Endgame Theory & Mechanics
AFK Endgame Theory + Mechanics v1.02 (Based on 1.59, updated for 1.63)
By: JD (JDCOOL#0988)
Honourable mentions: Ensign, Aimb, InSeas0n
Special thanks to Mr. Panafonic for decrypting the files and making this guide possible!
A shoutout to all the wonderful people on the AFK Arena Official Discord for your contributions and support!
(Consider joining us if you are not yet a part of our community)
Brief Self Introduction
I started playing AFK Arena ~18 months ago and am one of the first five F2P players to reach Ch 36 (I’m the youngest at s325). I have been fascinated by the maths and statistics involved in optimising progression, and I am writing this guide to share some of my findings and calculations on how to maximise progression rate for late-endgame players.
For haters: I am also F2P. Okay next section.
Waaaay Too Long; Didn’t Read
- In short, ‘RC cramming’ is the process of investing the majority or the entirety of your continuous diamond income into leveling your resonating crystal.
- Through a series of complex calculations, we can see that RC cramming is the optimal investment pathway for late-endgame players, more worth than stargazing, HCPing and Hero Investment (buying Reds and Poe)
- This guide only considers the best value (my definition of ‘value’, which is: the percentage increase in team strength per diamond (or equivalent) spent). It is ultimately up to you to choose what you spend your diamonds on, I am just here to provide an explanation on why RC cramming is the optimal min-maxing route.
- Make sure to do 5x FRs (Free 50 80 100 100), refresh store x2, buy all dust and Poe for gold, buy all exp and dust crates (not piles!), refresh bounty board as necessary.
- If you have doubts on anything, or are interested in how I derived my values and came to my conclusions, read on.
The Resonating Crystal (RC)
The Resonating Crystal, or RC, is the crystal pentagram that you place your heroes on to share their levels with the rest of the heroes on the crystal (if you are reading this guide, you should already know this.) Since this is a late-endgame guide, I’ll skip to breaking the crystal, after getting 5 lv240 heroes.
What is RC Cramming?
Before I continue with RC scaling mechanics, I want to introduce a concept (potentially new to some players) called “RC cramming”. What is RC cramming? In short, RC cramming is the process of investing the majority or the entirety of your continuous diamond income (depending on VIP) into buying resources to level up your RC (exp, dust).
To understand why RC cramming is so valuable, let’s first look at the RC stat scaling.
I datamined the increase in stats of each RC level and compiled + simplified them into a spreadsheet. You can see the stats in the link here if you are interested.
Based on the inflections of % increase in stats and costs, the RC spectrum (the entire lv1 – 841) can be split into several sections:
241-250: 1st RC Ramp (Worst Value) ~0.37
251-280: Early RC (Terrible Value) ~0.51
281-300: Tranquillity Zone (Good Value) ~2.97
301-359: Mid RC (Decent Value) ~4.21
360-364: 2nd RC Ramp (Worst Value) ~0.34
365-420: Late RC (Bad Value) ~4.00
421-478: Dead Zone (Terrible Value) ~2.52
479-501: Prosperity Zone (Ok Value) ~8.17
502-640: Endgame RC (Insane Value – Ok Value) ~17.35
641-841: Mystery Zone (??? Value) ~???
(Insane > Good > Decent > OK > Bad > Terrible > Worst) *The number is the ratio of % increase in stats vs % increase in costs
Since RC works differently pre-break and this RC zone doesn’t last very long, we won’t cover it in great detail. In short, the % increase of stats and upgrade costs both change very rapidly, with quite a large % increase in dust cost per 20 levels.
241-250 1st RC Ramp
RC Ramps are short sections of the RC spectrum in which the costs inflate dramatically (I believe they are Lilith’s attempt to actively increase the difficulty of progression). After just breaking your RC, the increase in stats per level is extremely high. However, unfortunately the increase in costs are even higher, averaging ~2.25% increase in stats and ~6.14% increase in costs (the percentage increase is different every level, refer to spreadsheet for more info). The cost efficiency ratio of this region is terrible (~0.37), hence making this one of the worst value sections in the RC spectrum. Note that although the additional costs do carry over to the rest of the RC spectrum, the levelling of these particular levels is not as valuable relative to the other regions.
