912

0.06^5=0.0000007776

Added together that is 0.2660959776

And whelp that's the number you gave me. Decimals matter.

Guess that's proof enough your method works.

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@Silith13 - So. Much MATH. (dies)

I've been watching the math. Though your first math post seems odd to me. I'm pretty sure you don't add the chances of getting 2, 3, 4 or 5 5* in one summon to 23.4%. I thought it was; of the 23.4% of pulling a 5*, these are the odds of pulling more than a single 5* in one summoning round. So of that 23.4%, 2.9% (that number is probably even lower now) would have two 5* units. I'm probably wrong, I'm a business student, not a mathematician. 

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2 minutes ago, TheTuckingFypo said:

@Silith13 - So. Much MATH. (dies)

I've been watching the math. Though your first math post seems odd to me. I'm pretty sure you don't add the chances of getting 2, 3, 4 or 5 5* in one summon to 23.4%. I thought it was; of the 23.4% of pulling a 5*, these are the odds of pulling more than a single 5* in one summoning round. So of that 23.4%, 2.9% (that number is probably even lower now) would have two 5* units. I'm probably wrong, I'm a business student, not a mathematician. 

We are trying (and succeeding) to calculate how big the chance is to get at least one 5* in a round of summons.

Naturally a situation where you get 4 scrubs and 1 5* is valid but in cases you pull more then 1 5* you are still good for the requirement. Therefor the chances for 2, 3, 4 and 5 pulls in one round DO matter.

The methods me and Ice Dragon performed are different but with the same outcome.

I calculated the four different amounts of 5*'s seperately and then added them together.

Ice Dragon took the opposite way by taking 100% and then deducting the chance of getting no 5*. A much faster method in this case.

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1 minute ago, Silith13 said:

We are trying (and succeeding) to calculate how big the chance is to get at least one 5* in a round of summons.

Naturally a situation where you get 4 scrubs and 1 5* is valid but in cases you pull more then 1 5* you are still good for the requirement. Therefor the chances for 2, 3, 4 and 5 pulls in one round DO matter.

The methods me and Ice Dragon performed are different but with the same outcome.

I calculated the four different amounts of 5*'s seperately and then added them together.

Ice Dragon took the opposite way by taking 100% and then deducting the chance of getting no 5*. A much faster method in this case.

Ah. I see. (No I don't. My brain hurts from looking at math.)  So you got the same answer two different ways?

 

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4 minutes ago, TheTuckingFypo said:

Ah. I see. (No I don't. My brain hurts from looking at math.)  So you got the same answer two different ways?

Yeah. Silith is adding all of the chances of a success from zero. I'm subtracting all of the chances of a failure from one. Same result in the end.

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Previous numbers.

Did two more full pulls, for a total of 14.  Current counts:

3 5* units (4.29%)
27 4* units (38.57%)
40 3* units (57.14%)

The new 5* I pulled skews the ratios a lot.  However, this seems to be in-line with the banner ratios.

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Welp.

Since my last post I've gotten 2 more 5*s in 3 pulls, Leo and Abel. x___X (Does... does anyone actually LIKE Abel....?? Why are ppl like him and Cain in the pool of potential 5*s? Of all the possible 5* units people can pull I'm pretty sure no one wants Cain or Abel compared to any of the numerous lords or other better-liked characters lol. Or maybe I'm just biased/unappreciative because I never played Shadow Dragon? But jeezus... If I'm wrong, just... he's so wasted on me lmao...)

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