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

Here are the quick links to my first four posts:

• The Personal Economics of Farmville
• The Personal Economics of Farmville, Part 2
• More Farmville Economics
• Farmville Economics: What Price Experience?

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:

• Farmville Economics: Sweet Seeds are *Almost* Genius
• Farmville Economics: Flowers & Updated Tables
• Farmville Economics: Cranberries, Pattypan Squash, Acorn Squash