Farmville Economics: Risk Adjusted Crop Profitability

It’s clear that my addiction to spreadsheets and Farmville knows no bounds, so as predicted, here is my fifth post on the topic.

gameBig_farmville

Here are the quick links to my first four posts:

The wizards at Zynga have been busy, and with regular updates every week (or even more frequently), a large number of new crops have been introduced.  As the comments on my other posts have become quite demanding, here are two of my original tables, updated for all the new crops (as of September 20, 2009):

Crop Profit / Day
Super Berries 900.00
Asparagus 183.00
Sugar Cane 177.00
Peas 176.00
Tomatoes 174.00
Green Tea 170.40
Grapes 170.00
Onion 166.00
Sunflowers 165.00
Coffee 162.00
Blackberries 162.00
Blueberries 156.00
Carrots 150.00
Raspberries 132.00
Broccoli 129.00
Cabbage 116.50
Red Wheat 84.67
Aloe Vera 80.00
Peppers 77.00
Yellow Mellon 77.00
Rice 72.00
Corn 71.67
Pumpkin 69.00
Pineapple 66.00
Potatoes 65.00
Strawberries 60.00
Yellow Bell 54.00
Watermelon 50.75
Cotton 39.00
Soybeans 33.00
Squash 33.00
Artichoke 29.75
Eggplant 24.00
Wheat 21.67

Assumptions: All numbers are normalized for one planting square per day, and assume a “perfect” farmer who can operate all 24 hours of a single day.  It’s assumed that you will need to harvest, plow, and plant every cycle for a given crop.

As it turns out, many times players are optimizing for experience per day, rather than for profit.  As a result, here is an updated table that shows experience per crop, with the same assumptions:

Crop XP / Day Cycle (Hours)
Super Berries 24.00 2.00
Strawberries 12.00 4.00
Raspberries 12.00 2.00
Blueberries 12.00 4.00
Blackberries 12.00 4.00
Aloe Vera 8.00 6.00
Pumpkin 6.00 8.00
Tomatoes 6.00 8.00
Sugar Cane 6.00 8.00
Green Tea 4.80 10.00
Asparagus 4.50 16.00
Rice 4.00 12.00
Carrots 4.00 12.00
Peas 4.00 24.00
Onions 4.00 12.00
Soybeans 3.00 24.00
Peppers 3.00 24.00
Grapes 3.00 24.00
Coffee 3.00 16.00
Sunflowers 3.00 24.00
Broccoli 2.50 48.00
Eggplant 1.50 48.00
Squash 1.50 48.00
Yellow Bell 1.50 48.00
Pineapple 1.50 48.00
Cabbage 1.50 48.00
Wheat 1.00 72.00
Cotton 1.00 72.00
Potatoes 1.00 72.00
Corn 1.00 72.00
Red Wheat 1.00 72.00
Artichoke 0.75 96.00
Watermelon 0.75 96.00
Yellow Mellon 0.75 96.00

It’s fairly obvious from the numbers above that crops that can be planted and harvested multiple times per day have a significant advantage. This advantage is largely due to the +1 XP you get from plowing a square, and the multiple turns per day. While the longer duration crops have higher experience, they don’t generate enough experience to match the multiple cycles of crops like the berries, or the 8-hour crops like Tomatoes.  Of course, this ignores the time value of money, the primary topic of my first blog post on Farmville Economics.

It seems as if Zynga has been doing their homework when building out their technology tree with additional crops.  Using my 15 coin / XP estimate, the table combining the value by coins and experience is dominated by the new crops:

Crop Profit + XP / Day
Super Berries 1260.00
Blackberries 342.00
Blueberries 336.00
Raspberries 312.00
Sugar Cane 267.00
Tomatoes 264.00
Asparagus 250.50
Green Tea 242.40
Strawberries 240.00
Peas 236.00
Onions 226.00
Grapes 215.00
Carrots 210.00
Coffee 207.00
Aloe Vera 200.00
Sunflowers 210.00
Broccoli 166.50
Pumpkin 159.00
Cabbage 139.00
Rice 132.00
Peppers 122.00
Red Wheat 99.67
Pineapple 88.50
Yellow Mellon 88.25
Corn 86.67
Potatoes 80.00
Soybeans 78.00
Yellow Bell 76.50
Watermelon 62.00
Squash 55.50
Cotton 54.00
Eggplant 46.50
Artichoke 41.00
Wheat 36.67

The title of this blog post, however, is Risk Adjusted Crop Profitability.  One of my orginal concerns was that measures of profitability were not properly taking into account the amount of risk that each crop incorporated.

When you plant a crop in Farmville, it grows for an allotted time.  During that time, you cannot harvest the crop, nor can you recover your capital.  It’s completely illiquid.  After that time period, you have an equivalent time period (100% of the growing time) to harvest the crop.  At that point, your investment is liquid and recoverable.  After the harvest time has expired, over the next equivalent time period (between 100% and 200% of the growing time), your crops will wither square-by-square, until none are left.

