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Freighters, as far as I'm aware, all follow the same basic design: cargo hull, trade module, and engines. But which engine configuration is optimal? If one makes some reasonable simplifying assumptions, the efficiency of a design can be calculated and compared to others. The goal is to identify the most lucrative set of engines given available technology, the distance to the target planet, the value of the trade route in bc per turn, and the turns required to build the design. Once we've done that I'll talk about general conclusions.
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First, we need to find a way to quantify the value of what a freighter offers. This is a bit tricky as trade routes pay a population-dependent dividend over many turns, and we can't see very far down that series of payments with much certainty. However, we don't have to. While the objective value of a trade route is difficult to calculate, the difference between two income streams is quite easy, as shown below.
A = 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + ...
B = 0 + 0 + 0 + 4 + 4 + 5 + 5 + 5 + ...
where the zeros in B are placeholders to represent turns B spends in transit. Subtracting B from A is simply (4 + 4 + 4) = 12, since all terms after the third are identical in the two series (they are independent of freighter design).
It would be convenient if at the end of this we have a formula that only needs the details of one ship design; however, as shown above the underlying math needs to be a difference between two designs. This next part is a little strange, but it simplifies the final math. We will compare ship designs under consideration to a hypothetical "perfect" ship, that is, a zero-cost freighter that arrived yesterday.
Let's get down to business. The difference (we'll call it Score) between a new design and the "perfect" ship is given by
Score = (income stream from perfect ship - income stream of new design) - (cost of perfect ship - cost of new design)
Score = (trade route bc per turn * turns for new design to arrive at planet) - (0 - cost of new design)
turns for new design to arrive at planet = build time + (distance to planet / speed of new design)
cost of new design = build cost + total upkeep cost = build cost + maintenance cost * (distance to planet / speed of new design)
Score = route value * (build time + (distance / speed)) + build cost + maintenance * (distance / speed)
where (distance / speed) must be rounded up. Note that the closer Score is to zero, the better the design; note also that this will only be useful for comparisons of freighter designs given a specific trade route distance and value. A Score calculated for Freighter A on Route 1 cannot be compared to a Score calculated for Freighter B on Route 2--it has to be the same route for the comparison to be meaningful.
Let's look at the value "build time." Do we use the integer value displayed on a planet or the decimal value of (build cost / military production)? Either will work, but they'll tell you slightly different things. If you use the integer, 200 cost and a 249 cost freighter will appear to have the same build time if you use 50 as the value for military production. This is accurate for a specific case. Using the decimal value, however, will reveal the general truth that the 249 cost freighter will actually cost about 25% more. We use the decimal value here so that our results are less sensitive to misleading changes in Score based on small changes in cost.
So, we can rewrite Score a little:
Score = route value * [ (build cost / military production) + (distance / speed) ] + build cost + maintenance * (distance / speed)
With (distance / speed) rounded up and (build cost / military production) left as a decimal. So, there's our final formula. What does this tell us about the ideal engine configuration for a freighter?
--
Let's look at some data from near the middle of my last game.
trade route value = 9
distance = 90
military production = 25
A: (3 impulse engines, 1 base speed, 2 tech bonus speed)
A: build cost = 139
A: speed = 9
A: maintenance = 3
A: Score = 9 * [ (139/25) + (10) ] + 139 + 3 * (10) = 309.04
B: (2 impulse and 2 warp engines, 1 base speed, 2 tech bonus speed)
B: build cost = 163
B: speed = 13
B: maintenance = 4
B: Score = 9 * [ (163/25) + (7) ] + 163 + 4 * (7) = 312.68
C: (4 warp engines, 1 base speed, 2 tech bonus speed)
C: build cost = 179
C: speed = 15
C: maintenance = 4
C: Score = 9 * [ (179/25) + (6) ] + 179 + 4 * (6) = 321.44
Of these, the best value is the slowest design using the old, large, but high speed/cost engines. This result surprised me a little; I had thought that the extra speed of the B model would pay off when I first sat down to calculate this. However, it is worth noting that while the jump from 9 speed to 13 doesn't improve the efficiency, it is "subsidized" to the point of being almost free, and there exist advantages to extra speed (such as evading enemy ships) that are not captured in this model.
----------
It's conclusion time!
- An ideal design cannot be given because it is highly sensitive to the route value, route distance, and military production of the home city. If you have these values available, you can plug them into the formula
Score = route value * [ (build cost / military production) + (distance / speed) ] + build cost + maintenance * (distance / speed)
as described above. Even without specific values, however, we can make some general observations by looking at the equation for Score.
- As trade route value increases, fast models become more attractive.
- As trade route distance increases, fast models become more attractive.
- As the military production of a city increases, fast models become more attractive. This also means that the extra build time for fast models may make them much less efficient in cities with low military production.
- As you add more speed to a ship, each additional point earns less (in decreased travel time) and costs more (due to lighter but lower speed/cost engines). Up to, say, speed 6 or 8, the value of adding more speed far outweighs the cost. However, as you get close to the maximum speed, the costs become significant. Premium freighters don't pay off (except perhaps for very long trade routes).
- If cargo space is taken up by life support or sensors, you will be forced to accept a less efficient engine configuration. Sensors and life support have a total cost greater than the direct cost of these modules.
- For the data I used, the difference between a ship stuffed with the most efficient engines and a ship that tried to strike a balance was very small--3 bc total difference. There are many things to like about 13 speed instead of 9 speed, and for a cost difference so small, it may be the preferred model. Perhaps the strongest conclusion that I can make about freighter design is to avoid the extremes: keep your speed at or above what you can get by filling it with your cheapest engines, but about 2 or more points below the maximum attainable speed. For small maps or low production cities, stay near the bottom of this range; for large maps, stay near the top.
