The Impact of New Bonus Hero Odds on Latest Legends

helix72

I thought it would be worth updating some of the previous analysis on how many pulls you need to have to 1) champ and 2) max champ the three latest legends given the new bonus hero odds.

Because this actually gets rather involved, feel free to skip to end for the results, but I do think it's helpful to understand the assumptions and limitations. Given how detailed an accurate model needs to be, I didn't have time to build everything in this first cut and will update as I get time to address the items laid out next. Plus--some of the regular posters on the forum are very strong analytically and I really need the peer review, so tell me what I got wrong!

A full calculation would need to take into account several things in addition to the chance to pull a cover for each character, namely:

1. Where to start: how many starting covers and shards do we assume? The new devs are much more generous giving us retro feeders and boss events in addition to the usual PvE and PvP events such that we're never really starting from 0/0/0 with 0 shards anymore.
2. Bonus shards: how do we handle shards and bonus shards? Which character(s) do we set as the bonus hero target for each pull?
3. Streakbreaker: how do we handle the bonus shard streakbreaker/pity factor? The devs stated, "we’ve also tweaked the formula to more quickly force Bonus Shards if you’re just unlucky and haven’t gotten one of these Bonus Shard sets", but they gave us no specific information on how the formula works.
4. Champ rewards: how do we factor in champ rewards for both the 5s and 4s we pull? We will expect to get back a bunch of LTs and CP from all the covers we pull, so for example even if it requires 1500 pulls to hit a milestone, we may only need 1400 pulls saved up because we expect to get another 100 pulls from all the champ rewards.
5. Cover swaps: do we allow for them? For the case where we are calculating what it takes to max champ 2 or 3 of the characters, do we/how do we factor in using cover swaps to get there?

For this first iteration, here's what I've done:

Calculated pulls to max champ (level 550) all 3 characters (one pull is one LT or 25 CP)
For the assumptions above, here's what's included in this initial run:
1) Where to start: each character started at 0/0/0 with 0 shards
2) Bonus shards: pulls were done one at a time. Before the pull, we assign whichever character had the least total covers + shards / 500 as our bonus hero. If a tie, we assign both and thus are flipping a coin.
3) Streakbreaker: I'm not even sure how to factor this in, so for this run it's not contemplated. Only the stated bonus hero odds are used.
4) Champ rewards: not factored in for this run but will be in the next iteration
5) Cover swaps: I assumed cover swaps would be done and shards would be applied only in a way that allowed maximum cover swaps (because I'm pretty sure you can't swap excess shards)

100 simulations
average pulls: 1980
min: 1715
max: 2185

100 simulations isn't a lot, but at the same time I expect the champ rewards will bring those numbers down materially and so I didn't want to waste a bunch of time on a number that will change soon.

I'll be posting again when I have some time to address the assumptions above and post improved estimates (or maybe one of our other eggheads will beat me to it), including not just max-champing but min-champing (all 3 to 450). In the meantime, I appreciate the read and welcome thoughts and feedback!

Zarqa

Looking forward to more details as they come, thanks! Am I correct to assume that it doesn’t matter odds wise whether you pull single or 50 at once, since the 50 pull is not a ‘pack’?

I don’t understand the difference between pack pulls and single pulls as IceX mentions on page two of the announcement thread, when he discussed pity timers. And I am also not sure if that is relevant for Latest pulls. Any insight would be appreciated!

KGB

A few weeks ago I did a back of the envelope calculation after the new odds came out and it worked out to ~2000 tokens and posted it here (I can find it if your interested). Your average of 1980 would seem to confirm that.

What we really need is a confidence interval posted. In other words do something like 1000 (or 10000) simulations. Then you post the percentage of successes at say 2000 tokens (lets say it's 50 of your simulations%) then the confidence interval for doing 2000 draws is 50% that you'll cover all 3 successfully. Then count up the successes for say 2100 draws and if that comes out to 75% then your 75% confident that 2100 draws gets you there and so on.

Incidentally, in my back of the envelope math I figured you'd get quite a few more 5* covers from 4* champ rewards (if you favorited the 3 feeders for the 5*) at 2000 draws. That really helps when you are slightly below 15% draw rate

KGB

helix72

@KGB you mean like this:

helix72

@Zarqa : thanks for the questions!

The comment about the difference between single pulls and pack pulls only applies to stores that offer multi-pack options with differing bonus hero structures. If you look at those stores, you'll notice that the shard rewards are not linear: for example, in the current Gwenomous Spider store, a single pull gets you 10 3* shards and 4 4* shards, but a 10 pack gets you 110 3* shards and 50 4* shards, which is more than what you would get from 10 single pulls. I am inferring then that since the base shards are higher in the multi-pack, the devs are also giving a higher bonus shard rate.

As for the latest legends, the pull 50 button is not a multi-pack, it's just a multi-pull, so pulling 50 with one press is essentially no different than pulling 50 one at a time, so the expected bonus hero rewards would be the same. The only minor wrinkle relevant to this analysis is in this first iteration of the model I assumed you could change who you set as your bonus hero after each pull, and if you pull 50 at a time, you would only potentially change it after every 50 pulls. While there are likely at least a few outliers who would do 1980 pulls one at a time, I suspect most folks would use 50 button, and in a future version of the model I'll have it do the adjustment after every 50 pulls.

Zarqa

@helix72 said:
@Zarqa : thanks for the questions!