As a result, a crop that yields a few more coins of profit, but that involves an up-front investment of fifty coins, may not actually be worth the risk of withering.

In case you think I’m being melodramatic, it’s a very common problem.  People invest all of the wealth into planting crops, get distracted or misunderstand the rules, and then end up with withered crops and no money left over to re-plant.  They have to depend on “lotteries” and “helping neighbors” to recapitalize.  (In fact many don’t, which may be a problem Zynga needs to monitor.)

So how do we model risk-adjusted profitability?

In typical financial modeling, you would have a “cost of capital” – namely a borrowing rate that would be your cost of money over a period of time.  However, for this analysis, it didn’t seem appropriate – maybe I’ll revisit sometime in the future.

To model the Farmville risk, I tried to literally focus on the following facts:

  1. How much capital (coins) up front you risk by planting one square?
  2. What is the risk that you won’t be available during the harvest time?
  3. Probability of harvest + Probability of wither = 100%
  4. Multiply the profits per cycle with the probability of harvest
  5. Normalize to a risk-adjusted profit per day

In order to model #2, I’ve used the following assumption: you are expected to check Farmville once every 24 hours.  You can replace this with your own number, but given that Farmville has 15M+ active daily users, this assumption seems fair.

So, assuming any hour is the same as any other (on average), there is a 1/24 probability that you will be able to check Farmville in a given hour.  24 * 1/24 = 100%

I’m also assuming that your ability to check on a crop in any given hour is independent of the ability to check any other hour.  This keeps the probability calculations simple.

This means that for shorter lived crops, there is real default risk:

  • There is a 23/24 chance in any hour that you will not check on the crop.
  • This means, for a 4-hour crop, there is a 23^4/24^4 = 279841 / 331776 = 84.3% chance that you’ll miss checking on the crop during harvest time for full profit.
  • This means, for a 4-hour crop, there is an 84.3% chance you’ll miss the withering time, where you’ll receive partial profit.  (I’m assuming a linear decay rate)
  • This results in a default rate of 71.1% on a four-hour crop.

Using calculations similar to those above, I generated an expected profit per cycle.  I’ve regenerated the table (ignoring experience) for the crops, and ranked them by risk-adjusted profitability:

Crop Risk-Adjusted Profit / Day Risk of Complete Default
Peas 226.53 12.97%
Broccoli 217.37 1.68%
Grapes 206.37 12.97%
Sunflowers 201.57 12.97%
Asparagus 185.57 25.62%
Cabbage 181.47 1.68%
Super Berries 154.22 84.35%
Coffee 153.35 25.62%
Red Wheat 142.52 0.22%
Onions 135.58 36.01%
Yellow Mellon 130.15 0.03%
Green Tea 126.03 42.69%
Carrots 125.98 36.01%
Corn 123.93 0.22%
Peppers 117.11 12.97%
Sugar Cane 115.57 50.61%
Pineapple 115.54 1.68%
Potatoes 114.40 0.22%
Tomatoes 114.27 50.61%
Yellow Bell 99.87 1.68%
Watermelon 91.44 0.03%
Blackberries 80.30 71.14%
Rice 79.19 36.01%
Blueberries 78.89 71.14%
Cotton 77.22 0.22%
Soybeans 74.87 12.97%
Squash 72.46 1.68%
Pumpkin 68.82 50.61%
Aloe Vera 67.61 60.01%
Eggplant 60.71 1.68%
Artichoke 60.47 0.03%
Strawberries 56.35 71.14%
Wheat 52.43 0.22%
Raspberries 38.19 84.35%

Now, I’ve made quite a few simplifying assumptions here, so don’t confuse this with a PhD thesis in Farmville Economics. But it’s amazing to me how this list of crops, more than any other table, best reflects my own internal preferences on what to plant. Maybe that’s because the “once a day” estimate of average availability best fits my own time table during the week.

Another way of revising this estimate is to look at the “risk of complete default” as highly correlated with the “stress level” you feel when you plant a given crop.  Super Berries are awesome, but there is no question that when I plant them, I am hyper-aware of the need to check on them within a 2 hour window to harvest my profits.

Definitely an interesting lens on the topic of profitability.  Please feel free to share alternative views on how to evaluate the risk-adjusted profitability of Farmville crops here in the comments.

Update:  Here are additional posts on Farmville Economics, published after this one:

23 thoughts on “Farmville Economics: Risk Adjusted Crop Profitability

  1. Pingback: More Farmville Economics… « Psychohistory

  2. Pingback: The Personal Economics of Farmville « Psychohistory

  3. I’ve read your posts about Farmville economics. I have one sugestion for this last post of calculating the risk as well as revenue.

    If we assume that the player consider what growing time that fits his IRL schedule best, he will consider to plant different crops depending on when to be able to harvest. I guess this will level out the risk a little but not too much.

