I usually farm for food almost exclusively, so I was really curious how much benefit the potash could really provide to farms. There wasn't sufficient info around, so I experimented a little. Feel free to look at my results, though they might be spoily. Feel free to compare notes or add to my thoughts. I have a couple of images too, but they're not too interesting. Maybe I'll host them later.
It does require a little micromanagement, but it is a lot less than what's involved with a full-scale magma forging operation, so don't let that pull you away from fertilizing. The main cost to be concerned over is the toll fertilizing takes on your wood supply. It used to be frustrating how growers would only slowly gain skill, but not when fertilization is occurring.
Here's my setup: (high forest map needed)
1 battle axe
1 pick
100 plump helmet spawn
misc food
2 dogs (dunno why really, instinct?)
4 proficient growers
1 proficient miner, proficient cook, and proficient potash maker
1 proficient woodcutter
1 proficient wood burner
The wood burner could use cooking instead of the miner, now that I know more about the skills, but it doesn't really matter. Mason, mechanic, carpenter, etc. can be done without wasting 5 points making a novice out of them.
The idea was to mine minimally and get water from the outside river. I knew how to save the miner even when a channel connecting was being built--make it 10 squares long and suspend and unsuspend it until the construction spot is far away. For consistency in my measurements, I always used a single 6x10 farm plot.
I read somewhere that fields should be created with 15 squares or of a multiple of 15. I'm inclined to think that they're right, though I didn't bother experimenting too much to find out exactly how "ft (0/#)" fertilization points are assigned.
I also didn't experiment with values of fertilization under the maximum or with growers of less than proficient skill, mostly because it wasn't interesting to me. I now plan to go back and find out how quickly skill in growing increases for a peasant or otherwise unskilled grower.
After a brief test with potash making, I decided that the skill itself only increases the speed of production, much like wood burning, digging channels, or cutting trees. There was precious little difference, if any, when someone other than my professional potash maker made the sweet stuff.
I didn't get things set up quite in time for year one: spring, but nonetheless, I had more than 1000 helmets by the end of year one. This isn't really impressive, I think, these statistics are difficult to compare with normal games. Plus, since I had so much extra food, I didn't want to bother making barrels for them all to keep them from rotting. Since the game is just for testing, I brewed them into wine and cooked that.
Fertilization, for some reason, greatly increases the speed that the growing skill was trained at for my four proficient growers. Increased skill was the main benefit--my growers were all legendary by the end of year 3. When I noticed that some dwarves were becoming novice growers when they were aiding in harvesting, I changed options to "only farmers harvest". Only farmers with the "farming(fields)" job harvested from then on.
I'm pretty sure that the skill gained from harvesting crops is dependent on the number of crops harvested. For example, with regular proficient growers, I tended to get maybe 1 to 4 units of plump helmet at each square from a single seed. When the ft points were increased up to 16, the crops produced from each square/seed jumped up to 2 to 7 units. More on this increase in yield in a second.
I also think that the act of fertilizing the field itself trained the growers' skill. Sticking potash in the field used the same skill as planting, meaning that it would be a pain to split up farming between fertilization and planting to train new growers with the fertilizer, and the manager does not allow specifying the workers for a particular field. As far as I can tell, the "ber" guild representative doesn't give any bonuses to my actual farming ability.
Back to increase in growth. I have a theory, completely unprovable of course, that there's a "base yield" of farming that's something like 0-2. I think that skill in growing adds a flat number to both the minimum and maximum value of this base, as a proficient grower always seems to give at least one plump helmet spawn regardless of other conditions. My legendary growers can also increase yield up to 6 without fertilizer. I think that fertilizer multiplies the base yield by a percentage from 100% at 0 ft to 200% at ft max (ft 16/16 in my case). This is because I have yet to see a single square/seed produce more than 9 helmets, even with fertilizer and legendary skill.
This also means that once growers reach legendary skill level, fertilizer is of less use than before. Fertilization only seems to give 1-2 extra plants per seed/square, which isn't too much when I'm already producing 2-7. They certainly plant those things very quickly (a second per seed) and there's seeds to spare for an extra farm or two to make up for any loss in production. The loss of wood just isn't worth it, especially because I have increased carpentry and smithing needs now (yikes!).
The most controversial benefit I've had is population growth. With more than 3000 units of food, maybe 1000 of which is a lavish meal, all at any given time, the worth of my fortress is immense (can't see it yet sorry). In my 3rd year I have 70 dwarves. All of them except 5 nobles are bunking in a tiny 3x3 barracks. The roasted wine is exceptional, however, and tends to keep my population very happy. Thieves seem to show up every month, though.
Now some simple math. My farm had 60 squares, and each square always produced 4-9 helmets with legendary growers and fertilizer. that's an average of 6.5 per square, or 390 helmets for 60 seeds. Not all that impressive, again, because nobody wants to have that many useless plants lying around.
These numbers are all really too big: with a farm half the size, two legendary growers, some quarry bushes and other useful plants, some other fun sources of food (tamed elephants anyone?) and 16 units of wood a year, a 200 population dwarf fortress could be sustained easily. Of course, four proficient growers could do just as well with more farms and no fertilizer, but those 70 extra points could easily be worked off with five years of micromanaging the fertilizer out and keeping population relatively low, for an interesting game IMHO.
Okay, that was a lot. I've run out of things to talk about. Maybe more useless stuff later.
Conclusion: Potash is required to train growing and otherwise of limited use. It can foster extreme population growth, however, if a player is capable of handling it.