251-280: Early RC
This region is defined as a separate RC region because the % increase in upgrade costs scale down instead of up like in the 1st RC Ramp. The cost efficiency ratio of this region (~0.51) is slightly better than the first RC Ramp (averaging ~2.17% in stats and ~4.25% in costs), but is still relatively low.
281-300 Tranquillity Zone
The next region is denoted as the ‘Tranquillity Zone’ due to the minimal variance in % increase of stats and costs per level. This means that players in this region will experience very similar wait times between each level and expect similar returns on their investment. The cost efficiency ratio of this region is ~2.97 (averaging ~2.10% increase in stats and ~0.71% increase in costs per level), making it much more worthwhile relative to the first two regions.
301-359: Middle RC
The Middle RC region sees a more rapid decline in % increase of average stats and % increase of average costs relative to the Tranquillity Zone. Further, there is a notable decrease in the % of DEF gained per level in Middle RC relative to both the Tranquillity Zone and the other stats (HP, ATK). Interestingly, this region is where DEF begins to increase slower than HP and ATK, which marks the beginning of the Glass-Cannoning Phenomenon (which I will cover in a separate guide). The cost efficiency ratio of this region is ~4.21 (averaging ~1.99% increase in stats and ~0.47% increase in costs per level), making it a very worthwhile investment.
360-364: 2nd RC Ramp
As with the 1st RC Ramp, the costs inflate dramatically yet again, making this region a terrible return on investment (but you have to go through this region regardless, so press on!). This region also serves as a bridge to late game (in terms of RC spectrum). The cost efficiency ratio of this region is ~0.34 (averaging ~1.97% increase in stats and ~5.79% increase in costs per level).
365-420: Late RC
This region is the final pleasant region before the Dead Zone. Players should expect to see major % increases in stats and relatively minor % increases in costs, but the increases decline as you progress further into the region. In addition, dust wall #2 usually returns near the beginning of this region. The cost efficiency ratio of this region is ~4.00 (averaging ~1.32% in stats and ~0.34% in costs).
421-478: Dead Zone
Level 421 marks the beginning of the dreaded ‘Dead Zone’, which sees a continuous increase in % inc. of costs without an increase in % inc. of stats. This region is projected to last the longest, and although the cost efficiency ratio isn’t too bad, the minimal % inc. in stats per level make this undoubtedly the most boring/painful region of the RC spectrum. This region also marks the current endgame or graveyard for f2ps, low spenders and even dolphins (VIPs 10-14). The cost efficiency ratio of this region is ~2.97 (averaging ~0.80% in stats and ~0.32% in costs).
479-501: Prosperity Zone
However, all hope is not lost. Introducing the Prosperity Zone: a region where the % inc in costs decrease dramatically and thus also increasing the cost efficiency ratio. Most notably, the dust required to level plateaus here (seemingly forever), so the expected amount of diamonds to spend on dust to level up once stagnant here. The % inc. of costs of gold and exp also sees a significant increase, making this one the most worthwhile investment yet. The cost efficiency ratio of this region is ~8.17 (averaging ~0.801% in stats and ~0.098% in costs).
502-640: Endgame RC
The Endgame RC region, which can also be called the “OP Zone” is… well, very OP indeed. With a cost efficiency ratio of ~20.43, this region undeniably has the most value of any region in the RC spectrum. What effectively happens at level 502 is that the % inc. of stats shoots up to 1.735% per level, whereas the % inc. of costs continues to decline. This means that a level in this region is more beneficial than two levels in the Dead and Prosperity Zones compounded (Yes it is insane indeed). At the time this guide is written, this region is exclusive to whales, which to be honest is pretty understandable. However, this also means that players in this region will quickly pull away from players in the previous two regions in LCT, which is a bit of a bummer to non-whales. The cost efficiency ratio of this region is ~17.35 (averaging ~1.61% in stats and ~0.093% in costs).
641-841: Mystery Zone
This region is unreachable for players and the Lilith has yet to decide on the upgrade costs at the time this guide was written, thus the cost efficiency for this region cannot be calculated. However, enemies do have levels in this region, and thus the % inc. in stats can be seen (~1.29% average). There seems to be no major inflections in this area, only a gradual decrease in % inc. in stats. Further, it is interesting that DEF is now back increasing at the exact same rate as the other two stats in this region.
