Bonus Hero drop rate: Is it actually 5%?

Aweberman

Short answer: No. At least, not for me.

Edit: This was originally posted April 3. I have posted two additional updates -- on April 10 and 17 -- in which I detail a reversal (or at least a moderation) in my fortunes. 

I have been tracking my Bonus Hero acquisitions since March 6, just a few days after Bonus Heroes started. (Here is the link to the sheet: https://docs.google.com/spreadsheets/d/ ... sp=sharing. Bonus Heroes are marked in bold, and whenever one is acquired, I begin a new line.) In that time, I have opened 608 tokens (cover packs) -- not including 10-packs -- and have received 17 Bonus Heroes, which translates to a rate of 2.80%, or barely more than half the advertised rate of 5%.

(Disclaimer: I probably opened about 75 tokens in the first few days, before I started tracking. I know that I got 5 Bonus Heroes in those first few days. If this were included, the overall rate rises to about 3.2%. Additionally, in Heroic 10-packs, of which I have opened 7, I have gotten 7 Bonus Heroes, which is a rate of 10%, or quite a bit better than the advertised rate of 8%.)

Though the overall rate is 2.80%, the week by week rate has actually dropped dramatically. As can be seen in AB55-AB58, the rate of Bonus Heroes has progressed from 3.88% in the first full week of tracking to 3.36, 2.78, and 1.33 for the week just ending. Curiously, if standard tokens are removed from the equation, the rate should be better, since the advertised rate for 3* in standard packs is about 2.3%; instead, my rate gets even worse, down to 2.67% overall.

Particularly troubling is my Elite token pulls. I have now opened 133 Elite tokens without receiving a Bonus Hero, which is a far cry from the expected 1 in 20 that a 5% rate implies. And while 28 of those 133 have been 3* -- or a healthy 21% -- only 7 in the last 61 have been so, a very unhealthy 11.4%.

I am not a statistician, so I can't tell you how unlikely it is to have a 5% chance of doing something and yet fail to do it 133 times in a row. But I suspect that number is quite low. Additionally, I understand that sample size is something that non-statisticians have a hard time wrapping their minds around. 600 pulls might seem statistically significant to me, but I don't know whether it really is or not.


Though I figured nothing would come of it, I decided to drop a note to support about my issue. Here's what I wrote:

"I don't believe that I have been receiving Bonus Heroes at the advertised rate of 5%. Of course, I understand that I cannot necessarily expect that 5 out of every 100 tokens I open will automatically generate a Bonus Hero. However, I believe that the actual rate at which I have been acquiring them is statistically anomalous.

On March 20, I received a Bonus Hero from a standard token, the first Bonus Hero I had received in several days. I did not receive another one for the next four days, even while opening 20-30 tokens every day. By March 24, I had a run of 58 Elite tokens with no bonus and 35 Heroic tokens in a row. Finally, I uninstalled and reinstalled the game on Friday evening, as I had a Heroic 10-pack from season progression and was assuming by this point that something was wrong with the installation.

Over the course of the 16 hours immediately following the reinstallation, I received 5 bonus heroes, from my 3rd standard, my 9th and 11th heroic, my 8th classic legend, and one from the 10-pack.

Now, in the last week, I have only gotten 1, again from a standard token.

At this point, I have opened 26 heroic tokens since my last bonus, 21 classic legends, 19 latest legends ... and 120 elite tokens. (Note: All of this is being tracked in a spreadsheet, accessible here: https://docs.google.com/spreadsheets/d/ ... sp=sharing)

I do not have the statistical background to compute the chances that I would miss on a 5% probability 120 consecutive times, but I do know that the statistical expectation for that run of pulls would be 6 Bonus Heroes, as opposed to 0.

Something seems to be amiss.

--Remy Gibson

P.S. I am playing on an iPhone 7 Plus that is on the latest version of the OS. I am also updated to the latest version of the game."


