Hey NW,

To paraphrase another post that had been made here -- "DARN YOU! DARN YOU TO HECK, NERO WOULD!"

I was planning on trying to do this as well and posting it, primarily to figure out whether has planted enough barley or flax farms to support breweries/weavers. According to Nerdicus's exhaustive survey (For which major kudos should be awarded.) a brewery/weaver can produce .03 goods per day, which translates into .47 per month (Due to a wasted fraction upon completion) or approximately 5.65 per year. So each brewer/weaver consumes 565 units of barley/flax per year as inputs.

Thus an optimal floodplain farm (appx 80% fertile with nearby work camp according to your measurements) will supply inputs for (roughly speaking) 1.4 workshops -- a ratio of five 'efficient' fields for seven workshops is optimal.

Of course this requires a reasonably good inundation in order for the floodplain farm to operate at peak efficiency. For this reason, I usually try to use meadows for barley when growing it for bear, and leave the floodplains for food crops -- I find it easier to deal with the vagaries of the flood in food storage rather than input storage. Given that meadow farms produce 6.08 barley per 'efficiency percentage,' one needs a combination of meadow fields with about 92% efficiency in order to supply one brewery -- one would probably do just as well to substitute 100% as a fudge factor. So 2 46% fertility fields will keep one brewery in operation -- assuming, of course, adequate placement of storage yards, etc.

Happy that I now have a 'rule' in my head that I can use when placing things at the outset, rather than just attempting to make adjustments on the fly. Thanks for all your bean counting, NW and Nerdicus.

Gunthebath

[This message has been edited by Gunthebath (edited 01-15-2000).]

Nero Would,
Absolutely the finest job of uncovering the underlying formulas for farming! I must say that I was going to be looking at this very soon (I had not quite started), but hey! first to publish... One real nice thing I noticed from your data was that you can actually get more grain, barley and pomegranates out of a high fertility meadow farm than you can from a floodplain one. Cool! I have checked your calculations and with a one extremely minor glitch I think you have absolutely nailed it on the head. To take the sting out I included a little gift at the end of this message.

The one glitch is that I think your round to nearest 0.05% is not quite right. I was testing your algorithm against a group of 6 barley farms I had siting around in North Dahshur and one was not quite coming out correctly. Specifically, it was a meadow barley farm with a fertility of 43%. Using your formula I calculated the daily production to be 43/(16*800) = 0.3359% which should then round to 0.35%. The meadow farm I measured was actually using a daily production of 0.30%. The other 5 meadow farms (69%, 72%, 83%, 86% and 89%) all were exactly correct using your algorithm.

I did a bit of playing with the rounding and could only get a fit for all six of these farms with the following equation:
Daily Production% = ( Floor(((2000 * Fertility%) + 32) / (16*8) )) / 2000
The Floor function, multiply by 2000 and divide by 2000 all just implement the round to 0.05%. In case you are not familiar with it, the Floor function in C just rounds down to the nearest integer. The add of 32 effectively adds the equivalent of 0.25% to your equation before rounding down to the nearest 0.05%. Why this works is beyond me, but it fits my farm data. The 0.25% has a possible error of +/- 0.0312% (plus or minus 3 in my equation) and the 0.25% is exactly centered in this range.

Also after playing with your algorithm for a bit, I noticed that the rounding causes some farms that are close in fertility to come out with exactly the same daily production and final yields. Since there are only 16 unique ranges it seemed the perfect way to organize a table of yields (not too big) for farming. Again I "equationized" your algorithm for calculating the yield and got the following:
Farm Yield = smaller of 800 or (8 * Floor(1600 * Daily Production% * Months of Growing))

Finally (surprise!) I took all of this data and made up a spiffy table to use instead of having to calculate the values everytime you need to know what your farms are going to yield. Hope this helps everyone to use Nero Would's great work. See what happens when you give a nerd a new toy?. The table is as accurate as I could make it, but if anyone gets different results with fully staffed meadow farms please send a message. I suspect just like with manufacturing the yield will drop off for partially staffed farms (I have no data on this, I just assume). Well, here goes:
-Nerdicus

[I have removed the table that was here because of errors. A new updated (and correct) table has been included in a following post. ]

[E1:2000Jan15 Messed up the farm product columns, silly]
[E2:2000Jan16 Combined Chickpea and Lettuce columns, added Flax]
[E3:2000Jan18 Removed old incorrect table.]