Why RC Cramming is the Best Value
Now that you understand the different stages and scaling of RC, let’s talk about why RC cramming is the best value regardless of your VIP level. I would like to start with my definition of ‘value’, which is: the percentage increase in team strength per diamond (or equivalent) spent. In other words, when I talk about ‘value’ in this guide, I am talking about how much stronger/ how much further you can progress with the same amount of time and diamonds, or how ‘optimal’ an investment is. If you want to play the game differently (maybe you really want to build a certain character) that’s fine, but be aware that doing so is likely to actively decrease your strength/progression, and these opportunity costs do compound infinitely due to the nature of loot and challenger coins. Next, I’ll explain why RC cramming is the highest value investment by comparing it to the other popular contenders: Stargazing, HCP and Hero Investment (Poe and Reds).
Comparison to Stargazing
Let’s begin with the most popular late game choice: Stargazing. As you all know (I hope, otherwise please read Aimb’s diamond spending guide first before continuing), doing 10x summons is the best way to spend diamonds in the game until you’ve built the vast majority of your core heroes. Next, the best value is HCPing (Hero Choice Pulling) the rest of your core hero copies and buying Reds and Poe from Lab Merchant with the remainder of your diamonds. However, many (perhaps even most) players are stumped on what to spend their diamonds from this point on, and many, after seeing how “OP” heroes like Alna and Lucretia are, decide to start gazing.Let’s consider how many diamonds it takes on average to gaze a celepogean copy. Now gazing rates are highly subjective, and your luck can range anywhere from insane to abysmal. However, we need a quantifiable expected gaze number, so I quantified the averaged rate based on three factors: In game stats, Ensign’s calculations and personal experience.
Lilith’s Claim: 2% (or 1 in 50)
Assuming Lilith is being 100% honest, we average a hero every 50 gazes. Since we need 14 copies to get a celepogean to A, it follows that the cost is 14 x 50 x 500 right? Wrong, as we did not factor in the value of the other rewards from gazing. Now, the actual cost of each gazer varies based on what rewards you value/care about, more specifically whether you have done/care about eye and call 5*, and whether you still need T0 M gear from AFK loot or not. I calculated the value of these rewards based on the cheapest way you can obtain them, or the maximum value they have. The value of shards is from comparing the value of shard chests during events to the diamond equivalent of reds (the price from lab merchant). I decreased the value of gold by 50% compared to the store because mentioned earlier, gold should not be a limiting factor in your RC cram if you don’t buy excessive amounts of emblems. The results show that each stargaze costs roughly 401.26 diamonds. Taking this value, we get: Cost per copy = 50 x 401.26 = 20063 diamonds, and cost of A = 14 x 50 x 401.26 = 280882 diamonds.
Personally, averaging the 20 copies of celepogeans I gazed, the average rate seems to be around 48 per gaze. Which means the cost of getting a celepogean is 48 x 401.26 = 19261, cost per A is 14 x 48 x 401.26 = 269647.
Ensign’s Estimation: (Taking the “likeability counter” into account)
From his calculations, Ensign proved the existence of an additional factor on top of the 2% that the game claims the stargazing rate is, which increases the more the times you fail to pull the hero. In addition, while I was digging around the stargazing code, I also encountered a similar variable denoted “likeability counter” which seems to line up with what Ensign found. Further, Lilith’s customer support also said something along the lines of “The chance of getting pulling the hero increases every time you don’t”, which further confirms this theory. The collection of stats on the gazing rates streamed by content creators also fall in line (Yes there is indeed an overwhelming amount of evidence supporting this xD). Taking everything into account, the recalculated average rates seem to be around 42 pulls per hero on average. Using the cost that we calculated from the previous section, the average cost is estimated to be 42 x 401.26 = 16853 diamonds per copy and 14 x 42 x 401.26 = 235941 per A.