And here is the response I received (predictably):

"Greetings D3 Go! Customer,

Thank you for contacting D3 Go! Customer Support.

Unfortunately, there is no guarantee to obtain a Bonus Hero when redeeming recruit tokens or purchasing recruit token packs. Drop rates can be both good or bad, and the rate at which you pull covers has its own probability. While some probabilities may seem low, they can still occur. Please keep in mind that each Token pull made does not affect the outcome of your following pulls. We are sorry to hear that you didn't receive as many Bonus Heroes that you were hoping for, and we hope that you have better luck in the future, but there is little we can do regarding this issue.

We understand your feelings regarding the drop rates. However, please note that probabilities for a given cover are not a guarantee. Since the outcome you observed is among the many possibilities, we will be unable to take any further action regarding this issue.

Many questions can be answered by visiting our helpful Marvel Puzzle Quest FAQ at: http://www.d3go.com/mpq-support/

If you require further assistance, please do not hesitate to contact us again and it will be a pleasure to help you.

Best Regards,
D3 Go! Customer Support Team (TJM)"

JamieMadrox

The odds listed are not guaranteed. It's a 5% chance on every pull, not a guaranteed 5% overall. Statistically there are going to be some people that get better than advertised odds, and some that get worse than advertised odds. Theoretically, over time, you'll even out and be at or near 5%. Unfortunately that time could be a few days or a few years. Welcome to the wonderful world of statistics and random number generation.

RemoDestroyer

i only tracked my lt pulls for march. i got 2 bonus 4*s and 0 bonus 5*s from 88 latest legends tokens. i have to work my way up to the 5% expected return. maybe i'll have better luck in april.

mpqr7

I pull at least 10-20 tokens per day (if not many more), and many days go by when I don't get any BH, not even for 3*s. But then there comes a day where I got a 5* BH that moved it from 3/4/4 to 4/4/4, so that makes all of the waiting worth it.

Orion

No bonus heroes in 120 pulls is a pretty easy calculation.

0.95^120 = 0.002 or about 2 in 1000 times. Yeah, so that's rare, but not impossibly small.

For me, I've gotten 2 BH RHulks just today, so I think I'm balancing out your luck on the other side. Sorry.

Orion

Also, to be fair, Standard tokens do not have a 5% chance for a bonus hero. Since the odds of getting a 3* from a Standard is a little less than 4%, so are the chances of getting a Bonus Hero.

So overall, you should expect a slightly lower % when you factor in Standard tokens. Certainly not at the level you've seen though.

nigelregal

I track only my Legendary token openings and have since November.

Since the change I have opened 7 bonus from Legendary tokens and opened 164 tokens total. This is about 4% open rate. Longest run was 58 tokens before next bonus.

Here is link to it: https://docs.google.com/spreadsheets/d/ ... sp=sharing

Anything in red is a dupe that is sold.

cooperbigdaddy

While I agree that you can't expect 1 Bonus Hero for every 20 tokens opened because of RNG (in my opinion, the literal worst way to progress in a game), I do think that there are some "dead days" where no matter how many you open you will not receive a Bonus Hero. I feel this is what happens with Shield Intercepts, though "dead days" becomes "dead weeks" in this case.

I guess a way you could test the dead days theory would be Standard tokens, so if you opened a 3* and did not receive a Bonus Hero, you know something's wrong. But besides this, I don't feel there's any way to figure out when is a good time/day/year to open tokens for this small percentage to get the positive change associated with vaulting.

SummerGlau

it's been my overall experience that bonus heroes work as intended, i don't keep stats but i don't feel cheated

it took a while to get a 4 star bonus but i now have recieved 4 in total

no 5 star bonus yet but only 1 5 since the feature was added

Ralph-Wiggum

Perhaps I have misunderstood how the bonus heroes work, but isn't it a 5% chance of a bonus hero only if you already pull a 3*, 4*, or 5*? So, in effect, the likelihood of a bonus 3* hero on any heroic token is .25 * .05 or a little over 1%.

