One trend I notice in players is a tendency not to make extra mills for their farms after their town centres and initial mills have been depleted. The result is that farms end up being displaced into secondary (and sometimes tertiary) layers, which greatly increases the average pathlength per journey. Without wheelbarrow, secondary layers sacrifice 20% efficiency and tertiary layers lose 33% of their efficiency. With wheelbarrow, secondary layers lose 17% and tertiary layers 28%. Putting up mills for extra farms saves on wood needed for food-intensive economies and for a mill accommodating 8 farms, the investment of 100 wood generally breaks even after around 3 minutes or so. The gains to be derived from an extra mill suggest that deer luring is redundant on open maps, as a close by mill can be reused for farms later in the feudal age, though this is merely an afterthought.
Quantifying the gather rate of farmers is somewhat difficult because villagers move around on the farm so much. On top of that, the average gather rate of a farmer depends not only upon the distance between the farm and the town centre, but also upon the angle at which the farm is placed relative to a line passing through the town centre. Farmers only move around in the 4 tiles on the left of farm, so farms to the right of the town centre yield the highest time-averaged gather rate while farms on the left provide the lowest returns, since the latter works in a space that is not directly adjacent to the town centre. Taking the origin to be a line starting at the town centre and moving out to the right, the average gather rate increases with the farm's angle to this line until it reaches the left hand side, then decreases again. This makes determining the depletion rate of a farm's food very difficult to determine.
Fortunately, there is a very easy way around this, and that is to check the Genie Editor, which tells us that farmers gather food at a rate of 0.53 per second. However, this on its own is of very little use to us in any practical calculations. In order to understand the average gathering of food on farms, we also need to know how far the farmer walks on a farming trip. Unfortunately, this varies not only with the farms position, but also with time. Thankfully, the journey to and from the farm space and the path taken while farming are largely independent. The best we can do is find an average pathlength for the villager's wandering through the farming space, then we can add the distance to the nearest drop-off point and use the resulting number to calculate an average gather rate at a new distance.
First, we need the average pathlength of a villager walking around a farm placed directly adjacent to a town centre. Suppose we knew this pathlength, and we call it l; then if a villager has a gathering rate r, speed v and gathering capacity c, then the villager gathers c resources in a time
t=c/r+l/v
Dividing c by this expression gives an average gather rate
a=1/((1/r)+(l/cv))
Substituting r=0.53 food per second, c=10 food and v=0.8 tiles per second gives
a=1/(1.89+l/8)
Or
l=8/a-15.09
If we know a, then l follows. We determine a experimentally, as it is a function of observable data. To avoid bias, we place 8 farms around a town centre and take the average of their gather rates. I found in the scenario editor that a=0.33 or so. Inserting this above gives l=9 tiles or so.
Now we examine the efficiency of secondary and tertiary farms. A secondary farm will be 3 extra tiles from the nearest drop-off point, so this means we add 6 tiles to the path length (because it's 3 extra tiles there and 3 extra back again). Using l=15 gives a=0.27, which is a reduction of around 20% efficiency. Going one worse and having a third layer of farms gives l=21 and a=0.22, which is a reduction of 33%. If we decide to research wheelbarrow, then the formula becomes
a=1/(1.89+l/11.44)
The first layer of farms gives a=0.37, the second layer 0.31 (17% less efficient) and the third layer 0.27 (28% less efficient). In fact, one could go one step further and seed a T90 farm. In this case, our value of l will be exhorbitantly high, possibly equivalent to a fifth-layer farm (though note that this is a cautious estimate). With wheelbarrow, we get a=0.21 for a reduction in efficiency of 44%, and without wheelbarrow, we get a=0.17 for a whopping reduction of 50%. At that stage, you'd be better off milling the shorefish in a random oasis on desert Arabia and hoping that there are no wolves nearby.
The cost of 100 wood for a mill does reduce the efficiency of only having first layer farms. It is still worth putting up an extra mill for the very simple reason that it gets rid of the need to spend wood on extra farms. This speeds up gathering food to advance to the castle and imperial ages and makes booming easier. To avoid taking on more complicated calculations, note simply that every trip on a second layer farm takes around 7 extra seconds. In this time, you could have gathered 2-2.5 resources. 40-50 such trips would waste the same amount of resources needed to build a mill. An extra mill surrounded by 8 farms will pay itself back in 6 trips or so, which happens in around 3 minutes.
