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Disclaimer and a General Note (Please Read at Least this Section)
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This spreadsheet is experimental, use it at your own risk.
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If you find any errors in the calculations please reach out to me (Chaliia) on Mattjestic's discord.
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Also, please ignore spelling/grammer mistakes, it is not my strength :)
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With that first disclaimer out of the way, I want to take a moment ot talk about perceptions and play-styles. Lost Ark is a video game, there are people who play video games seriously and
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people who play to casually. BOTH are valid ways to play the game! Neither way is better than the other, and I am not here to tell you how to play the game. This calculator is hopefully
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helpful for all types of players. If you are hardcore this calculator should help you min/max all of yor resources. If you are casual, hopefully this calculator helps you spend the materials
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you have wisely.
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Remember, however you enjoy the game is perfectly fine. If you just want to randomly use upgrade materials because you have a "good feeling," go for it. I'm here to tell you that on
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average that will be less efficient (materials/gold) than if you followed a calculator like this, but again that's fine if it's how you enjoy the game!
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Now, I do want to set one thing straight. For T3 honing you need to go in with the mindset that you are going to fail, and you are going to fail alot. Depending on your luck in T1 and T2,
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you may or may not know about the pity system called Artisan's Energy. Generally, this system is in place to ensure that after a certian number of attempts you are guarenteed to
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succeed your upgrade. I go into greater detail about this system below but for now lets completly over-simplify it and say: this system is fail 5 times and your 6th is guarenteed.
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In T1 and T2 you may have never failed the upgrade on a single peice 5 times, in T3 I can almost guanrentee that you will (multiple times in fact). For those interested, the last sheet in
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this document is a bunch of statistics for you to browse and understand just how many times the average person is going to fail upgrades in T3.
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Main take-away: You are going to fail upgrades, but so is everyone else. Ya, it might not feel great when you see the failure screen, but it's going to feel great when you hit on a 10%
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upgrade. Item level is just one measure of character power, if you ran out of resources for upgrading go get some skill points or engraving books.
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With all that out of the way, for those interested, I want to outline how the math and simulations in this spreadsheet work. I would reccomend that everyone read through this and
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check it against your understanding of honing, but if you have blind faith then hop on over to the T3 Honing Calculator sheet and get started.
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Calculating Expected Costs
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Let's take a brief moment to talk about how we are getting the expected costs for each upgrade. The first part of this discussion will be guided by the key-terms (highlighted in Blue)
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that you need to understand to use the calculator. Understanding the first key-term is hopefully fairly straight-forward. We need to calculate the cost that we expect to spend on each
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upgrade. As expected we start by taking each material and multipling the cost of that material times the number of them you need. This calculation is refered to as the
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"Material Raw Cost" in the main sheet and is properly understood as the price we should expect to pay to press the hone button once.
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The next step is that we need to weight the "Material Raw Cost" because for most upgrades we should not expect to succeed on the first attempt. Disreguarding enhancments for now,
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the proper way to weight our cost is to divide by the probability of succeeding (or equiveltly, multiply by how many times we would have to try before expecting to succede).
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That might be a bit confuzing, so let's take a look at a couple simplified examples:
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First consider an upgrade that has a "Material Raw Cost" of 1000 gold. For this example, let's also say that there is a 100% chance to succed on this upgrade.
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Therefore our expected cost is 1000 / 1, or just 1000 gold.
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Now a slightly more complex example. Lets stick with our 1000 gold "Material Raw Cost", but now lets say our chance to succeed is only 50%. On the first hit 50% of people will succeed
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and be done with the upgrade but this means that 50% of people are going to fail. Those people now have to try again, having to spend another 1000g, they once again have a 50%
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chance to succeed. For those very unlucy folks who fail that attempt they yet again have to spend 1000 gold, so on and so forth. For this simplified example, on average we should expect
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to fail 2 times. This number is just the inverse of our chance to succeed:
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50% = 1/2 -> (1/2)^-1 = 2
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If we expect to fail two times, then our expect cost should be:
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1000 gold per attempt * 2 attempts = 2000 gold
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or equivently:
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1000 gold per attempt / 50% chance to succeed attempt = 2000 gold.
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This calculation is the "Base Expected Cost" fom the main sheet. I will note here that the percentages we are dividing by are NOT the basic 60%, 45%, 30% etc. that you may expect,
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but more on that below. First, lets finish this part of the discussion with enhancment materials.
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The next key-term to understand is the "Base Enhancment Cost". As its name suggests, the "Base Enhancment Cost" is calculated by multiplying the cost of the enhancment materials
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by how many you have selected to use.
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The "Enhanced Expected Cost" is then the same expected cost calculation as discussed above, but we add the cost of the enhancment materials and update the percentage
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to account for the increase we get for using those enhancment materials. Let's look at another example:
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Again, say our item has a 1000 "Material Raw Cost", and we are going to use 1000 gold worth of enhancment materials ("Base Enhancment Cost"). The base upgrade chance is 50%, but
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our added enhancment materials give us an extra 25% chance. So the "Enhanced Expected Cost" is:
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(1000+1000) / (0.5+0.25) = 2667
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The last column, "Expected Gold Difference," is just the difference between the "Base Expected Cost" and the "Enhanced Expected Cost". For our previous examples this would come out to:
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2000 - 2667 = -667
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The negative tells us that on average we would expect to LOSE 667 gold by using the 1000 gold worth of enhancment materials. This concludes the basic discussion, and should
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give you a good understanding of what the calculator is telling you. The next couple sections are going to dive into more detail on a couple of behind the scenes aspects.
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Calculating Accurate Success Percentages
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As mentioned above we are not, and should not be, using the base 60%, 45%,30%, etc. rates that you will find listed as the base success rate to determine our expected costs. In this section
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I am going to explain why we don't use these numbers, and why this makes our lives a bit more complicated. I think the best way to start is to jump into an example:
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For a 45% upgrade we should expect to fail 55% of the time, and if we fail, the next time we
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try to upgrade it the chance is higher than 45%. This increase is determined as 10% of the
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original base rate. So as the images on the right show, for our 45% upgrade, we fail and the
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next one is 49.5%. If we failed again our success chance woud increase to 54%.
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This increase appears to have a cap, as noted by the yellow text in the center image.
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However, until you get to your +15 upgrades this cap does not matter because of the
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"pity-system" known as Artisan's Energy, which I will hash out in the next section.
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So hopefully it is now clear why the percentage we use to calculate the expected cost is
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not the flat 45%. On average, we should expect to fail a couple times and we need to
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account for this increase in rate on subsiquent attempts.
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Now, combining percentages analytically is not trivial. So we turn to a tried and true method:
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Simulation
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