[This message has been edited by Nerdicus (edited 01-18-2000).]

Gunthebath: Sorry I beat you, but as you can see, Nerdicus was on my tail. I spotted the Devourer of Souls lurking around my kitchen this morning, did you send him? (obscure paraphrase).

Nerdicus: Thanks for spotting the rounding quirk, good work. I can't think of a reason for it, maybe it's an accidental result of some data type conversion. And GREAT work on the table, it's much easier to use than what I came up with.

If this keeps up, we're going to need a speed challenge like Dragon2. Maybe "who can document the prosperity rules the fastest". Actually, that's not such a good idea, the prosperity rules are complex and a cooperative effort would be better.

Oops! I just noticed I left Flax Farms out of my list of meadow farms with one harvest a year (it's in December). I'll go back and edit the original post to add it.

Nerdicus: do you have room in your table to squeeze another column in for them? If not, maybe chickpeas and lettuce can share a column since they are both April harvests.

Nero Would,
I put the chickpea and lettuce (salad farms?) together and added Flax to the end. I just edited it in place for now.

By the way, does this table correspond to your data? I noticed that some of the examples you gave in your original post are not the same as the entries in the table. I was just wondering cuz I only looked at the 6 barley farms in my North Dahshur. Everything else I uhh.. extrapolated (he says in a worried voice).

Hehe. Yeah it does seem that we have been racing to "publish" our findings recently. I have just recently had 3 impacted wisdom teeth removed and doing this kind of puzzle solving stuff actually keeps my mind off the pain. Umm, there's really not much pain, the nice doctor gave me some GREAT pills.

Hey Nerdicus, Nero Would, et al.,

In my own rush to publish a very minor deduction based on the excellent empirical work of N and NW, I made a pretty serious error -- barley meadow farms have two growing seasons. So an aggregate fertility of .46 meadow farms (I'll call this .46 fertility units.) is necessary to supply one brewer. Flax meadow farms require .92 'fertility units,' with the qualification that because the maximum yield is 800, a meadow can't be worth (much) more than .68 fertility units for flax. Because of the rounding procedure, these figures have to be used with some caution -- a small fudge factor.

To Nero Would: Sorry about the 'D.o.S.' But you know the saying: 'Publish or Perish' -- I figured with you out of the way, I'd have a better chance to survive myself!

Gunthebath

[This message has been edited by Gunthebath (edited 01-17-2000).]

Nerdicus: I hadn't checked the numbers in your table against my result until just now. It looks like we're still not quite in synch on the rounding formula. I have a couple of data points that are correctly predicted by my version and not by yours. Here are the data points I know about:

Daily Prod . Fertil(Nero) . Fertil(Nerdicus)
0.05% .. . . . . . 9
0.25% . . . . . . 31
0.30% . . . . . . . . . . . . . . 43
0.55% . . . . . . . . . . . . . . 69/72
0.60% . . . . . . 75
0.65% . . . . . . 83/84 . . . . . 83/86
0.70% . . . . . . . . . . . . . . 89
0.75% . . . . . . 94/97

My version of the formula doesn't predict your 0.30% per day for 43% fertility, and your version doesn't predict my 0.60% per day for 75% fertility or my 0.75% per day for 94% fertility. I haven't been able to come up with a formula that fits all the data points. I'll try double-checking my experimental results, perhaps you could recheck your 43% result. It's frustrating, we're only off by a tiny fraction, but I would like to be able to make it exact.

[This message has been edited by Nero Would (edited 01-17-2000).]

