Math of Bonus Heroes, worst case? (aka: check my math)

herm1978

So, lets say I have a 5/5/0 Star Lord (I do).

Assume that almost all of my 4* comes from Legendary tokens (true?).

How many Legendary tokens would it take to be able to champion him (on average)?

Math:

There is a 0.05 chance to get one for every Legendary token I cash in. I would need to get that one specific color (red), that is 0.33 chance to get just that one.

0.05 x 0.33 = 0,0165 (that is a 1.65% chance to get a red cover per token)

I then need to get three of them:

0.0165x (individual draw rate multiplied with the number of tokens I would need "x") = 3
x = 3 / 0,0165 = 182

/Math

That would mean (assuming math is correct and you rely on Legendary tokens for your 4*s) that it would take, on average, 182 tokens to get the three lacking covers.

Feel free to add a resonable number of Heroic tokens per Legendary to this, and recalculate the number of Legendary tokes to success

Quebbster

If I were in your shoes, I'd probably just wait until I got a red Star-Lord cover through other means (a progression reward, most likely), then spend 240 CP to buy two more covers.
That's assuming you want to champion Star-Lord, of course. He lacks some oomph without red covers, but he's fairly playable as long as you have yellow covers.

broll

You also need to factor in that there's only an 85% chance that any bonus hero from Legendary tokens is a 4* because there's a 15% chance it will be a 5*.

So it's

0.05 x 0.85 x 0.33 = 0.014025 or ~1.4%

3/0.014025 = ~213.9 so 214 pulls

You're comment about almost all 4* coming from legends is mostly true, but there are still:
- Event progression and Placement rewards
- Rare drop from HP could still do bonus
- Rewards from 3* champ system
- Hopefully vaulted will still show in vault tokens (80 vaults and the horribly priced 20s)
- Buying for 120 CP.

My plan is to not favorite anyone with 5 of anything as it's just going to lead to frustration and wasted covers. I will try to get the finals through 1 of the above (probably 120 CP more often than not). The odds are just too unfavorable to put a 5/5/x into favorites. It's pretty ugly even for 5/x/x. Another reason this system sucks.

Chrono_Tata

herm1978 wrote:

Math:

There is a 0.05 chance to get one for every Legendary token I cash in. I would need to get that one specific color (red), that is 0.33 chance to get just that one.

0.05 x 0.33 = 0,0165 (that is a 1.65% chance to get a red cover per token)

This is correct.

I then need to get three of them:

0.0165x (individual draw rate multiplied with the number of tokens I would need "x") = 3
x = 3 / 0,0165 = 182

/Math

But this is wrong. You need to remember that each draw from the token is independent from each other, so there is no amount of draws that will get you 3 red SL for sure. The more tokens you open, the more "likely" that you will draw at least 3 red SL, but it never reaches 100%. You can calculate how many draws it would take to get to a "good" chance (say, more than 80-90%) that you get at least 3 red SL, but the calculation is a little bit more complicated than what you have above. I can't really explain it all here since it would take way too long, but I can tell you that opening 186 tokens only gives you a 59.40% chance of at least getting 3 red SL.

However like already mentioned, opening 186 tokens would get you a ton of extra stuff which probably get you enough resources to get you the covers you want.

waywreth

broll wrote:

You also need to factor in that there's only an 85% chance that any bonus hero from Legendary tokens is a 4* because there's a 15% chance it will be a 5*.

So it's

0.05 x 0.85 x 0.33 = 0.014025 or ~1.4%

3/0.014025 = ~213.9 so 214 pulls

You're comment about almost all 4* coming from legends is mostly true, but there are still:
- Event progression and Placement rewards
- Rare drop from HP could still do bonus
- Rewards from 3* champ system
- Hopefully vaulted will still show in vault tokens (80 vaults and the horribly priced 20s)
- Buying for 120 CP.

My plan is to not favorite anyone with 5 of anything as it's just going to lead to frustration and wasted covers. I will try to get the finals through 1 of the above (probably 120 CP more often than not). The odds are just too unfavorable to put a 5/5/x into favorites. It's pretty ugly even for 5/x/x. Another reason this system sucks.