We don’t know for sure what the expected rate for stargazing is, but Ensign’s Estimation seems to be the closest to the true value due to how many sources support his claim, so let’s take his estimation as the true value.Let’s assume the worse case scenario for late game players: you are currently stuck in the middle of the Dead Zone, where the cost efficiency ratio is terrible for a long stretch of time. Is it time to stargaze? Let’s look at the opportunity cost of gazing a hero to A. In the lowest value period, it costs approximately 17k diamonds to level your RC up once. 235940.88/17000 = 13.88 levels. We know that the stat increase is 0.8% per level, so the opportunity cost in % increase in stats = (1.008^13.88-1) x 100 = 11.69% for each hero.
In the current meta, most players use/swap around 30-35 different heroes for pushing campaign, and at least 15 heroes for LCT. Since the team that gets the player stuck changes almost every multi, we must take into account the benefit for all of these “commonly used” heroes. In other words, for Alna or Lucretia to be worth, their marginal contribution to the entire 5-team setup (the fact that they are there instead of someone else) must surpass the 35 x 11.69% statistical buff (or 22.7% effective buff) the equivalent diamond value of RC cramming gives, which they certainly do not, especially since mercs exist. Note that this is the worst case scenario, think about the difference between RC cramming and stargazing in the Prosperity Zone and Endgame RC regions. You can’t skip RC regions and pick ones to cram, thus not cramming in a bad region would only mean staying there for longer and result in a higher opportunity cost. Meta-shift is another factor which makes RC cramming more valuable, I’ll discuss that later in this guide.
Comparison to HCP
Another popular diamond sink for late game players is HCPing heroes. The maths for HCP probability is not as complicated as stargazing, as it operates on a ‘pity’ system rather than a ‘likeability counter’ system (please don’t argue with pity factor, I’ve seen it in the code). Taking pity into account, players average around 1 hero in every 23 pulls, so the cost of getting 8 copies of a hero is 8 x 23 x 300 = 55200. However, this is not the total cost of ascending a hero, as you also need 10 E+ fodder heroes, which is 180 blues. The expected number of blues from each HCP 10x pull is 4.37, so the 8×23 pulls done to get the 8 copies would yield approximately 80 blues, which means you still need 100 more. The standard value of a blue is around 180 diamonds, which makes a total of 73200 diamonds to get to A. Using a similar method to gazing, each 4f hero’s opportunity cost is 62611.2 diamonds. Again, for HCPing to be worth, they must have 62611.2/17000 = 3.68 , (1.008^3.68-1) x 100 = 2.98%, 35 x 2.98% statistical increase (5.25% effective increase) for HCPing to be worth. The meta does change fast and power creep is real, but there aren’t enough new core heroes that demand focused building (more than just MV + random pull) that makes HCPing actually worth it.
You might say: “Yes, but what if I HCP someone like Raku during his heroic ship? I get a lot of free rewards from there too!”, and yes, I have accounted for that too. The rewards from heroic ship is worth ~6500 diamonds + whatever you think of the avatar, so that’s potentially only 56111.2 diamonds for the hero to A. However, the downside with HCPing heroes during ship is we don’t know how well it fits into the meta (if at all), and the hero you HCPed could very well become the next Respen. In that case, you pretty much just wasted your diamonds. If you really like collecting avatars, then I guess HCP would be the best option for you.
Comparison to Hero Investment (Reds and Poe)
The third area people tend to spend their diamonds on is hero investment, more specifically buying Poe and Reds with diamonds. The cheapest place to buy them is from lab merchant (10 Reds for 1584, 600 Poe for 480). This means that each +30 costs 47520 diamonds.Poe is a bit more complicated since it’s a pulling system. The chance of getting an M furn is also around 1 in 23, and every 90 pulls you also get an additional furn, so you get ~4.91 M furn per 90 pulls, which is around 0.055 M furn per pull. However, since there is a chance for dupes (which is basically a wasted M furn) equivalent to 1.11 dupes per 9 M furn pulled, the actual average per pull is around 0.0478 M furn per pull. Since you can recycle furn, each pull is slightly cheaper. Assuming you recycle all E and L furn, each pull gives you 0.5425 x 10 + 0.3054 x 50 = 20.7 Poe, so each pull actually only costs around 279.3 Poe. This means that it costs roughly 5839.8 Poe per M furn (including dupes), which means 17519 Poe per 3/3 and 52558 Poe per 9/9, or 14015 diamonds per 3/3, 42046.5 diamonds per 9/9. However, since you can’t target who’s furn you pull, it would take a very long time before you can get a specific 3/3 or 9/9 built.
