I Hate Math: How to Calculate Sacred Crystal Spending in a Collection Event
I figured I’d write this out since there will be future collection events coming and it will be a useful method to work on to maximize your Sacred Crystal expenses to get the optimum amount of collection items. They are pretty straightforward though you will want to work on the math a bit here and there. Before you continue reading however, I would remind that this is best done when the event is revealed and you have gone through a bit of the maps because it is pointless to draft predictions until you are absolutely sure how well you are in tackling the event maps and how the event is getting rolled out, whether there are maps being withheld or not.
Context Fixing
With every mathematical calculation some variables have to be kept constant for accurate results. For collection events these are a few variables that you must know and set before approaching the prediction math:
1 Target
You have to set a target as to what number of collection items you are aiming for. This is naturally the goal of the calculation, and without the end target you will not have an end goal to work with.
2 Drop Rate
Understandably without a constant output you cannot calculate or project your expenses as accurate as possible. In most collection events the last couple of maps will always have a 100% drop rate to certain collection item packs; some events will have more, others less. Knowing the drop rates are important, especially the 100% ones because not only it helps in the calculation, it will also help you decide which map is the target map you want to farm.
3 Target Map
Once you have the drop rate info, you want to set a target map that you will farm on. This is important as it gives you an idea of the stamina and charisma you are looking to spend on every run, and to a certain extent the experience gain from these maps for you to plan for any possible stamina/charisma refill in the middle of the event (the latter most likely will happen). Also be realistic to the target map; pick the one that you know you absolutely can generate the sure drop items 100%. Misses will skew your prediction pretty hard.
Tools
Once you’ve done fixing constants you are good to go, but before you start you will want to use a couple of tools to help you out. Of course because it is mathematics a paper and a pen is all you need, but if you are playing on a computer then software can help to speed up the process quite nicely.
Naturally you want to use a spreadsheet tool. It covers all the required software you need individually; a calculator, an organized worksheet, can cope with data updates well.
However if you feel that you want something that isn’t too complex (surely spreadsheet tools aren’t that complex right?), I only use a Sticky Note and a Calculator software.
The Math
We are here finally. I can actually write a mathematical equation for this, but lets go with step-by-step. A few things have been set as constants at this point, so we want to start from these constants and work the way up.
1 Free Runs
Going into the event once you have found a consistent map to farm you want to calculate the free runs you can make throughout the event. First you want to calculate the ratio of charisma/stamina spending to know when is the right time to spend your crystals. In most scenarios the charisma cost will not be as heavy as stamina cost due to their recovery rate.
Regardless, always use the one with the slowest recovery time for each run as the counter. For example, Vampire Bride’s Map 8 takes 60/6 each run, attributing to 3/6 hours of recovery per run. Take 6 hours and you make up 4 runs per day.
Then you determine the start and finish point of the event to get the total free runs left. You need 2 information to do this correctly: the time when the event ends and your current charisma/stamina status. For example, Vampire event ends at 6am PST on the 30th. Today is 23rd, and the time is 12.00pm PST. Your current stamina is 4, and will become 5 at 12.30pm. This means that right now your counter is 0, and will become 1 at 1.30pm PST when your stamina turns 6. Then you just keep adding the daily runs you can get which is 4 in this case up to the last possible run you can get which is 1.30am on the 30th, giving you 26 free runs in total. Note that you always want to set the time at 3.00am PST instead of 6.00am unless stated at the poster to provide a buffer in case a maintenance kicks in.
2 Collection Item Math
Once you get the total number of free runs it is time to calculate your item. Firstly, always assume the minimal drop to get the worst case scenario. For example, the worst drop you can get from the map you are farming is 10, with the best drop at 16. Take the 10 instead of the 16. With a total of 26 free runs left you can generate at least 260 collection items.
Then, add this value to the current collection item you already have to get a projected total if you do not spend any crystals. In this case say you now have 600 collection items. Adding this to 260 that you can get you are now at 860.
Now take the target amount you initially set and subtract 860 to get the required amount you are still short of. If the value is negative you don’t have to spend any crystals at this point. If it is a positive value you will have to spend. So say your target is 1000; you are short of 140, so spend away. If your target is 800, you are looking at a 60 surplus, no spending required.
The number of crystals you have to spend depends on your generation limit. Taking stamina for example, If you are at level 120 one crystal spending gives you 14 stamina and this is added to your current stamina count allowing overflows so you don’t waste any bit. Example: You have 2 stamina right now and are at level 120, 1 crystal will set you at 14+2 = 16 stamina. If you are level 140 you get 15+2 and so on. With this in mind, you now can calculate how many crystals you have to spend to generate 140 items. Using the minimum drop rate of 10 you need 14 runs, which is 64 stamina. Taking this and divide by your stamina limit gives you the total maximum crystal you need. For example you are at level 120 (14), 64/14 = approximately 4.57. For any decimal point you get you round up and not down, so even if it is 4.1 you are going to spend 5 crystals max.
Other Important Tips
Here’s a couple of extra tips (and math) if you are a stringent and frugal spender.
1 When to spend your crystals
A rule of thumb when I spend is always at the point when I know I have enough charisma to cover every run possible such that my stamina won’t overflow after completing the spending run. For example, if I am farming a 60/6 map and falls between level 120-139, I will spend when I have more than 120 charisma and less than 5 stamina. This gives me 19 stamina when a crystal is spent, and I can run 2 rounds putting myself at 7 stamina. Even if my charisma is 0 after the 2 runs they will recover in 3 hours of which I will only be holding at 10/14 stamina then for another run, dropping my stamina further down to 4/14.
2 Spend crystals at the recovery refresh timer to maximize efficiency
This can be too much, but I only spend my crystals when the stamina timer resets. For example, I will spend when the stamina timer is around 55.00-60.00. Anything below that (0.01-54.59) I will rather wait for another hour. This allows me to keep track of my stamina refresh rates so I can better time my free runs. Note that because the math only works on minimal output and because every crystal spending will reset the number of runs you can get the total number of free runs you can get might differ depending on the surplus stamina you gain from the spending. This means that you have to repeat the math after every spending preferrably to calibrate your data.
3 On the last few runs, react to minute details
I don’t see a lot of players doing this most of the time, but for my case I do. Due to the minimal output prediction you might come to a situation where you can actually save a crystal because the extras you get is enough for you to hit the target without having to farm your target map, but another map with a lower surefire drop. For example you target 1000 items and going into the last run you are at 994, at this point you ran out of stamina and notice that by naturally waiting it to recover you will only gain 5 stamina before the event ends. At this point you can either spend the crystal to get 1004 minimum, or farm another map that drops exactly 6 items but cost 5 stamina to run. While situations like this don’t happen often when it happens it is a matter of 1 crystal which is huge for a free player.