I agree with your plan. There's going to be nothing more frustrating than actually getting a bonus cover (which for the record - I've gotten 0 bonus 4 or greater covers in about 50 Heroic and 20+ CP/Legendary pulls), and having it be for a character you already have 5 covers in a color and have no easy way to get the covers to champion them.

broll

waywreth wrote:

I agree with your plan. There's going to be nothing more frustrating than actually getting a bonus cover (which for the record - I've gotten 0 bonus 4 or greater covers in about 50 Heroic and 20+ CP/Legendary pulls), and having it be for a character you already have 5 covers in a color and have no easy way to get the covers to champion them.

I've pulled 70 legends since launch. I've gotten 1 4* and 1 5* (2.85% way lower than 5%).
The 1 4* I got was a yellow Ant-Man unsable for my 3/4/5 Ant-Man, literally the only cover I couldn't use and now I have 2 dying on the vine.

Detailed pull data:
viewtopic.php?f=7&t=60544

deadtaco

Quebbster wrote:

If I were in your shoes, I'd probably just wait until I got a red Star-Lord cover through other means (a progression reward, most likely)

The issue there is that covers from progression (or reward) tend to be of only one color variety. They may have to wait until Starlord has been the 4* reward 3 times before getting the red cover. With 45 (or whatever) 4*s now that would take ages.

blargrx

broll wrote:

You also need to factor in that there's only an 85% chance that any bonus hero from Legendary tokens is a 4* because there's a 15% chance it will be a 5*.

So it's

0.05 x 0.85 x 0.33 = 0.014025 or ~1.4%

3/0.014025 = ~213.9 so 214

Ouch, when the math comes out I feel sad that we're that desperate for 1.4%

We're all hoping for that slim sliver of sunshine from rng! That it will shine upon our rosters lol

smkspy

Other option is to accelerate your 3 star feeder to get those covers. 3 star drops are gonna happen more frequently, so placing gamora as your only 3 star favorite will get covers a but faster than favoring a 4. Not perfect but it is a option. I plan to eventually favor Gamora just so I can get that 13th starlord, and am currently doing this with 3carol to get my 13th Peggy.

Straycat

Isn't it still better than before tho? If all characters were available there would be 1/43 for a character and 1/3 it is the right color. So thats 1/3 of 2.3% or .0077%
So it would take 387 pulls on average to theoretically get 3 specific covers before bonus heroes were introduced.

Gmax101

Straycat wrote:

Isn't it still better than before tho? If all characters were available there would be 1/43 for a character and 1/3 it is the right color. So thats 1/3 of 2.3% or .0077%
So it would take 387 pulls on average to theoretically get 3 specific covers before bonus heroes were introduced.

But... but... but... "vaulting BAD!! Smash!!"

I do get the frustration but this so beautifully sums up the actual maths

MissChinch

Gmax101 wrote:

Straycat wrote:
Isn't it still better than before tho? If all characters were available there would be 1/43 for a character and 1/3 it is the right color. So thats 1/3 of 2.3% or .0077%
So it would take 387 pulls on average to theoretically get 3 specific covers before bonus heroes were introduced.

But... but... but... "vaulting BAD!! Smash!!"

I do get the frustration but this so beautifully sums up the actual maths

This point completely neglects that the numbers before signify working on all 4*s in parallel, the current numbers work on the vaulted 4*s in series...

So before we could be working on over 30 4*s all at the same time... now even if you wanted to discount all but 6 of the retried 4*s youre into the 1000s in terms of number of draws before you will see a single cover for your 6th... anecdotally, most people I know in the game were shooting to cover and champion all their 4*s... not just get the last few covers on 5-6 of em...

Straycat

MissChinch wrote:

Gmax101 wrote:

Straycat wrote:
Isn't it still better than before tho? If all characters were available there would be 1/43 for a character and 1/3 it is the right color. So thats 1/3 of 2.3% or .0077%
So it would take 387 pulls on average to theoretically get 3 specific covers before bonus heroes were introduced.

But... but... but... "vaulting BAD!! Smash!!"