In other words, for buying Reds to be worth, your next +30 must improve your 5-team setup at least2.25% per hero on average statistically and 4.11% effectively. For buying Poe to be worth, your next 3/9 must similarly increase your team by 0.66% and 1.17% respectively (you know what the number are for) and 9/9 by 1.99% and 3.55% respectively. As mentioned earlier, these hero investments are worth when you are investing in your first few core heroes (e.g. Thoran +30, Ainz 9/9 etc.), but is no longer worth after you’ve done most of your core.
In addition, there is another factor which devalues the three popular investment pathways: Meta shift. The underlying principle behind AFK Arena is that Lilith wants players to pay, and the most common way they do that is by building heroes (from scratch). Since Lilith basically never nerfs heroes, it is inevitable that new heroes become more and more busted in comparison to older heroes in order to fulfil the power-creep and encourage spenders to continue spending. However, since there are only 5 comps in campaign (up to at least ch42), this means that the majority of old heroes will eventually fall off, regardless of how broken they are right now (this affects carries like Gwyn much more than supports like Rowan, but supports will also eventually fall off, e.g. Nemora/Numisu etc). This means that the investment you put into the current meta heroes is likely to eventually go to waste, especially if Lilith decides to not release any more swap scrolls. So whether it is stargazing the Talene at the time (the old Lucretia/Alna), HCPing the Shemira at the time, or taking Gwyn to + 30 9/9, all these investments will eventually be meaningless in the long term. The addition of new power-creep systems such as Sigs, Tree and Furn further devalue extreme levels of investment into old systems.
However, what never loses its value regardless of how crazy the meta becomes is your RC. Newer heroes can simply replace the slots of older heroes that are no longer in meta and carry 100% of their investment over. Newer power-creep systems can simply amplify the current stats/strength of your heroes (add a multiplier). Thus, in the long run (since we are talking of theoretical endgame), the value of RC cramming is elevated even more.
What to Buy When RC Cramming?
So now that I have convinced (hopefully at least some of) you to invest into your RC, I am going to explain what you should invest into, since like with pretty much all resources in this game, some deals are better than others. The three main areas that you should spend diamonds in when RC cramming includes: the store, FRs (fast rewards) and Bounty Board.
The source of diamond expenditure should be the store. Outside the common sense daily routine (2x refresh for 200 diamonds, buying all dust and Poe coins for gold), you should also buy all dust crates (the 3×8 hour chests, not the piles!) for 300 diamonds each and all exp crates you encounter for 192 diamonds each. However, since FoS and VIP doesn’t affect crates, keep in mind that the value of buying exp crates decreases the higher VIP you are, so if you are noticing a decline in diamonds, stop buying these crates unless you are also exp walled. VIP does not affect dust, so dust crates are still extremely worth regardless of your VIP level.
The second source is FR (the 2hr fast reward thing next to your loot chest). According to Ensign’s calculations, the estimated value of a FR is approximately 192.8 diamonds after balancing (this is taking into account every possible reward and their loot timers). However, your VIP level does affect how many resources you gain from FRs, so their value would increase with your VIP level. In other words, VIP 10s should do 5 FRs every day (Free 50 80 100 100), VIP 11-14s should do 6 (Free 50 80 100 100 200), VIP 15+ should do 7 (Free 50 80 100 100 200 300). I don’t have access to the costs beyond 7 FRs, so cannot provide an accurate answer for even higher VIP players, but I know that at least 7 is worth it.
The final main source is bounty boards, or more specifically rerolling them. Now I know many players hate refreshing bounty boards as it feels like gambling, but there is a simple rule to follow to ensure you make the most of the rerolling mechanic. From the code, the probability distribution of bounty quests with a maxed bounty board is 90:8:2 (L, M and A quests respectively). Within these, the distribution of quest reward types is 3:3:1:1 (gold:dust:stones:diamonds respectively). Out of these rewards, only dust and diamonds are relevant to RC cramming. Blue stones are okay too, but as you probably know, the value of fodder decreases massively the later you go. Gold quests, needless to say, are very trivial. Therefore, you should reroll all gold quests and L stone quests. When rerolling, dispatch all quests that are worth keeping (everything that you shouldn’t reroll) and then count the number of quests remaining. I won’t go into the maths in depth here, but in short it’s worth rerolling quests until there are only 2 left (only 1 left during double bounty events).