Nero Would,

Yeah I just checked to make sure but the 43% fertility barley farm did produce 224 barley and the partial sequence I did on its production was as follows (may as well post all of my farm data):

43=04,04,04,05,05,05,06,06,06,06,07,07,07,08,08,08,09,09,09,09,10,10,10,11,...28%=224 barley
69=07,08,08,09,09,10,11,11,12,12,13,13,14,14,15,15,16,17,17,18,18,19,19,20,...52%=416 barley ( same data for 72%)
83=09,09,10,11,11,12,13,13,14,14,15,16,16,17,18,18,19,20,20,21,22,22,23,24,...62%=496 barley ( same data for 86%)
89=09,10,11,11,12,13,14,14,15,16,16,17,18,18,19,20,21,21,22,23,23,24,25,25,...67%=536 barley

Like I said the only fit I could find using an analog to your equation was the one with the weird rounding. I will spend some time looking at the edge cases and see if I can come up with something that fits all of the cases, sigh. There may be some other rounding effects that we have not taken into consideration (having to do with how the %done is stored for each farm).

Well, back to work.
-Nerdicus

I have also been looking at how the game determines the fertility of a particular piece of land that the farm is sitting on.The theory I have come up with is pretty simple but seems to work:
Calculation of Farm Fertility:
Each meadow/floodplain square of land in the game has a fertility of from 0% to 10% in 1% increments. The fertility of the farm is calculated by adding the 9 squares' fertility together. The minimum fertility of a farm is 2%, and the maximum fertility is 99%. A meadow farm can be placed on a group of 9 non-meadow squares as long as one edge of the farm touches a meadow square. The fertility of this "edge" farm is the minimum 2%. As reported elsewhere irrigation increases the fertility of a meadow farm by 40% and a floodplain farm by 20%. Note that in the case of a floodplain square, the underlying squares are depleated when the farm is harvested, and they are replenished depending on the size of the inundation that year.

Seems obvious but it took a bit of work to confirm. It is nice that with irrigation, even the most worthless farm can produce a respectable amount. This might even be a good point to base a map design on. ie Several widely scattered 1% squares are the only local food source. Kind of a desert farming challenge.

[This message has been edited by Nerdicus (edited 01-17-2000).]

------------------
Homage to thee, Osiris, Lord of Eternity, King of the Gods, whose names are manifold, whose forms are holy, thou being of hidden form in the temples, whose Ka is holy."
-- Book of the Dead (1240 BC)

Nerdicus: I think you have the fertility rate calculation pretty much sorted out. I have a couple of tweaks to suggest.

I didn't think of doing this until I read your post, but I looked at the .map file for the Sandbox mission (I have an early version of the source code for the unofficial map editor to help with the file format). As you say, there is a fertility number for each square, but the numbers I have seen range from a low of 6 to a high of 99. I found the location of the farms I used when measuring production rates, and it seems that the fertility of the farm is the average fertility of the 9 squares (rounded down to a whole number) plus 2. I haven't checked farms on very high fertility squares, but I presume that fertility is limited to 100 or 99 (probably 99).

For example, the squares under one farm had fertility of 8,0,8,33,41,33,57,57,66=303
The fertility of the farm was Int(303/9)+2=35

[This message has been edited by Nero Would (edited 01-18-2000).]

Nero Would,
Well, I have spent much more time than I should have, but I think I have a correct table now. I did it by pure brute force and have sequenced more farms that I ever thought I would have to. With the exceptions of farms with fertility 19%, 30% and 80% I have confirmed all of the edge conditions of the table. I used four different maps with irritation on and off, and then I still had to build a special farm test world in sandbox to pick up the spares.

The final equation for daily gain I came up with was:
Daily Gain% = 0.05% * Floor( Fertility% * 500 / 31 )
with the caveat that a fertility less than 7% gives a daily gain of 0.05% and a 99% fertility gives a daily gain of 0.80%. I built this equation from the edges rather than trying to predict it, so there was no inspiration in this just perspiration.

For the record these are the farm sequences I have data on if you want them for something:

0.05% = 02%,04%,05%,06%,12%
0.10% = 13%,16%,17%,18%
0.15% = 20%,21%,23%,24%
0.20% = 25%,26%,29%
0.25% = 32%,35%,37%
0.30% = 38%,43%
0.35% = 44%,46%,48%,49%
0.40% = 50%,55%
0.45% = 56%,57%,61%
0.50% = 62%,63%,65%,68%
0.55% = 69%,71%,72%,74%
0.60% = 76%,78%
0.65% = 81%,83%,85%,86%
0.70% = 87%,89%,91%,92%
0.75% = 93%,98%
0.80% = 99%

By the way, for floodplain farms I have seen 9 and 9.5 months sometimes for the growing period of these farms (ie not inundated). I assume from your messages that you have seen 10 months? I put the full range on the table and put chickpeas and lettuce in separate columns.