I do get the frustration but this so beautifully sums up the actual maths

This point completely neglects that the numbers before signify working on all 4*s in parallel, the current numbers work on the vaulted 4*s in series...

So before we could be working on over 30 4*s all at the same time... now even if you wanted to discount all but 6 of the retried 4*s youre into the 1000s in terms of number of draws before you will see a single cover for your 6th... anecdotally, most people I know in the game were shooting to cover and champion all their 4*s... not just get the last few covers on 5-6 of em...

The whole point of this thread was about covering one specific character at 5/5/0, not about vaulting in general.

TimGunn

Here's my guide on ways to get older 4 stars, now that you can't draw them from most tokens. viewtopic.php?f=6&t=60345

For star-lord
-pvp - he just came up, so it probably won't be until August/Sept that he is a reward in PVP again

-pve - he will likely come-up in PVE rewards in the next month or so!!! - Edit, just to clarify, the last time he was featured in PVE was October 2016. And there are only 5 other 4 stars who have had a longer absence. So...

- tacos - probably several months, he was last featured in January

- daily resupply - pink (day 670) and yellow (day 700), but i'm not seeing any red

So i'd wait to see what comes up in PVE before spending CP on him.

broll

Straycat wrote:

Isn't it still better than before tho? If all characters were available there would be 1/43 for a character and 1/3 it is the right color. So thats 1/3 of 2.3% or .0077%
So it would take 387 pulls on average to theoretically get 3 specific covers before bonus heroes were introduced.

I don't have the math skills to portray what the percentage would be, but in the old system you getting that .0077% against all 40ish characters, so while you may not get what you want, as long as you don't have a ton of characters 5/5/x chances were good you you're misses were hits for a different character. Here every bonus miss, is a miss, the cover is unusable. It may take you 45 pulls to get that one Ant-Man Blue you need, but the journey there got you on average 1 cover for every other 4*, instead of 3-4 for each of the 12, many of which will go to waste if you don't have them champed or have 5/5/x.

I pulled 70 covers and 20% of them are going to go to waste because I got 4 Spider-Woman Blacks I can't use plus 5 others I couldn't use.

Straycat

broll wrote:

Straycat wrote:

Isn't it still better than before tho? If all characters were available there would be 1/43 for a character and 1/3 it is the right color. So thats 1/3 of 2.3% or .0077%
So it would take 387 pulls on average to theoretically get 3 specific covers before bonus heroes were introduced.

I don't have the math skills to portray what the percentage would be, but in the old system you getting that .0077% against all 40ish characters, so while you may not get what you want, as long as you don't have a ton of characters 5/5/x chances were good you you're misses were hits for a different character. Here every bonus miss, is a miss, the cover is unusable. It may take you 45 pulls to get that one Ant-Man Blue you need, but the journey there got you on average 1 cover for every other 4*, instead of 3-4 for each of the 12, many of which will go to waste if you don't have them champed or have 5/5/x.

I pulled 70 covers and 20% of them are going to go to waste because I got 4 Spider-Woman Blacks I can't use plus 5 others I couldn't use.

The op said nothing about what you would get in the 182 pulls mathematically needed to get a specific cover from bonus heroes. I was just pointing out that while it seems impossible now to get specific covers for vaulted characters, it was pretty hard to do that before too.

I'm not saying this system is perfect, but I'm starting to like it. Personally, the previous system had more chances at unusable covers. It also had more chances at usable covers in the form of champ rewards. 18/43 champs, so thats 41%. I have 6 fully covered and 11 others with 5 in at least 1 color. Thats roughly 40% chance at unusable covers. In the new system, I have 2 champs, and 3 others with 5 in one power. Thats 16% chance at champ levels, and roughly 25% chance at unusable.

I think the ability to cover new characters faster is good, and I'm happy to not champ out of spite anymore. Well, for a while anyways. I don't know if I will have to champ all of the latest 12 before it changes.

MissChinch

broll wrote:

Straycat wrote:
Isn't it still better than before tho? If all characters were available there would be 1/43 for a character and 1/3 it is the right color. So thats 1/3 of 2.3% or .0077%
So it would take 387 pulls on average to theoretically get 3 specific covers before bonus heroes were introduced.

