Is 1 Heroic Token really better than 3 Elite Tokens?

Hadronic

broll wrote:

halirin wrote:

Am I the only one who noticed the analysis after the probabilities is wrong? I saw a bunch of replies and had big hopes, but....

It would be more helpful if you explained how they were incorrect and provide correct ones...

I wouldn't be surprised if they were wrong. Never taken a stats class, but generally good at math so I kinda guessed. I'd love to see someone correct any issues in my ghetto stats.

Alright, lets start with comparing 1 Elite Token to 1 Heroic Token and then increase the number of Elite Tokens

Assumptions:
Elite Token Odds: 75% 2star, 25% 3star
Heroic Token Odds: 70% 2star, 25% 3star, 5% 4star

Combining these we can construct the following table:


With single tokens it is quite easy to determine when each token is better since we can just use the star rating as the discriminating variable.
The diagonal yellow boxes are the probabilities you get the same star rating from each token
the red box under the diagonal is when the Elite token yields a better cover
the green boxes above the diagonal are when the Heroic is better

So the final results for 1Elite vs 1 Heroic are:
58.75% of the time you get the same rarity, so doesn't matter
17.5% of the time the Elite token will be better
23.75% of the time the Heroic token will be better

So clearly in a 1 to 1 comparison Heroic tokens are better, not by much though.

3 Elite tokens complicates the decision of which is better, but the underlying process is the same

First we need to know all the probabilities of pulling different combinations of 2 and 3 stars out of the 3 tokens. The binomial distribution is useful for this:

zero 3* = .75^3 = 42.1875%
one 3* = 3*.75^2*.25 = 42.1875%
two 3* = 3*.25^2*.75 = 14.0625%
three 3* = .25^3 = 1.5625%

Just like above we can build the following table for comparison; however, color coding based on which result is better isn't as trivial as before, its subjective. Some people may value three 3* covers more than a single 4*, others might not.

I chose 3 ways of color coding the table based on the following criteria
1. Higher rarity cover trumps lower rarity covers regardless of how many lower rarity covers there are (This is the same as I did for single token above)
2. Convert to Iso and just compare ISO values (I used the ISO sell prices here of 250, 500, 1000)
3. Convert to CP (I used the cost to purchase a specific cover at that rarity 0, 20, 120)



It should be obvious that no matter which criteria you use 3 Elite tokens is statistically better.

Is this analysis more up to your standards halirin?

Megdar

It get more complicated then that.

Getting a 3* make you closer to the 4* it give in champ level, it also get you closer to next Heroic Token reward.

When you factor this in, for advanced roster, Elite token have hidden percentage of giving you 4* eventually.

The Heroic token do that to, but you get 3 Elite, so 3 time the chance.

JVReal

I think Standard tokens should stay how they are, Elites should stay how they are (no 1* pulls), and Heroics should be upgraded to exclude 1* & 2*'s. LT's exclude 1*, 2* & 3* ...

Heroics just don't seem to fit correctly into the lineup anymore. Don't they have the largest pool of characters to pull from?

mpqr7

So maybe the next level should be 1 Heroic and 1 Elite, instead of just 1 Heroic.

SummerGlau

only if you get a 4 star

veny

1 elite is even better than 1 heroic... comparing 3*s i got from ET and 4*s I got from HT (mostly those i had maxed)... I would prefer elite token over heroic one.