Given the twists in the daily gain calculation I suspect that the game actually just uses a table to get the daily gain. Ill put the new game mechanics notes I have in the post with the table.
-Nerdicus

This post is intended as a compendium of current knowledge on farming that has been collected by me (Nerdicus) and Nero Would, with the help of information from Grumpus the Elder and others. I have updated the farming yield table to fix some earlier errors and I have included some other new information on farming. I will be removing the old farming table from the previous post in this thread to avoid future confusion.

Farming Fact #1: Minimum farm fertility is 2% and maximum fertility is 99%
The fertility of a farm is calculated as the average fertility of the 9 squares under the farm plus 2%. If a farm has no meadow squares underneath but is placed with a meadow square touching one edge of the farm, the fertility of that farm will be 2%.

Farming Fact #2: Irrigation increases the fertility of a meadow farm by 40% and a floodplain farm by 20%.
An irrigation ditch must be within at least 2 squares of any square of a farm, and the increase will not push the fertility of the farm over the maximum of 99%. Irrigation to floodplain farms does not require a water lift, just start a ditch connected to the river.

Farming Fact #3: Each farm type is harvested during day #2 of its harvest month.
Each type of farm has a different harvest month and in the case of meadow grain, meadow barley, and meadow pomegranates are harvested twice a year. The harvest month of a floodplain farm is determined by the location of the city on the world map. Typically a city that is far south will have an earlier harvest month (because the inundation comes earlier). All farms send the harvest to the city on the second day of the month. See the table below for the specific harvest months of the various farm types.

Farming Fact #4: The yield of a farm is 800 * its production % complete.
The yield of a farm on harvest day is its production % complete rounded down to the nearest 1% multiplied by 800. An equivalent equation would be = Min( 800, (8 * Floor(Production Complete% * 100))). The function Floor() rounds down to the nearest integer. The function Min() selects the smallest value from a comma delimited list. The blessing of Osiris will double the yield of floodplain farms up to a maximum of 1600. A grain farm (both floodplain and meadow) will produce 100 straw no matter how small a harvest from the farm.

Farming Fact #5: Each 1/16th of a month a "Daily Gain" is added to a farm's production.
The current production % complete rounded down to the nearest 1% is displayed in the farms information window (right click on farm). Each day (1/16 of a month) the daily gain is added to the production % complete. The daily gain for a farm is calculated as = 0.05% * Max(1, Floor(Fertility% * 103.5 * 20 / 128)). The Max() function selects the largest value from a list and in this case enforces a minimum daily gain of 0.05% regardless of the farm's fertility. Nero Would noticed that this equation is equivalent to a basic farm production rate of 103.5 units per month for an ideal (and impossible) 100% fertility farm.

Farming Fact #6: A shortfall of farm employees affects meadow farm yield.
Like production buildings, a lack of staff causes the farm to yield correspondingly less product. While I have not calculated the exact shortfall I suspect the daily gain is multiplied by the current number of employees/10 (fully staffed meadow farm uses 10 employees). The above would be equivalent to the effects of employee shortfall on production buildings.

Farming Fact #7: A meadow farm will continue growing even if the cart pusher does not return for harvest.
This is especially interesting for the biannual meadow farms. A meadow farm will continue growing up to 100% complete even if its cart pusher does not make it back for the next harvest. I typically have the barley meadow farms deliver their goods directly to the breweries. If I am overproducing barley, sometimes a cart pusher will not be able to deliver the barley and then return to the farm. Once he does return, the meadow farm will wait until the next harvest month before sending the cart pusher out with two harvests worth of product (up to the maximum of 800 units). For lower fertility meadow farms this means you can treat a biannual farm just like it was an annual farms for calculations like maximum distance to deliver goods.