I don't have the math skills to portray what the percentage would be, but in the old system you getting that .0077% against all 40ish characters, so while you may not get what you want, as long as you don't have a ton of characters 5/5/x chances were good you you're misses were hits for a different character. Here every bonus miss, is a miss, the cover is unusable. It may take you 45 pulls to get that one Ant-Man Blue you need, but the journey there got you on average 1 cover for every other 4*, instead of 3-4 for each of the 12, many of which will go to waste if you don't have them champed or have 5/5/x.

I pulled 70 covers and 20% of them are going to go to waste because I got 4 Spider-Woman Blacks I can't use plus 5 others I couldn't use.

If you only have a single retired 4* left to cover the bonus hero / vaulting system will get it done faster than the old way. If you have more than one you'll spend a little less than twice as long on average to cover him as you have to work on them in series now not in parallel... If you have more than 2-3 retired 4*s you want covers for, this change removes token pulls as a useful way to get those covers.

Straycats math for a single character is right, people trying to use that to show that your retired 4*s will now get covered MORE quickly than before aren't understanding the issue (or they all champion 4*s as fast as they get released and only have a single retired 4* theyre concerned with getting covers for)

killerkoala

if odds were perfect for pulls and bonus, and you get all 13 covers with no dupes, favorite 1 (4*) only, starting from 0 covers. 6/7 legendary would be 4* covers pulls. 1/20 being bonus.

6/7 (odds of being 4*'s) x 1/20 (chance of bonus) x (y= Number legendary opened)= 13 covers

y= 304 , so u'd open 13 to 304 legendary max

buts say ur star lord is 5/5/0 and ur pulls and bonus is perfect but with color odds.

6/7 odds x 1/20 x 1/3 (color odds) x (y) = 3 covers needed

y= 210 , so u'd open 3 to 210 legendary max

Mercalla

I think I'm stealing everyone else's chances on bonus heroes. Of the 4 legendary pulls I've done, 3 triggered bonus heroes (one of which was a 5*!). On 3*'s, I'm probably around 40% BH triggering.

(activates 24-hour PvP shield)

herm1978

Straycat wrote:

MissChinch wrote:

Gmax101 wrote:

Straycat wrote:
Isn't it still better than before tho? If all characters were available there would be 1/43 for a character and 1/3 it is the right color. So thats 1/3 of 2.3% or .0077%
So it would take 387 pulls on average to theoretically get 3 specific covers before bonus heroes were introduced.

But... but... but... "vaulting BAD!! Smash!!"

I do get the frustration but this so beautifully sums up the actual maths

This point completely neglects that the numbers before signify working on all 4*s in parallel, the current numbers work on the vaulted 4*s in series...

So before we could be working on over 30 4*s all at the same time... now even if you wanted to discount all but 6 of the retried 4*s youre into the 1000s in terms of number of draws before you will see a single cover for your 6th... anecdotally, most people I know in the game were shooting to cover and champion all their 4*s... not just get the last few covers on 5-6 of em...

The whole point of this thread was about covering one specific character at 5/5/0, not about vaulting in general.

Well, actually, the point was to exemplify one specific case of BH. Before, I had a relatively low risk of drawing a duplicate Star Lord cover, whereas now (should I "heart" him) I have to look forward to a lot of potential heartbreak everytime I'm lucky enough to get a Bonus cover.

herm1978

Chrono_Tata wrote:

herm1978 wrote:

But this is wrong. You need to remember that each draw from the token is independent from each other, so there is no amount of draws that will get you 3 red SL for sure. The more tokens you open, the more "likely" that you will draw at least 3 red SL, but it never reaches 100%. You can calculate how many draws it would take to get to a "good" chance (say, more than 80-90%) that you get at least 3 red SL, but the calculation is a little bit more complicated than what you have above. I can't really explain it all here since it would take way too long, but I can tell you that opening 186 tokens only gives you a 59.40% chance of at least getting 3 red SL.

However like already mentioned, opening 186 tokens would get you a ton of extra stuff which probably get you enough resources to get you the covers you want.

Yes, I know (that % chances cannot be added together). But to my defense I did say "on average", even if that may not be entierly correct.