Using Decision Analysis to find Lowest Cost

Decision analysis is a management tool designed to help remove emotion from decision making. It breaks everything down to objective numbers so we can make the most financially sound decision. The more experience we get as managers, the more valuable our instincts or “gut feelings” are, but most sociological studies show that gut feelings are often wrong. Going with your gut is like flipping a coin–you’ll be wrong half the time. By charting everything out, we can be more confident in our decisions, and also help explain them to others in a rational manner.

For one of my classes this semester, Project Risk Analysis, we were tasked with constructing a decision analysis table and a decision tree. We could apply this to any project or scenario, even made-up ones, and I decided to do something a bit different. I’ll likely write my final research paper on the Panama Canal, since this year is the anniversary of its building and I’ve been reading about it, but I decided to perform decision analysis on my other current hobby: ArcheAge.

ArcheAge is a Massively Multiplayer Online Role-Playing Game (MMORPG), and one of the activities in which I am engaged is farming. I plant crops, harvest them, and then use them to make other things in-game. For this decision analysis project, I decided to calculate the most financially efficient method of getting Medicinal Powder. This powder can be generated from four different plants, and it is used in Alchemy, another craft on which I focus.

There were a number of variables to take into account. First, each plant yields a different amount of medicinal powder when it is processed. Second, the seeds for each of the four plants cost a different amount. And third, there is a small chance when harvesting to “crit,” which results in having 3 times as much of the plant as you would normally harvest. And since the plants process into different amounts of medicinal powder, that crit amount has to be taken into account.

In general, I broke everything down to the cost of 1 medicinal powder, but to calculate crit rate on yield, I calculated harvest rates of 1000 of each plant.

Without further ado, let’s get to the tables. You can find this in an Excel spreadsheet in my OneDrive, but I’ll copy and paste some of the relevant data in here. I also created a Decision Tree as part of the assignment, but I don’t personally find the graphical format terribly helpful.

A standard against which I am measuring is the cost of purchasing one medicinal powder on the auction house, which is 1.47. For those familiar with MMOs, the currency is the standard gold, silver, copper system, where 100 copper equals 1 silver, and 100 silver equals 1 gold. For the purpose of these calculations, I standardized on silver, so a mushroom cost of 1.98 means that it costs 1 silver and 98 copper. Ginseng at 10.74 is 10 silver and 74 copper for one ginseng.

Purchase on Auction House to Refine

Plant Current Market Value (per 1) Processed Yield (per 10) Cost per 1 Medicinal Powder
Mushroom 1.98 15 1.32
Thistle 2 23 0.869565217
Aloe 5.85 47 1.244680851
Ginseng 10.74 77 1.394805195

Even while building the tables for this analysis, the prices of plants on the auction house were fluctuating wildly. The game is still very new, and it will be a while before things settle down and become standardized. The conclusions presented here may change as market value changes.

The calculations here are very straightforward, and it is obvious that buying materials from the auction house to create medicinal powder is very expensive. It is less expensive than buying medicinal powder outright, and I’ll talk more about why the cost is so high in the conclusion.

Purchase Seeds, Plant, Harvest, and Refine

Plant Seed cost (per 1) Average per harvest Cost (per 10 unprocessed) Processed Yield Final cost per 1 Medicinal Powder
Mushroom 1.4 3 1.555555556 15 0.09673853
Thistle 4 3 4.444444444 23 0.18025813
Aloe 11 3 12.22222222 47 0.242581419
Ginseng 20 3 22.22222222 77 0.269216687

 

For the sake of brevity, this table shows the final cost when taking crits into account. You can see the spreadsheet for the math on critical harvesting success.

I had suspected the above was true, but it is really nice to have the math confirm this. There are two parts of the analysis I haven’t revealed yet, though, and those are Time and Labor.

Time is the amount of time it takes to plant, harvest, and refine, and I haven’t yet gathered the data and done the math to calculate the opportunity cost of planting/harvesting/refining versus some other task that would make money and let you purchase medicinal powder. It’s entirely possible that there is an alternative investment of time that yields a lower overall cost for medicinal powder than growing it, but that’s beyond the scope of this analysis.