The Farm Production Yield Table
I have designed this table to (hopefully) make calculating the expected yield of a farm easier. To use the table, just find the row with the farm's fertility and then move over to the column that describes the type of farm. The value at this location is the exact amount of product that you should expect when the farm is harvested. This value is the maximum and will only be reached when the farm has had a full staff for the entire season and started growing at the beginning of this growing season. Note that the biannual farms have two growing seasons per year and for some farm types the seasons are of different lengths. I would like to hear from anyone who has comments or has detected errors in the following. Im not great at color schemes or layout so comments on that are free game too.
-Nerdicus

Farm Production Yields

Fertility	Daily Gain	Floodplain		Biannual Meadow Farms						Annual Meadow Farms
Farm Product->		All Farms		Grain		Barley		Pomegranate		Chickpea Lettuce		Fig	Flax
Harvest Day2->		Summer		Jan	May	Feb	Aug	Jun	Nov	Apr		Sep	Dec
Grow Months->		9 to 10		8	4	6	6	7	5	12
02%-12%	0.05%	56	64	48	24	32	32	40	32	72
13%-18%	0.10%	112	128	96	48	72	72	88	64	152
19%-24%	0.15%	168	192	152	72	112	112	128	96	224
25%-30%	0.20%	224	256	200	96	152	152	176	128	304
31%-37%	0.25%	288	320	256	128	192	192	224	160	384
38%-43%	0.30%	344	384	304	152	224	224	264	192	456
44%-49%	0.35%	400	448	352	176	264	264	312	224	536
50%-55%	0.40%	456	512	408	200	304	304	352	256	608
56%-61%	0.45%	512	576	456	224	344	344	400	288	688
62%-68%	0.50%	576	640	512	256	384	384	448	320	768
69%-74%	0.55%	632	704	560	280	416	416	488	352	800
75%-80%	0.60%	688	768	608	304	456	456	536	384	800
81%-86%	0.65%	744	800	664	328	496	496	576	416	800
87%-92%	0.70%	800	800	712	352	536	536	624	448	800
93%-98%	0.75%	800	800	768	384	576	576	672	480	800
99%	0.80%	800	800	800	408	608	608	712	512	800
Farm Production Yield Table, Version 1.21 - Last updated 2000Jan19 Original formulas for farming production discovered by Nero Would. This table's design and any errors care of Nerdicus.
The following two equations are used to calculate this table's values. The function Floor() rounds down to the nearest integer. The function Min() selects the smallest value from a list, while Max() selects the largest. Daily Gain% = 0.05% * Max( 1, Floor(Fertility% * 103.5 * 20 / 128)) Farm Yield = Min(800, (8 * Floor(Daily Gain% * 100 * 16 * Months)) )

[E1:2000Jan18 - Added comment on 100 straw.]
[E2:2000Jan19 - Updated fertility calc; Changed to Nero Would's daily gain equation ]

[This message has been edited by Nerdicus (edited 01-19-2000).]

More great work Nerdicus. You must be sick of looking at farms by now. I have a few small points to add.

In fact #2, I believe fertility is the average of the nine squares plus 2% (with a maximum of 99%). This shouldn't really matter except to map designers.

I came up with a version on the daily production formula that avoids the need to create an exception for 99% fertility.
Daily Gain = 0.05% * Max(1, Floor(Fertility% * 103.5*20/(16*8))
This is the equivalent of a nominal monthly rate of 103.5 units with the daily gain being rounded down to a multiple of 0.05% (the Max function implements the minimum daily gain of 0.05%). This version of the formula produces the same numbers as your chart for every fertility level.

As far as the 10 month growing season is concerned, I can't confirm that it ever happens. In my original post I said that it should be possible to max out floodplain farms with approximately 80% fertility, but I never followed up to find the exact number.

Thanks again for your help.

Nero Would,
Yeah, if I dont see another farm for a few days I will be much happier.

I have updated the table and text to use your equation for daily gain. Nice, I much prefer the equations to have something to do with the data under observation. Linking it to your original analysis' assumptions works well.

hi everyone

i'd like to know if there is any updated data about henna farm production? regarding Meadow Farms, is it a biannual or annual crop? and its harvest month?

thanx

Wow how do you go about finding this info. Or is it a state secret.

Hi Pajeh Southwind. According to my notes, henna meadow farms harvest once a year in December. So the production data should be the same as for flax. I don't have Cleopatra installed at teh moment, so I can't double check that.