    One other consideration that will add risk for “short time” crops is the fact that it’s harder to keep up the work effort needed during night time or during working hours.

    I think the most profitable way in Farmville is if you manage to get a lot of friends. The more friends you got the more gifts you get. You get trees for free and that will really put the profit/day table up-side-down.

    I have one other question: How can I best spend my FV cash? Most of the stuff that I can buy is only for looks! But I haven’t got so far yet so there might be a good way to spend it later.

      • Hi Niclas,

        My previous posts deal with the time value of different crops – please check them out, you’ll like them.

        Raspberries never gave any experience. However, to do a “cycle”, you have to harvest, plow, and plant. Plowing a square gives you 1 XP, so if you plant Raspberries all day, you’ll end up with 12 XP, just from the plowing every 2 hours.

        Gifts are fine, but I ignore them, since they are just free money (or better, free ongoing income streams).

        Adam

  4. I could be wrong here,
    but I looked at some profit tables like yours and they all say that sugarcane is better profit then tomatoes.

    At the moment Tomatoes and Sugar cane both take 8hrs to grow and both give 1XP.
    Tomatoes cost: 100 for 173 Profit
    Sugar cane cost: 165 for 239 Profit

    Using simple divide by cost method that leaves me:
    Tomatoes cost: 1 for 1.73
    Sugar Cane cost: 1 for 1.45 (rounded up)

    So it seems to me, since they both take same amount of growth, tomatoes are the better choice…?

    • Hi Jan,

      You are confusing Return on Investment with Profit. They aren’t the same thing.

      You make 74 coins of profit with Sugar Cane over 8 hours. You make 73 coins of profit with Tomatoes over 8 hours. Thus, Sugar Cane is slightly more profitable.

      Now, Tomatoes have a higher return on investment as you point out, because you invest far less in capital than in Sugar Cane. However, in Farmville, I was assuming you had enough money to plant anything. As a result, you aren’t capital-constrained, you are opportunity-constrained (there are only so many squares on your farm).

      So, if you want to maximize the raw quantity of profit you make, Sugar Cane beats Tomatoes. If you are worried about risking your capital, or if you don’t have enough money to plant every square, then Tomatoes are better than Sugar Cane.

      Tables based on ROI are interesting, but I don’t find them useful. For example, if Farmville rolled out a crop that cost 1 coin to plant and returned 5 coins, I still wouldn’t plant it, even though the ROI would be 400%. 4 coins of profit just wouldn’t be worth the time. I’m trying to get the most coins period, not the best return on my coins.

      Hope this helps.
      Adam

      • (Replying to your last paragraph..)
        However, having a higher return on coins means that you can achieve money making easier.
        (To everyone else..)
        To work out the amount you are going to profit, take the cost away from the ‘Sell For’ amount. If you’re working out the profit for your whole farm, identify how many land squares are being used on your farm and multiply the original profit sum by this amount (of land squares).

  5. Hi Adam,

    Completely correct,
    I was looking at it the wrong way!

    Thanks a lot, I’ll be planting sugar Cane from now on 🙂

    Keep it up!
    Great Work overall!

    • If you have a crop that takes N hours to grow, they will stay fresh for N hours after they ripen, and they will progressively wither over the next N hours.

      So, if you plant a four-hour crop, they take 4 hours to grow, they stay fresh for 4 hours, and then they randomly wither until they are all dead in 4 more hours.

      Adam

  6. Im just wondering what the actual return would be on a crop….factored in with plowing after? (as after i harvest a crop i automatically plow the land and replant)

    i think that information would help out alot.

    • As I explain on the replies to other posts, you have to factor in the plowing per cycle – you can’t add it later. Ignoring the value of plowing is the way that most people end up planting inefficient crops, because they end up ignoring the # of cycles per day.

      Look at the number of comments from people who challenge why you’d plant Raspberries, which give zero experience. The reason is that you have a 2 hour crop that actually gives you 1XP per cycle, when you include plowing.

      Adam

  7. Pingback: The Personal Economics of Farmville, Part 2 « Psychohistory

  8. Pingback: Farmville Economics: What Price Experience? « Psychohistory

  9. I am running some stats now, but what is really interesting is figuring in our responce time. Given that we have to sleep sometime, and that we have lives outside the farm. All I can say is that Grapes are King the longer you stay away from the computer. I will send you the data if you like.

  10. Pingback: Farmville Economics: Cranberries, Pattypan Squash, Acorn Squash « Psychohistory

  11. Hi Adam,
    Just as the industrial revolution caused great upheaval in the labor market of the time, so does the arrival of fully automated Farmvile “bots” change the yield analysis of crops and animals.
    Steps that were too labor intensive to consider before (like your plow/delete exchange of coins for experience) can now be fully automated making them available at zero cost. Other operations, such as turbo charging chicken coops, further introduce new market dynamics. Even though it feels like Farmville has run its course for the gamer, there is plenty interesting food for thought for a post-industrialization analysis don’t you think?

    LotM

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s