Brief Spending Guide
I’m not very experienced when it comes to whaling guides, but here are some general tips you should follow. If you are F2P, skip this section but make sure to select the exp and dust regal every ‘season’. If you are a plankton spender (only buying 1$ deals and extreme value packs), buy the monthly subscription. The benefit to cost ratio for that deal is insane, if you take into account how much it helps pushing (which gives compounding opportunity benefits) as well as all the apparent benefits. If you are a shrimp to a dolphin (only buying value deals suck as ARs, regals, monthly card etc.), make sure to buy the exp and dust regals every ‘season’. If you are a whale, continue buying what you are currently buying, but make sure to select dust crates as the reward whenever you have the option to do so.In addition, for events that do have dust or exp crates as rewards (there has only been one so far), make sure to consider their value using the store price and buy them if they are at equal or higher value than the other rewards. For the trading hub, make sure to only the dust crates with your bound dragon crystals every day until your crystals run out.
When Should You Start RC Cramming?
Now you know why and how you cram your RC, let’s talk about when you should start. As mentioned earlier in the RC regions section, different regions have drastically different investment values, but since regions cannot be skipped, it’s best to start as soon as possible due to the compounding opportunity benefits.However, you shouldn’t start RC cramming until you have:
- Ascended most of the core heroes.
- Invested into most of your core heroes (varies based on current progression)
Playing optimally, you should start cramming as soon as you’ve completed the two requirements above (ask in the #questions channel on discord if you want help), and should start cramming by Late RC at the latest (if you are still not done, start cramming anyways).
In conclusion, RC cramming is by far the most ‘valuable’ investment you can make if you want to maximise progression and team strength for PvE and LCT. However, since this is a game after all and people play it for different reasons, it is ultimately up to you to choose what you spend your diamonds on, I am just here to provide an explanation on why RC cramming is the optimal min-maxing route.
Thank you for taking time to read this guide. I hope that by now you have either been convinced to start RC cramming, or have learnt a thing or two about RC scaling and investment values. Feel free to find me on the Official AFK Arena discord server if you want to discuss anything in the guide! Hope you enjoyed it!
- If you want to learn more about this, refer to Aimb’s guide
- Diamond income which comes either daily or in a regular periodic manner (so not events)
- The reason why gold is not included is that the rate of gold income from all renewable sources, including guild hunts, AFK loot, betting, lab rewards etc. far outweighs the amount required to level your RC, so there’s no reason to count it in the value calculations, just don’t buy emblems. More on this later.)
- ‘Stats’ loosely refers to HP, ATK, DEF. However, DEF generally increases less than the other stats.
- The ratio of the average % increase in stats compared to the average % increase in costs in that region
(% inc. in stats / % inc. in costs)
- The stats in this region is currently irrelevant to RC cramming and is mainly used for other calculations.
- Note team strength is not the same thing as team power. Team strength is how strong your team is, specifically in PvE and LCT PvP.
- I want to add here that Alna is a much better choice than Lucretia if you are a f2p/low-spender looking to maximise your progression, unless you care a lot about AE (ping me on discord if you want further explanation).
- Refer to the stargazing value tab of the spreadsheet for stats on calculations.
- The actual benefit of the stats is actually a lot higher than this (around 22.7%). I will discuss this further in my damage formula guide, stay tuned!
- Also keep in mind that this calculation disregards the fact that the two highest value celepogeans (Alna and Lucretia) cannot be used in a decent manner until A, whereas RC cramming is continuous (and thus there are compounding costs for gazing, since strength = progression = faster resource income rate).
- Credit to Ensign for working this out
- The cost of these make up the majority of the 17000 diamond cost used in earlier calculations, the rest is derived from estimated exp crate costs.
- This value can vary based on how many artefacts you want to build, whether you care about M gear or not, how many +10s and +20s you have left to build etc, but is roughly ~190-195 diamonds.