Finally, the use of extra mills for farms leads to an interesting paradox; that of luring deer on open maps. If deer are close by, they are easy to lure. On the other hand, milling them is a useful investment because you will be able to place farms around it later. On the other hand, far away deer that cannot be lured without sacrificing a lot of map visibility need to be milled to be worth it, yet the mill cannot be reused. This suggests that more economical builds on open maps should mill deer regardless of context and that deer luring should be reserved for fast castle maps, such as arena. However, this is most likely a matter of what a player's needs are for a particular strategy and to a certain extent is a matter of taste, as well as how easily defended said farmland will be.
Quantifying the gather rate of farmers is somewhat difficult because villagers move around on the farm so much. On top of that, the average gather rate of a farmer depends not only upon the distance between the farm and the town centre, but also upon the angle at which the farm is placed relative to a line passing through the town centre. Farmers only move around in the 4 tiles on the left of farm, so farms to the right of the town centre yield the highest time-averaged gather rate while farms on the left provide the lowest returns, since the latter works in a space that is not directly adjacent to the town centre. Taking the origin to be a line starting at the town centre and moving out to the right, the average gather rate increases with the farm's angle to this line until it reaches the left hand side, then decreases again. This makes determining the depletion rate of a farm's food very difficult to determine.
Fortunately, there is a very easy way around this, and that is to check the Genie Editor, which tells us that farmers gather food at a rate of 0.53 per second. However, this on its own is of very little use to us in any practical calculations. In order to understand the average gathering of food on farms, we also need to know how far the farmer walks on a farming trip. Unfortunately, this varies not only with the farms position, but also with time. Thankfully, the journey to and from the farm space and the path taken while farming are largely independent. The best we can do is find an average pathlength for the villager's wandering through the farming space, then we can add the distance to the nearest drop-off point and use the resulting number to calculate an average gather rate at a new distance.
First, we need the average pathlength of a villager walking around a farm placed directly adjacent to a town centre. Suppose we knew this pathlength, and we call it l; then if a villager has a gathering rate r, speed v and gathering capacity c, then the villager gathers c resources in a time
t=c/r+l/v
Dividing c by this expression gives an average gather rate
a=1/((1/r)+(l/cv))
Substituting r=0.53 food per second, c=10 food and v=0.8 tiles per second gives
a=1/(1.89+l/8)
Or
l=8/a-15.09
If we know a, then l follows. We determine a experimentally, as it is a function of observable data. To avoid bias, we place 8 farms around a town centre and take the average of their gather rates. I found in the scenario editor that a=0.33 or so. Inserting this above gives l=9 tiles or so.
Now we examine the efficiency of secondary and tertiary farms. A secondary farm will be 3 extra tiles from the nearest drop-off point, so this means we add 6 tiles to the path length (because it's 3 extra tiles there and 3 extra back again). Using l=15 gives a=0.27, which is a reduction of around 20% efficiency. Going one worse and having a third layer of farms gives l=21 and a=0.22, which is a reduction of 33%. If we decide to research wheelbarrow, then the formula becomes
a=1/(1.89+l/11.44)
The first layer of farms gives a=0.37, the second layer 0.31 (17% less efficient) and the third layer 0.27 (28% less efficient). In fact, one could go one step further and seed a T90 farm. In this case, our value of l will be exhorbitantly high, possibly equivalent to a fifth-layer farm (though note that this is a cautious estimate). With wheelbarrow, we get a=0.21 for a reduction in efficiency of 44%, and without wheelbarrow, we get a=0.17 for a whopping reduction of 50%. At that stage, you'd be better off milling the shorefish in a random oasis on desert Arabia and hoping that there are no wolves nearby.
The cost of 100 wood for a mill does reduce the efficiency of only having first layer farms. It is still worth putting up an extra mill for the very simple reason that it gets rid of the need to spend wood on extra farms. This speeds up gathering food to advance to the castle and imperial ages and makes booming easier. To avoid taking on more complicated calculations, note simply that every trip on a second layer farm takes around 7 extra seconds. In this time, you could have gathered 2-2.5 resources. 40-50 such trips would waste the same amount of resources needed to build a mill. An extra mill surrounded by 8 farms will pay itself back in 6 trips or so, which happens in around 3 minutes.
Finally, the use of extra mills for farms leads to an interesting paradox; that of luring deer on open maps. If deer are close by, they are easy to lure. On the other hand, milling them is a useful investment because you will be able to place farms around it later. On the other hand, far away deer that cannot be lured without sacrificing a lot of map visibility need to be milled to be worth it, yet the mill cannot be reused. This suggests that more economical builds on open maps should mill deer regardless of context and that deer luring should be reserved for fast castle maps, such as arena. However, this is most likely a matter of what a player's needs are for a particular strategy and to a certain extent is a matter of taste, as well as how easily defended said farmland will be.