Labor is a mechanic in the game that is a governor on performing tasks like harvesting and refining. It is generated at a rate of 5 labor every 5 minutes while logged out of the game, or 10 labor every 5 minutes while logged in, and it caps at 5000.

These four different plants have different growing times that go along with the different yields of medicinal powder they have.

Time Cost per 1 Medicinal Powder

Plant Time to mature (minutes) Time per 1 medicinal powder (minutes)
Mushroom 120 8
Thistle 345 15
Aloe 855 18.19148936
Ginseng 2040 26.49350649

 

Labor Cost

Since Labor is generated automatically over time, it does not seem to be calculated by many in the process of growing and harvesting and refining materials. It is a hidden cost, but there is a way to purchase additional Labor through the auction house in the form of a Workman’s Compensation potion, and this lets us include the cost of labor in our analysis.

Cost 1098
Labor 1000
Cost per Labor 1.098

Many may never buy a labor potion, so this cost calculation may not be relevant to everyone, but it is relevant for two groups. First, those who buy labor potions regularly can see the increased cost of that investment. Second, it helps illuminate the difference between the labor spent in harvesting plus refining as compared to buying materials from the auction house and then refining. In the latter scenario, which we have seen is more expensive than growing materials when labor isn’t taken into account, we can examine if buying has a net cost that is less than growing when taking labor into account.

Plant Cost via Auction House with labor included Cost via harvesting with labor included
Mushroom 6.81 6.68473853
Thistle 6.359565217 6.76825813
Aloe 6.734680851 6.830581419
Ginseng 6.884805195 6.857216687

When taking labor into account, we find that the least expensive way of generating medicinal powder is actually to buy thistle plants from the auction house, a conclusion that is totally different from the calculation without labor. Again, most people use the labor they generate over time for free, so this may not be relevant to them, but for those who are either buying labor potions often or who are feeling the pinch of limited labor and are evaluating the opportunity cost of spending labor to harvest, it is helpful data to have.

Conclusion

Decision analysis does not make decisions for you. The decider still needs to take into account all the variables and choose the option that makes the most sense for them. When dealing with matters of probability, particularly in risk analysis (which I did not address above), the final outcome is still open to chance and will not be influenced by the analysis. But by taking the time to really think through the options and do the math so you have a more objective lens to examine the question, you can make more informed and better decisions.

For my money, when working to generate medicinal powder, I will continue to plant mushrooms. I generate labor over time and don’t buy potions, and I’m focused enough on alchemy that the opportunity cost of investing my labor in harvesting and refining mushrooms is low.

That said, the maturation time of mushrooms often works against me: it is so fast compared to the other options that it wears me out planting and harvesting so often. If you can only harvest once every day or two, you’ll certainly get a higher yield from a different plant, and your availability to harvest may change your calculations. It could be that you are less concerned about minimizing cost and more focused on maximizing yield when you can only harvest every day or two, and in that instance, you might choose to plant ginseng despite its higher cost.

Remember as well that, at the time of this writing, medicinal powder was 1.47 per one powder from the auction house. Without taking labor into account, it is slightly less expensive to buy materials and make the powder yourself. That increased cost is due to the refiner’s investment of time and labor. But when we take labor into account, we see that 1.47 is actually very inexpensive for medicinal powder. If you’re buying both materials and labor potions, it is far, far less expensive for you to buy medicinal powder right now rather than making it.

I hope the above is helpful as you decide what path works best for you in getting medicinal powder. My next ArcheAge-related decision analysis, based on requests from my guild, will be the most cost effective way to generate lumber.

Editor’s note on 2014-12-29: I’m no longer playing ArcheAge (and haven’t for some time) due to the ongoing brokenness of the game, so there won’t be a follow-up article.

One thought on “Using Decision Analysis to find Lowest Cost

  1. This analysis was very helpful and I look forward to applying this to my own work. I also am looking forward to the lumber analysis.

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