Quick Glance at Bonus Heroes Math

PeelmanPeelman Posts: 31 Just Dropped In
edited March 2017 in Theories and Statistics
Trying to make sense of this new feature, as I'm sure many are, so I'm throwing my math and thoughts here.

Latest/Classic Legends
It is easiest for me to start comprehending it on the Legends tokens. For either the Latest or Classic, there is ~1:7 chance of pulling a 5*, otherwise it will be one of the 12 most recent 4* releases. So, ~6:7 pulls will be one of the 12 4*s. That gives a little bit more than 7% chance of pulling any one of those particular 4*s.

Among all of the pulls, there is a 1:20 or 5% chance of getting one of the "bonus heroes." So that means there is a ~0.714% chance of pulling a bonus 5* and a ~4.285% chance of pulling a bonus 4*. If you only have one 5* or one 4* character listed as your favorite, that's the character you are getting. If you have multiple favorites selected, it will randomly be one of your favorites. If you have zero favorites selected, you will get a random character out of all possible options (none of the limited release characters).

My takeaway is that if you had just 1 4* as your favorite, that wasn't already among the latest 12, then you would get a bonus of that character at a little more than half the rate of the recent release characters. Out of a 100 pulls of either Latest Legends or Classic Legends, on average, you would get 7 of each of the listed 4*s and 4 of your bonus character. If you only had one favorite 4* and it was the same as one of the ones already featured in the pack, then you would get 11-12 of that character and 7 of all of the others.

It's all personal preference, but I prefer just listing one favorite. If you listed 2, then out of 100 Legend pulls, you could expect 2 of each. If you listed 4, then out of 100 Legend Pulls, you could expect 1 of each. If you listed all of the 4*s as your favorites, then you could only expect 4 covers out of the 40+ 4*s that aren't too new or limited release. I see this as an opportunity to specifically level specific older or new characters at a faster rate.

The Five Stars are a bit different since their inclusion rates are different based on the Latest/Classic difference. I'm going to assume you make 1 favorite 5*. In the Latest, if you have ~1:7 chance of pulling any five star, that means you have a 4.762% chance of pulling any one of the particular three 5*s in the Latest Legends. ... I'm suddenly realizing the math I've been doing could probably have been a lot easier. They probably list ~1:7 since it is the closest ration to the 15% draw rate we are used to seeing. I have been calculating these things as 1:7 rather than 15%, which is a much more round number. Oh well ... so anyway, in 100 Latest Pulls, you would get 4-5 covers of each of the three 5*s on average and you would get maybe 1 (the math comes to about .75) of your favorite 5*.

For the Classic, these percentages will get worse as time goes on. There are currently 10 possible 5*s in the Classic Legends. If I use the more math friendly 15% pull rate for 5*s, that means you have a 1.5% chance of any particular 5*. I suspect they may cap it somewhere around the 10-15 5* mark, similar to making only 20 4*s available in these packs. The chance at a bonus 5* hero in these packs is the same as the Latest at 0.75%. This means you will earn a bonus of your favorite 5* at half the rate of the 10 5*s featured ... or if your favorite is one of those 5*s, you would earn that character 50% more than the other 5*s.

Heroic Tokens
It gets a little different on the Heroic tokens because there are different odds whether you are buying a single token, 10 pack, or 40 pack. First, for a single token, there is a ~1:14 chance of one of the most recent 12 4*s, a ~1:4 chance of one of the 20 3*s the developers have selected, and all other times (~19:28) you will get a 2*. The 5% chance to draw a bonus 3* or 4* is across all pulls. You have around a 3.889% chance to pull your bonus 3* and a 1.111% chance to pull your bonus 4*.

If you buy a 10-pack or 40-pack, the odds of getting a bonus hero increases to ~1:12 or just over 8%. In their news release, they state it goes up from 5% to 8%, so I'm going to use a flat 8% for my calculation. At 8%, you would get a 3* bonus character 6.222% of the time and a 4* bonus character 1.778% of the time.

So if you bought 100 individual Heroic Tokens, on average, you would get about 5 bonus characters, 4 3*s and 1 4*.

I know previously if you bought a 10-pack or 40-pack you base draw rate for the 3*s and 4*s would go up. That is no longer explicitly stated, but you do get the increased odds on the bonus draw. You would now, on average, get 8 bonus characters, 6-7 3*s and 1-2 4*s.

My instinct on this new feature was to throw money down and start ripping Heroics like a madman. However, it doesn't seem like that will build my 4*s any quicker. Even at the 3* level, on 100 Heroics, I'd only get 1 cover of most of the featured 3*s and a second on about 5 others. Add to that 4-7 extra of the 3* Bonus Hero I select (assuming I'm only picking one favorite) and I'm not building those super fast either. This sounds like Heroics will behave the same way. So you do start building your favorite 3* quicker by way of the Bonus Hero, but you won't be max champing them unless you are pulling thousands of Hero Tokens. On the 4*s, you will only be getting 1-2 extra Bonus Heroes on 100 pulls, so they won't be shooting up Champ levels either.

This feature will make a difference in the Legendary Tokens and 4* pulls in general. Limiting the releases from these tokens to only the latest 12 4*s means we will get more covers of the new characters more often. If there is a particular older character we still want to cover, we can mark it as a favorite and get some of those as a bonus. Similar behavior with the 5*s. This isn't a way to build any of these guys super quickly, it is simply a way to try and get better control over which characters you receive covers for.

What this also means is we will not be getting additional covers of older characters except through vaults or event specific packs that may bring in one of those guys. My 13-cover 4* Wolverine and X-23 will not be getting that Champion cover from a Heroic or Legends pack unless I make one of them my Bonus Heroes. Perhaps this will work to my favor. I don't have to worry as much about pulling one of these covers, needing to spend the ISO to level my character to 270 so I can champ him, and then applying the cover before it expires. It gives me some control of that.

The downfall is the same as the strength. Being at the start of the 4* transition, I am now stuck with many undercovered, older guys. I won't be earning covers too quickly for my Professor X to finally get Charlie's Angels going. I could make him a favorite, but should that really be my priority? I don't think it is. I think I can put my focus on earning covers of some of the new good characters a little quicker, like Peggy. Since she is already one of the featured 12 4* characters, I'll already be earning her stuff more quickly. Maybe I make her my favorite to try to get her champed quicker, then move on to one of the other top 10 characters. In all that time, I won't be getting that Professor X cover I need, or the cover I want to champ my Wolverine or X-23, but I won't be getting another Elektra or Mr. Fantastic either.

To each their own, but I think I can find a way to make this work. It is a good opportunity to earn new characters quicker or focus on covering a particular older guy that is lagging behind. I don't think the real power is how it affected the Heroic draw rates, but in how it has changed how the Legendary Tokens will work. The quest for CP gains continues!

After updated math and understanding: What I stated before pretty much still applies. You can build a selected 3* a little faster as a Bonus Hero through the Heroic Tokens ... but it will only be a little faster. This will best be used to control the characters you get through the Legendary Tokens. You will now get the newer 4*s at a higher rate and then should select 1 of the older guys you still want to get covers for. If you start selecting dozens of favorite Bonus Heroes, you will be getting them so slowly that it will not have much impact on your roster. The reason they implemented this feature is to do just the opposite, help players focus on particular characters.


  • PeelmanPeelman Posts: 31 Just Dropped In
    So my math is wrong for the heroic packs. You can't get 2* bonus heroes. Even though you can't select them, I thought you would just get a random 2*. This is wrong. You only pull Bonus Heroes on 3* and 5* pulls, so this means an increase in the drop rate for those. I'll have to redo that math.
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