Monday, December 8, 2014

Astral Refining – Cost Analysis

(by Ashira of the DolyGames Team; Edits by Cosmos)

Hey guys, a lot of information has been provided on astral refining over the past weeks – to sum it up briefly, the main aspects about astral refining are:
  • You refine astral slots, not astrals! So you can train an astral slot to a certain level and then switch around your astrals to get the right effect for the situation you are facing.
  • It is a lot more valuable to refine % astrals than stats astrals: If you have Level 5 refinement on a Level 10 Enhanced Determination astral, your crit damage is increased by an additional 5% (as it is now 55% increased crit damage instead of the 50% you got from the Level 10 astral itself). If you have Level 5 refinement on a Level 10 Holy Force (or Holy Mysticality) astral your PATK/MATK “only” increases by 144, which is a nice boost, but nowhere near the effect of crit hits dealing 5% more damage.
  • Refinement for Deflection and Regeneration astrals is not very valuable: If the refinement would increase the trigger chance, that would be great, but it only affects the damage (for Determination) or healing (for Regeneration) effect, and since these effects are capped at 50k HP, this is not a very good boost.
The thing that has not been discussed a lot about astral refinement is the gold cost associated with it. There is some confusion about the maximum refinement level, and other sources have stated that astral refining is capped at Level 5, but this is clearly not the case, as you can see in the picture below (which is taken from my character).

So from this – and since the maximum level for astrals is Level 10 – it is quite likely that the maximum astral refining level is also Level 10. Let us take a closer look at the costs for the levels we know about, and the expected costs for refining up to Level 10:

Blessing Points per Astral Refinement Level

  • The first refinement requires 10 Blessing points (1 Blessing point usually means spending 1 million gold, with the chance of getting lucky and getting 5 Blessing points from 1 million gold).
  • From Level 1 to Level 2 it requires 16 Blessing points (60% increase – compared to previous level).
  • From Level 2 to Level 3 it requires 54 Blessing points (237.50% increase).
  • From Level 3 to Level 4 it requires 128 Blessing points (137.04% increase).
  • From Level 4 to Level 5 it requires 250 Blessing points (95.31% increase).
  • From Level 5 to Level 6 it requires 432 Blessing points (72.80% increase). 
These are the things we know for certain – the data is presented in the graph below!

Incremental Cost per Level: The amount of Blessing Points needed to move to the next higher level.

Relative Cost Increase from Current Level to Next Level.

Estimating the Costs up to Level 10

As can be seen in the graph of the relative costs, the relationship between level and cost increase is non-linear (blue line) – first the cost increases considerably (by over 200% from Level 2 to Level 3), but then there is a steady decline in the cost increase from Level 3 to Level 6. In order to make a vaguely reasonable prediction, we have to rely on the mean (and/or median) value, as no clear functional pattern can be derived. The mean relative cost increase from one level to the next is 121% (dashed red line), and the median relative cost increase – which is more robust to the extreme value that is observed for the refining step from Level 2 to Level 3 – is 95%. A third scenario that is worth considering is ignoring the early part of the pattern (up to Level 3) and to take a closer look at the declining part of the graph, which seems to asymptotically move towards the value that was observed for the first step, 60%. As the relative cost increase from Level 2 to Level 3 seems unnaturally high, we will not consider the mean case and stick to these two scenarios in order to produce a realistic prediction of the refining costs from Level 6 to Level 10:

(a) The relative cost increase per level from Level 6 up to Level 10 is 95% based on the mean,
(b) it is 60% based on an inspection of the functional shape, as a lower bound.

Note from Cosmos: theoretically, there is 1 more possibility, which is that the requirement flats out like Fate Auras or Whips at a fixed rate for higher levels. Ashira points this out in the conclusions below.

2+ billion gold for level 10

The graph below shows the cost for the Level 6 to Level 10 refinement steps for these scenarios. As you can see, the cost for the higher level refining can be expected to be enormous. To most players, the cost of moving from Level 5 to Level 6 (which we know costs 432 Blessing Points, so roughly 350 – 400 million gold, depending on how lucky you are) is already extremely high. Based on the predictions, refining an astral from Level 9 to Level 10 will cost 2831 Blessing Points (so definitely over 2 billion gold) assuming the relative cost increase per level is 60%, or as much as 6246 Blessing Points (so probably between 5 and 6 billion gold) assuming the relative cost increase per level is 95%. Now everybody will have to decide for himself/herself whether or not spending so much gold just to get 1% of additional astral effect is worth it – personally, I already consider the 432 Blessing Points (so roughly 350 – 400 million gold) a lot for just 1% of additional astral effect for one astral spot. However, it always depends on the alternatives: Is there a better opportunity to spend the gold on? There are already quite a few people with maxed out astral levels, so more or less the only way to spend their gold for them is astral refining or Holy Forge.

Note from Cosmos: specifically for the Illusion astral an additional percentage point might be worth considering even at high cost.

Astral Refining Conclusions and Takeaways

  • There definitely is no reason to “worry” that we might run out of opportunities to spend gold on in the future. Even with maxed out astrals, and even after maxing out Holy Forge, which will take its time but will eventually happen, there’s always astral refining. Even when we use the “lower bound” estimates from above, refining an astral spot from scratch to Level 10 costs 7287 Blessing points, so 58302 Blessing points for all 8 astral spots that can be refined, which is around 50 billion gold. Based on the median value estimates it would even cost 12824 Blessing points to refine one spot to Level 10, so a total 102597 Blessing points for all 8 spots, which is not too far from 100 billion gold.
  • Knowing the way Wartune works, it might be the case that the cost for a level upgrade caps at some point (as it does with Fate Stone training at 408 per level, or for converting high-level gems). So based on the information we have at the moment, the calculations above seem most realistic, but the real costs might turn out to be lower, if they decide to cap the cost per level instead of increasing the cost for every new level.
  • We do not have data on the probability of lucky refinement steps (so when you get 5 blessing points from spending 1 million gold). So if you guys drop a huge amount of gold into astral refining, it would be helpful if you send Cosmos data on it, for instance: “I used 20 million gold on astral refining today and got 32 blessing points from it” (which would mean that 3 out of the 20 refinement steps were ‘lucky’ steps).
We might not know the exact cost of astral refining, but what is rather obvious after this analysis is that it will take a long time to max out this feature of the game. So since we will always have things to spend gold on and gold will always be an important element of the game – try to play efficiently when it comes to gold!