If that is correct, then tracking all pulls from heroic tokens doesn't make sense. You would need to calculate how often you pull a bonus hero only when you pull a 3*, 4*, or 5*. A quick glance at the Google Doc makes it look like you are taking 2* pulls into account when calculating your bonus hero rate.

GurlBYE

Orion wrote:

No bonus heroes in 120 pulls is a pretty easy calculation.

0.95^120 = 0.002 or about 2 in 1000 times. Yeah, so that's rare, but not impossibly small.

For me, I've gotten 2 BH RHulks just today, so I think I'm balancing out your luck on the other side. Sorry.

SO I guess you're getting them.

Because I've had him as my bonus hero since the introduction of this feature and got 2.

and one was the color I had 5 of.

GurlBYE

Ralph-Wiggum wrote:

Perhaps I have misunderstood how the bonus heroes work, but isn't it a 5% chance of a bonus hero only if you already pull a 3*, 4*, or 5*? So, in effect, the likelihood of a bonus 3* hero on any heroic token is .25 * .05 or a little over 1%.

If that is correct, then tracking all pulls from heroic tokens doesn't make sense. You would need to calculate how often you pull a bonus hero only when you pull a 3*, 4*, or 5*. A quick glance at the Google Doc makes it look like you are taking 2* pulls into account when calculating your bonus hero rate.

edit: That's exactly NOT how it works see below. lol

Orion

GurlBYE wrote:

Ralph-Wiggum wrote:

Perhaps I have misunderstood how the bonus heroes work, but isn't it a 5% chance of a bonus hero only if you already pull a 3*, 4*, or 5*? So, in effect, the likelihood of a bonus 3* hero on any heroic token is .25 * .05 or a little over 1%.

If that is correct, then tracking all pulls from heroic tokens doesn't make sense. You would need to calculate how often you pull a bonus hero only when you pull a 3*, 4*, or 5*. A quick glance at the Google Doc makes it look like you are taking 2* pulls into account when calculating your bonus hero rate.

That's exactly how it works which is why it feels poopy for some because 5% doesn't seem that low.

If it were generally just a 5% chance at random on all tokens, that'd be nice, but unrealistic.

The purest 5% chance you have is from a legendary because both tiers are eligible for a bonus pull.

No that's not how it works. They've given the math several times and it comes out to 5%, even if you factor in 2* draws. Here's the explanation from the Bonus Heroes thread:

Anthony, Demiurge wrote:

Let's take the Heroic Pack. You have a ~71% chance to get a 2-Star, a ~23% chance to get a 3-Star and a ~6% chance to get a 4-Star. When you open a pack, you have an overall 5% chance to get a Bonus Hero. The way we get to that math is to set the chance to get a Bonus Hero per rarity that you draw. When you draw a 3-Star or 4-Star, you have roughly a 17% chance to get a Bonus Hero. When you multiply the chance to get a cover of that rarity with the chance to get a Bonus Hero, you get the [percent] chance to get a Bonus Hero from any one pull from a Heroic pack (~4% for 3-Stars and ~1% for 4-Stars).

In other words, because 2-Stars don’t have Bonus Heroes available, the Bonus Hero drop rate is actually 17% for 3-Star and 4-Star pulls, and factoring the 2-Stars into the equation is what drops it down to 5%

GurlBYE

Orion wrote:

GurlBYE wrote:

Ralph-Wiggum wrote:

Perhaps I have misunderstood how the bonus heroes work, but isn't it a 5% chance of a bonus hero only if you already pull a 3*, 4*, or 5*? So, in effect, the likelihood of a bonus 3* hero on any heroic token is .25 * .05 or a little over 1%.

If that is correct, then tracking all pulls from heroic tokens doesn't make sense. You would need to calculate how often you pull a bonus hero only when you pull a 3*, 4*, or 5*. A quick glance at the Google Doc makes it look like you are taking 2* pulls into account when calculating your bonus hero rate.