The comment about the difference between single pulls and pack pulls only applies to stores that offer multi-pack options with differing bonus hero structures. If you look at those stores, you'll notice that the shard rewards are not linear: for example, in the current Gwenomous Spider store, a single pull gets you 10 3* shards and 4 4* shards, but a 10 pack gets you 110 3* shards and 50 4* shards, which is more than what you would get from 10 single pulls. I am inferring then that since the base shards are higher in the multi-pack, the devs are also giving a higher bonus shard rate.

As for the latest legends, the pull 50 button is not a multi-pack, it's just a multi-pull, so pulling 50 with one press is essentially no different than pulling 50 one at a time, so the expected bonus hero rewards would be the same. The only minor wrinkle relevant to this analysis is in this first iteration of the model I assumed you could change who you set as your bonus hero after each pull, and if you pull 50 at a time, you would only potentially change it after every 50 pulls. While there are likely at least a few outliers who would do 1980 pulls one at a time, I suspect most folks would use 50 button, and in a future version of the model I'll have it do the adjustment after every 50 pulls.

Thank you! I never realized until now that pulling packs give you better rewards. Appreciate the explanation.

KGB

@helix72 said:
@KGB you mean like this:

Yes, exactly like that. So 90 percent likely at 2100 draws. In reality probably 100 percent when u factor in 4 star champ rewards giving 5 star shards.

KGB

Kolence

@helix72 said:
...
3. Streakbreaker: how do we handle the bonus shard streakbreaker/pity factor? The devs stated, "we’ve also tweaked the formula to more quickly force Bonus Shards if you’re just unlucky and haven’t gotten one of these Bonus Shard sets", but they gave us no specific information on how the formula works.
...

Didn't Ice say that even in the worst case scenario, the pity timer should still produce twice as good effects or work twice as fast, something like that.

I haven't tracked mighty or heroic tokens, or even standard tokens (thinking of the odds for a 3*), but as for legendary pulls, the guaranteed bonus would take 56 or 57 pulls at most. I believe the 5* bonus chance was the lowest one of all, so it would be safe to assume 30-ish pulls at most with the new system?

P.S.

Here's that quote from Ice's post. Not specific specific info, but still something. Once more (tracked) pulling is done, it should become more clear.

"Especially since we’ve also tweaked the formula to more quickly force Bonus Shards if you’re just unlucky and haven’t gotten one of these Bonus Shard sets. The overall effect of this is that you’ll be getting Bonus Shards anywhere from 3x-7x more often depending on the pack, and if your luck with proccing these is just THAT BAD, you’ll be getting them forced about twice as quickly."

entrailbucket

Someone with enough pulls (or someone who can put together a multiplayer tracking project) should be able to work out the exact "pity timer" details, as well as the exact nature of the bonus shards update.

I wouldn't be surprised if this is already underway somewhere (Line, probably) -- the problem is that it'd never be shared with the rest of the community.

That's exactly why this forum is important.

Borstock

Fascinating. Doubt I will ever be a 550 player, but it's still interesting to learn about it. Thanks for showing your work.

atomzed

@helix72 thanks for doing this! I was waiting for someone to do this. Even a ballpark figure (like what @KGB ) had done is sufficient to get a sense of the numbers required for 550.

While we may not know the exact number for pity timers, we can always make some educated guesses. Like 5% or 3%. You can then put the range of guesses into the model, and see how the numbers change.

Can I request you to use the same model to give a 90% confidence for champing (ie 13 cover)? In the past the broad figures were around 240 - 300 pulls. The current figures will probably much lower, I am just wondering how much lower.

Based on my experience as SCL10 PVE player, along with boss pve and retrospective shards from 4*, I reckon the numbers may go as low as 180 pulls to fully champing a 5*.

Timemachinego

@atomzed said:

Can I request you to use the same model to give a 90% confidence for champing (ie 13 cover)? In the past the broad figures were around 240 - 300 pulls. The current figures will probably much lower, I am just wondering how much lower.

Based on my experience as SCL10 PVE player, along with boss pve and retrospective shards from 4*, I reckon the numbers may go as low as 180 pulls to fully champing a 5*.

I'd reckon it's actually a fair bit lower than that. I don't track my exact earnings but my hoard has only been growing between character releases now and I think I'd be being very kind to place myself even at 2~ tokens generated a day. Jeff and Magik are already "finished" at this point, so I'd say it's roughly something closer to 120-150 if you can assume 1 cover from the feeder, 2 from the boss events and the 2.5? you'd earn from scl10 play.

atomzed

@Timemachinego said:

@atomzed said:

Can I request you to use the same model to give a 90% confidence for champing (ie 13 cover)? In the past the broad figures were around 240 - 300 pulls. The current figures will probably much lower, I am just wondering how much lower.

Based on my experience as SCL10 PVE player, along with boss pve and retrospective shards from 4*, I reckon the numbers may go as low as 180 pulls to fully champing a 5*.

I'd reckon it's actually a fair bit lower than that. I don't track my exact earnings but my hoard has only been growing between character releases now and I think I'd be being very kind to place myself even at 2~ tokens generated a day. Jeff and Magik are already "finished" at this point, so I'd say it's roughly something closer to 120-150 if you can assume 1 cover from the feeder, 2 from the boss events and the 2.5? you'd earn from scl10 play.

I agree. Your numbers of 120-150 could be the bottom end (which you have a lucky streak). Whereas my 180 May be the higher end. 120-180 is similar in range from old quoted numbers of 240-300.