View Full Version : Empowered gem math

01-27-2017, 09:47 AM
TLR - you will need to recieve 1155 stellar gems on average before you have a perfect set.

I should preface this post my saying that I am not a mathematician, nevertheless I've done my best to calculate the odds ratio of receiving a perfect empowered gem. If someone knows better than me and can correct my mistakes I would greatly appreciate the input.

I have made the following assumptions:
- Each stat has a 1/7 chance of occurring in any given slot
- 1, 2 and 3 star gems occur evenly at a 1/3 ratio
- Gem colour occurs at a 1/3 ratio

I have ommited the gems passive abilities from my calculations. I'm not clever enough and i suspect my findings will be quite revealing without having to do so.

so to start with, I calculated the odds of receiving a gem with perfect stats at 3/7 / 3 = 3/21 or 1/7. Then we require the gem to be 3 stars, with an incidence rate of 1/3 we are left with 1/21 empowered gems having a perfect baseline to begin upgrading.

Assuming no empowered gems are currently equipped or would be unequipped, the first perfect gem can be any colour as all three slots are currently unoccupied.

The ratio for receiving and equipping the first perfect gem is therefore 1/21.

To calculate the second gem, we now only have 2 slots available to equip a gem in. A perfect gem of the same colour can occur twice but is only usable once per character. Therefore we are left with a 2/3 chance that the next gem gem will be perfect, so we take the 1/21 and apply the 2/3 probability that it will be a colour that we still need.

This equates to our second gem probability of being perfect to 2/63, or 1/31.5

Applying the same reasoning to the third gem slot, except this time with only 1 colour still available we take the 1/21 and apply the a 1/3 probability this time as only one colour remains open.

The odds of receiving our final perfect empowered gem are therefore 1/63.

to summarize:
1st gem 1/21
2nd gem 1/31.5
3rd gem 1/63

On average then a player will need to open 63+31.5+21=115.5 stellar empowered gem boxes to receive 3 perfect empowered gems.

Now, to begin with the upgrading process. I will assume that by the time a player has managed to acquire sufficient critical hit chance through dragon passives, emblems and small gems that the most desirable upgrades at levels 5, 10 and 15 are either critical damage or phys/magic damage. Each upgrade interval therefore has a 2/3 chance of leveling one of the two desirable stats.

I have calculated this part using percentages because I'm bad at maths.

2/3 = 66.6r%

the first upgrade is therefore 66% the second is therefore 66% of 66% = 44% and the third upgrade interval is 66% of 44% = 29.2%

Thus, 29.2% of the empowered gems with a perfect baseline are going to successfully upgrade in a desirable manner, and this has to happen 3 times for us to receive a completely perfect set of 3 perfect stat gems. So i divide 29.2% by 3 and am left with about 9.5%

To summarize this section, 9.5% of our perfect stellar gems will upgrade in the most desirable way.

To conclude the post, if we apply the 9.5% success rate by the average of 115.5 Stellar empowered gems needed to receive perfect stats, applying the 10% success rate (rounded), can we assume that a player will need to receive 1155 stellar gems on average before they can say they have the perfect gems? per character. Omitting gem passive abilities.

now, if a player can recieve at most 15 empowered gem boxes a week (pulled the 15 out of nowhere, but was generous) of which, again, being generous, 2 are stellar gems and the remaining radiant gems are broken down to craft a 3rd, a player will receive 3 stellar gems a week meaning that 1155 / 3 = 385 weeks before receiving the perfect stellar empowered gem set up.

I'm all for a grind, but i think 7.5 years is a bit much, don't you? And if you think the 65:00 pack containing 10 empowered gem boxes is good value for money, I disagree. Assuming that each pack gave you 5 stellar gems, you would have to spend 15'000 on average to receive perfect gems.

I feel as though im digging my way through a mountain equipped with nothing more than a needle.

Also, i understand the notion that gems can always be improved and never perfected, but why? why would it be such a terrible thing if this were the case. It would still take a considerable amount of time to achieve

01-29-2017, 02:55 PM
Yeah, I really wish there was some way to earn empowered gems through play (and by that I mean not just the weekly timer). Even if it was indirect, like having Gem Empowerment boxes be random in gem chests. Let us combine 5k or 10k gem dust and two of the empowered gem fragments into a colored Empowered Gem box. Something. Anything.

While it might take that long to get absolutely perfect stats, it wont take nearly that long to get very, very good stats, within a few percent. At that point I consider it like trying to get a perfect gear set in Diablo 2. So rare and long-term that I question whether someone is cheating when they attain it.

01-29-2017, 09:22 PM
I'm honestly more sad about normal gems. I already have 2/3 perfect empowered gems, as one of them is a class gem. I don't want to grind 10k gem boxes to get six perfect (or even remotely good) PD/CH/CD lesser gems. That's simply not fun, and will make me want to quit.

01-30-2017, 05:48 AM
That's simply not fun, and will make me want to quit.

Honest question here... What are you going to do once you have a full set of perfect gems? Grind for fun? Grind a new class?