That's exactly how it works which is why it feels poopy for some because 5% doesn't seem that low.

If it were generally just a 5% chance at random on all tokens, that'd be nice, but unrealistic.

The purest 5% chance you have is from a legendary because both tiers are eligible for a bonus pull.

No that's not how it works. They've given the math several times and it comes out to 5%, even if you factor in 2* draws. Here's the explanation from the Bonus Heroes thread:

Anthony, Demiurge wrote:

Let's take the Heroic Pack. You have a ~71% chance to get a 2-Star, a ~23% chance to get a 3-Star and a ~6% chance to get a 4-Star. When you open a pack, you have an overall 5% chance to get a Bonus Hero. The way we get to that math is to set the chance to get a Bonus Hero per rarity that you draw. When you draw a 3-Star or 4-Star, you have roughly a 17% chance to get a Bonus Hero. When you multiply the chance to get a cover of that rarity with the chance to get a Bonus Hero, you get the [percent] chance to get a Bonus Hero from any one pull from a Heroic pack (~4% for 3-Stars and ~1% for 4-Stars).

In other words, because 2-Stars don’t have Bonus Heroes available, the Bonus Hero drop rate is actually 17% for 3-Star and 4-Star pulls, and factoring the 2-Stars into the equation is what drops it down to 5%

Ahh ok thanks for the explanation then.
So we all just have more terrible luck then we thought I guess.

And the standard is the only one that just has a different set of percentages.

I just figured they were all set like the standard, where it's 100% but only after a 3 actually pops.

Ruinate

My 3* Thanos is feasting. He went from lowest level among my 3's and soon he will be showing up on the front page. He's quickly becoming my most used 3*.

4* not so much. Maybe 5-6 total. Still, got a couple LT rewards thanks to being able to choose your bonus.

0/28 on purple pulls which is really bad.

Ralph-Wiggum

Ah - my point is retracted then! Thanks for the clarification!

OneLastGambit

For me personally I feel as though the 3* rate is much higher than advertised as I tend to get a 3* BH every 7 pulls or so (from heroics)

For 4* I feel it's probably about advertised as I've had 7 BH from roughly 120 or so pulls (give or take a little)

For 5* it's...wait... bonus heroes applies to 5* draws? are you sure? Just kidding I know it does but I've never seen one...however someone I know recently cashed a stash and got 3 bonus 5* panthers so they do happen...just not to me

Alsmir

10-pack Heroic

2x Gwenpool green, 2 x bonus Cyke blue

Like winning the lottery.

Mordee

One pull doesn't influence the next pull.

It's like flipping a coin. In theory, someone could have the coin lands Tail ten times before it lands on Head.

Or like Roulette, betting on black or red. One spin does not influence the next. Although having some history of the outcomes will trick our mind into thinking otherwise.

5% is already very low, so there is a high chance you will not get a bonus hero.

GrumpySmurf1002

Of note, not that it fixes your pulls on other tokens, but Standard tokens do not operate at 5%. It's whatever the 3* rate is for those tokens, which is roughly 2%.

So if you're grouping those together, then your baseline isn't 5, it's going to be lower than that.

Aweberman

Update for 10 April:

My rate continues to plummet after another week of pulls.  Heroic tokens are ticking over nicely, but if my own pulls are any indication, Bonus Heroes have completely disappeared from Elite tokens; I have pulled one from there since March 27.

This week
Standard: 0 out of 33
Elite: 0 out of 57
Heroic: 2 out of 17

Total (all types): 2 out of 119

Overall rate (all types): 2.34%
Overall rate (excluding standard): 2.21%

However, my Heroic rate is approaching 5%, as it is up to 4.62% overall.

But I have now opened 180 Elite tokens without getting a Bonus Hero.

(Please note that I would have edited my first post to indicate that I was providing new information, but apparently that isn't allowed anymore.)