No state secrets involved here Czech Centurian, just some experimentation.

[This message has been edited by Nero Would (edited 10-31-2004 @ 06:35 AM).]

I refresh this one as an example to newcomers of the richness of information that can be found here. And the richness of the game itself.

Resently, I was trying to calculate to the expected yield of my flooded farms. The above table shows an expected yield given a farms is attenden by worker for 9 or 10 months. For me this is a rare case: work camps can be far away from the farms or they are too few.

Is there a method to calculate, how fast the work on the farm will beginn after flood?
How fast do workers from work camps move and how fast they generate workers?
Also, how do workers from different work camps choose to what farm they will go? Especially as the might be workcamps near the fields and distand workcamps near he monument.

How many farms per workcamp is a good number, assuming the worker pool is not to abudant?

Quoted from GUdrusltd:

flooded farms. The above table shows an expected yield given a farms is attenden by worker for 9 or 10 months

I don't think a growing season of 10 months is possible. 9 may be possible, if the city has a short flood and if there are lots of work camps in an efficient arrangement. I assume no more than an 8-month growing season, usually less.

Quoted from GUdrusltd:

Is there a method to calculate, how fast the work on the farm will beginn after flood?

Not exactly, since farms emerge from the flood gradually and you can't tell which work camp will send a laborer to each farm. But with a good arrangement, most farms will get a laborer from a nearby work camp. In general, the effect of a bad flood will be considerably worse than having a few farms get laborers from a significant distance.

In you are interested in a lot of detail, see Trium's Invisible random walkers (and work camp laborers) and Floodplain and Monument Laborers (Making Work Camps Tick).

Quoted from GUdrusltd:

How fast do workers from work camps move

Laborers move at the same speed as most non-military walkers: 54.4 road tiles/month.

Quoted from GUdrusltd:

how fast they generate workers?

Ignoring monument constructiton, a work camp can generate 4 farm laborers per month. However, only 4 laborers from a work camp can be heading for farms at once, so if the farms are less than a month's journey away from the work camp then the work camp will generate 4 farm laborers per month.

With monument construction, it is much more complicated.

Quoted from GUdrusltd:

how do workers from different work camps choose to what farm they will go?

When a work camp generates a laborer, when he appears he decides where to go. If there is a farm that needs a laborer and doesn't already have a laborer heading to the farm, and the laborer has a road connection to the farm, and the farm isn't too far away (no more than 40 tiles "as the crow flies" to the N tile of the farm}, he will go to the closest such farm. If there isn't such a farm and there is monument construction to do, he will work on a monument. Otherwise, he will disappear.

Quoted from GUdrusltd:

the might be workcamps near the fields and distand workcamps near he monument

If there is no road connection from the work camps near the monument to the farms (or if the farms are too far away), laborers from those work camps will not go to the farms. However, laborers from work camps near farms may go to a distant monument.

Quoted from GUdrusltd:

How many farms per workcamp is a good number,

I have had from 2 farms per work camp (in Menat Khufu) to 11 farms per work camp (in Bubastis). 5 farms per work camp is a reasonable number.

[This message has been edited by Brugle (edited 06-22-2019 @ 02:14 PM).]

What is exactly the “40 tiles as the crow flies”? 40 tiles are easy to count if counting exactly North, East, etc. What if you go Northeast, Southwest, etc. Do you count the diagonal tiles the same way, or do you have to acount for longer actual distance?

In essence, do all farms that sit within a square of 80x80 tiles (workcamp exactly in the midle) get worker supply? Or only farms that sit within a circle (Radius 40 tiles, workcamp in the middle) get supplied?

Quoted from GUdrusltd:

What is exactly the “40 tiles as the crow flies”?

The calculations are fairly simple: 1 tile in any direction, along an axis or diagonally, is the same.

Quoted from GUdrusltd:

40 tiles are easy to count if counting exactly North, East, etc.

I think it is easier to count along an axis, going northeast, southeast, southwest, or northwest. North, east, south, or west is diagonal and seems to me to be harder to count.

Quoted from GUdrusltd:

do all farms that sit within a square of 80x80 tiles (workcamp exactly in the midle) get worker supply?

Actually, it is a square of 81x81.