I performed some research about the apostle fragment boxes that you can purchase for Battlefield Coins.
There are four possible fragments (Yustiel/Triniel/Vaizel/Lumiel) you can get from the box. You can combine 100 fragments of the same type into one contract.
Unless we get any official word that there will be other sources, I will assume that this is their only source for the following calculations and feedback. I will also consider the only scenario in which you receive a "reward" to be when you receive a total of 100 of the same contract fragment, as the fragments by themselves are not useful to players until 100 have been accumulated.
I will analyze two cases in this post: The absolute worst case and the average case. We'll start with the former. I'll reserve my personal judgment until the end and merely present the statistics I've gathered for now.
Worst Case Scenario
"When am I guaranteed to receive a reward for the effort and resources I spent on this system?"
We will assume that the distribution of fragment drops is absolutely equal to simulate this case. This means that when you buy four boxes, we assume that you get one fragment of each contract - no exceptions. This depicts the absolute worst case scenario because it requires the highest amount of purchased boxes before getting the first reward from this system.
The simulation for this scenario is simple. As the distribution rate is absolutely even, you would need to buy 397 of these boxes to definitely get the first contract. At 396 boxes, you would have exactly 99 of each contract fragment in your inventory, still assuming that the rates are absolutely equal. The 397t, 398th, 399th and 400th boxes would provide you with one reward each, being the respective contract. If you have the worst imaginable luck possible, you would then get 99 times the type of fragment you just combined into a contract before obtaining the next contract. The latest possible point to receive the second contract therefore is at 497 boxes, and every 100 boxes thereafter.
Even if you have the worst luck imaginable, the 397th box is guaranteed to give you a reward, as no matter which fragment you get, you will end up with 100 of any one type.
If one box costs 20 Battlefield Insignias, you would need to spend 7940 Battlefield Insignias to get a guaranteed reward. That's 1588 Runatorium/Ashunatal wins before you are guaranteed to receive a reward in this scenario.
If you play these instances fully active (2 Runatorium and 3 Ashunatal Dredgion runs every day) and win 100% of the time, getting this amount will take roughly 317 days. This time span is irrelevant, though, as the real limitation is the weekly purchase limit. You are hard capped at buying 4 of these boxes per week. These are also fully untradeable, so there is no way to speed it up with alts.
Due to this, you're not hard pressed to win 100% of your runs to not lose out on any weekly sales limit, but roughly a 50% win rate is sufficient. I did not account for Battlefield Insignia gains from other PvP instances or losses in this simulation as the cap is the weekly sales limit, not the PvP instance wins, and the instances mentioned are merely for demonstration.
Given this limitation, it would take you 100 weeks, or 2 years, to get a guaranteed reward under the worst possible circumstances. Realistically, you may - and, likely, will - get more than this, but definitely not less.
Average Case Scenario
"When am I - on average - going to receive any reward for the effort and resources invested into this system?"
The case outlined above is the most pessimistic take on the situation, so let's try to check this from a slightly more realistic approach. To figure this out, we'll have to take a closer look at the underlying mechanics than just scratching the surface. I don't have access to the source code of Aion, so the implementation of these mechanics will once again be based on the assumption that every contract fragment has the same drop chance.
The most direct route to check this is simple trial and error. One "attempt" is considered successful once you get a single transformation contract, or 100 of the same fragment. For this purpose, I've written a program that simulates the process.
It works like this:
- Initialize four empty stacks.
- Initialize a counter at 0.
- Repeat until one of the stacks has a size of 100:
- Add one element to any of the stacks. The stack is selected at random.
- Increment the counter.
This simulates a single player's attempt to get a single transformation contract. This, however, is a very small sample. We need a larger sample size for the statistic to be accurate. Therefore, I ran this test 1 million times. This graph visually demonstrates how many boxes had to be opened to get one contract for each individual attempt. After receiving one contract, the test was considered successful and stopped.
Based on these results, I took the sum of the amount of opened boxes and added them together after each attempt. I then divided this sum by the amount of attempts made up to that point. This tells me the average amount of opened boxes over the course of all attempts. Dividing this by 4 tells me how many weeks it takes to get one contract.
The following graph illustrates how taking the average of the total sum of boxes opened becomes more and more accurate with each additional iteration, eventually evening out:
Conclusion
It would take - on average - 360 boxes, or 90 weeks, to get the first transformation contract from this feature. Given that this is a legendary contract - some may argue that it's "legendary tier 2" for some class/form combos - and not an ultimate contract, as well as this being the only source of these fragments, the amount of time, effort and resources needed to get a reward feels disproportional for players of all backgrounds.
For new players, these rewards are unlikely to be obtainable at all as they need to frequently run and win PvP instances to accumulate a sufficient amount of currency to buy the boxes. As a result, they are unlikely to get their first (or second, or third...) legendary form from this.
For existing players, the rewards are obtainable after playing actively for what feels like a disproportional amount of time for the reward on offer. That aside, the currency used to buy these boxes is shared with other much needed items such as Legendary Daevanion Skills (for those who don't have theirs fully enchanted yet) or Ultimate PvP Enchantment Stones (for those who don't have their set fully enchanted yet or are working on additional sets). Those who buy all of these resources will have to wait even longer to get one of these contracts.
For endgame players who already have an ultimate form, the rewards offer very low benefits as they amount to 30 Spell Fortitude, 30 Strike Fortitude, 323 Evasion and 323 Magic Resist from collections. Those are by no means insignificant benefits, but the effort required to obtain them is not up to scale.
With the amount of people that have obtained ultimate transformations through sheer luck by now (or using the cash shop... and then having sheer luck), legendary forms can pretty much be considered obsolete at this point. Having to wait an average of 90 weeks - and invest time, effort and resources into it in the meantime - to get an obsolete reward doesn't provide me with any incentive to even buy these fragments. It feels like it's more likely for the vendor for these to be removed 90 weeks into the future than it is for me to obtain the first reward from it.
Even if the reward was an ultimate contract instead of a legendary one, the payoff time would still feel far too long to me. An ultimate contract after 90 weeks of active participation sounds like a system that would have been welcome if it was implemented when the transformation system was introduced in patch 6.0 (although still a far too long payoff time - having to wait two years to be able to play to the fullest extent of my abilities does not sound right), but not if it is introduced two years later and then makes me wait an additional two years until I get anything out of it.
