Farming, and especially which crops to farm, is one of my favourite aspects of the game. It feels mostly historical, has substantial mechanical depths, and things depend on the situation enough that there is no simple “one is best” solution. Things to consider are (in rough order of importance):
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Output: No point growing crops that provide resources you won’t use or will spoil before you can use them.
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Seasonal dependency: No point growing a crop if it’s going to freeze / burn in the ground. In practice this means peas, turnips, and carrots need to go at one end of the farming year; while beans, buckwheat, and wheat need to go in the middle.
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Weeds: Having 1 crop maintenance per 3-year rotation is a simple, fast, and effective way of keeping weeds close to 0 no matter what the other crops are.
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Crop diseases: While diseases don’t currently spread between fields, they do randomly appear whenever you plant a crop. If a crop is planted when a disease is already present, the infestation strength will increase (or decrease if it was not susceptible to it). This means that you need to plant a minimum of 1 other crop between crops that are susceptible to the same disease (for some, like stem rot, having at least 1 gap of two in your rotation is better because the infestation decreases very slowly). Crop maintenance does not count as a gap, and neither does winter between the end of one year and the start of the next, and neither does planting nothing at all (although clover does count)
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Fertility: The negative fertility impact of plantings (and also crop deaths) have their full impact on every field, but the positive impacts are modified by the EFF (Environmental Fertility Factor). So with a 65% EFF, clover would only give +2 rather than +3. Besides crops and grazing animals, compost also gives +8 fertility (modified by EFF) each time it’s used, irrespective of field size.
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Soil Composition: Different crops prefer different soil types. This can be adjust easily for a small amount of clay or sand and only makes a +10% difference (unless you get it violently wrong) so it’s not very important, but it’s a nice extra bonus when you can have it.
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Work Distribution: Being able to use as few workers as possible for the same amount of farming is nice. This can be achieved with crop rotations that scatter when the “off” times are, such that farmers always have somewhere to work and you rarely need them all at the same time. Note that crops require work to plant and harvest, but not in the middle, and there’s a fair amount of leeway given.
For the rotations below I’m assuming an EFF of 75% or more, which is about as low as you need to use on every map except arid highlands, which is a completely different ball park. I’m also assuming that you’ve had 1 year of x3 maintenance to get rid of rocks and most weeds before starting these.
STARTER PACK
This is by far my favourite early game crop rotation. It’s hugely fertility positive and provides everything you need in the early game. It’s also easy to tailor to your exact needs on the fly. Need more fertility? Replace one of the peas with clover? Need to feed animals? Change the first year to maintenance → hay. Need more food urgently? Replace flax with cabbage. Need some grain? Replace the 2nd year with flax → buckwheat or peas → rye or peas → wheat. Need more food to pickle? Change that year to carrots → rye. If you’re not fussed about optimising farming or using lots of fertiliser, these variations can have you covered for the whole game.
GRASS & GRAIN
In the middle game, balancing fertility is less of an issue because your fields should be highish already (either from running Starter Pack for a while, or opening new fields on land where animals have been grazing), and compost is regular enough to make a real difference. At that stage, this rotation is a great way to complement the above. It’s also customisable depending on your fertility, replacing clover with peas and/or rye with wheat works well.
GREEN HAY
For the late game, this rotation (a variant of the above) provides a lot of food to be eaten in the short/medium term for both your villagers and your animals. 4 out of the 5 crops also like the same clay-heavy soil for extra performance. It does need to be composted every ~5 years to balance fertility. Sadly, getting villagers to actually eat their greens and beans can be tricky in vanilla, but I find the Balanced Diet mod really makes the eating priority and food delivery logistics make sense.
OMNI CARROT
To balance out the short term food provided by Green Hay, it’s good to have long term food for stockpiling. For crop fields this mostly means root veg for the preservist. We also need grain and flax for various production chains. This rotation provides copious amounts of all of this with 4 crops that all like the same sandy soil. The draw back is that it’s a heavy drain on fertility, needing composting every ~3 years, though this can be reduced if you let animals graze on it during the fallow year (I’m to forgetful to rotate my pasturing so regularly). No point focussing so heavily on carrots if you don’t have the preservist and glass supply to pickle them either. A less taxing variant is to replace one of the carrots with peas to makes this a very well rounded rotation.
The negative fertility requirements of those later two rotations might seem off putting, but they’re easy to handle. I was able to do so on a custom map (max 70% EFF, starting fertility ~40%) with a mod (Further Farming) which severely nerfs composting. I found that a ratio of 2 Omni Carrots per Green Hay, with some slight customisation when needed) works very well; this is what my fields look like around year 40.