----------
A quick footnote about the assumptions made in this post:
1. The value of money is constant with respect to time, that is, 1 bc now is worth the same to you as 1 bc next turn. This is rarely completely true; for example, whenever you buy with a payment plan you're effectively stating that 1 credit now is worth many credits later (probably because right now you're broke and need a warship).
2. A freighter will go straight to its destination and do nothing else during its lifespan, like explore, say, or get attacked and die.
3. There is no opportunity cost to devoting production to a freighter beyond the direct production cost. This isn't strictly true, as building a ship, in addition to the bc you have to put towards production, also occupies your production capacity when you could be building something else of value. This opportunity cost will be significant in cases where you have more money than production capacity, and not significant in cases where you have more production capacity than money. Recognizing this additional cost has the effect of making cheaper freighters more attractive, as they do not occupy your precious production capacity for as long.
4. Trade route values grow slowly enough that I can treat the value of the first few turns as a constant
--
First, we need to find a way to quantify the value of what a freighter offers. This is a bit tricky as trade routes pay a population-dependent dividend over many turns, and we can't see very far down that series of payments with much certainty. However, we don't have to. While the objective value of a trade route is difficult to calculate, the difference between two income streams is quite easy, as shown below.
A = 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + ...
B = 0 + 0 + 0 + 4 + 4 + 5 + 5 + 5 + ...
where the zeros in B are placeholders to represent turns B spends in transit. Subtracting B from A is simply (4 + 4 + 4) = 12, since all terms after the third are identical in the two series (they are independent of freighter design).
It would be convenient if at the end of this we have a formula that only needs the details of one ship design; however, as shown above the underlying math needs to be a difference between two designs. This next part is a little strange, but it simplifies the final math. We will compare ship designs under consideration to a hypothetical "perfect" ship, that is, a zero-cost freighter that arrived yesterday.
Let's get down to business. The difference (we'll call it Score) between a new design and the "perfect" ship is given by
Score = (income stream from perfect ship - income stream of new design) - (cost of perfect ship - cost of new design)
Score = (trade route bc per turn * turns for new design to arrive at planet) - (0 - cost of new design)
turns for new design to arrive at planet = build time + (distance to planet / speed of new design)
cost of new design = build cost + total upkeep cost = build cost + maintenance cost * (distance to planet / speed of new design)
Score = route value * (build time + (distance / speed)) + build cost + maintenance * (distance / speed)
where (distance / speed) must be rounded up. Note that the closer Score is to zero, the better the design; note also that this will only be useful for comparisons of freighter designs given a specific trade route distance and value. A Score calculated for Freighter A on Route 1 cannot be compared to a Score calculated for Freighter B on Route 2--it has to be the same route for the comparison to be meaningful.
Let's look at the value "build time." Do we use the integer value displayed on a planet or the decimal value of (build cost / military production)? Either will work, but they'll tell you slightly different things. If you use the integer, 200 cost and a 249 cost freighter will appear to have the same build time if you use 50 as the value for military production. This is accurate for a specific case. Using the decimal value, however, will reveal the general truth that the 249 cost freighter will actually cost about 25% more. We use the decimal value here so that our results are less sensitive to misleading changes in Score based on small changes in cost.
So, we can rewrite Score a little:
Score = route value * [ (build cost / military production) + (distance / speed) ] + build cost + maintenance * (distance / speed)
With (distance / speed) rounded up and (build cost / military production) left as a decimal. So, there's our final formula. What does this tell us about the ideal engine configuration for a freighter?
--
Let's look at some data from near the middle of my last game.
trade route value = 9
distance = 90
military production = 25
A: (3 impulse engines, 1 base speed, 2 tech bonus speed)
A: build cost = 139
A: speed = 9
A: maintenance = 3
A: Score = 9 * [ (139/25) + (10) ] + 139 + 3 * (10) = 309.04
B: (2 impulse and 2 warp engines, 1 base speed, 2 tech bonus speed)
B: build cost = 163
B: speed = 13
B: maintenance = 4
B: Score = 9 * [ (163/25) + (7) ] + 163 + 4 * (7) = 312.68
C: (4 warp engines, 1 base speed, 2 tech bonus speed)
C: build cost = 179
C: speed = 15
C: maintenance = 4
C: Score = 9 * [ (179/25) + (6) ] + 179 + 4 * (6) = 321.44
Of these, the best value is the slowest design using the old, large, but high speed/cost engines. This result surprised me a little; I had thought that the extra speed of the B model would pay off when I first sat down to calculate this. However, it is worth noting that while the jump from 9 speed to 13 doesn't improve the efficiency, it is "subsidized" to the point of being almost free, and there exist advantages to extra speed (such as evading enemy ships) that are not captured in this model.
----------
It's conclusion time!
- An ideal design cannot be given because it is highly sensitive to the route value, route distance, and military production of the home city. If you have these values available, you can plug them into the formula
Score = route value * [ (build cost / military production) + (distance / speed) ] + build cost + maintenance * (distance / speed)
as described above. Even without specific values, however, we can make some general observations by looking at the equation for Score.
- As trade route value increases, fast models become more attractive.
- As trade route distance increases, fast models become more attractive.
- As the military production of a city increases, fast models become more attractive. This also means that the extra build time for fast models may make them much less efficient in cities with low military production.
- As you add more speed to a ship, each additional point earns less (in decreased travel time) and costs more (due to lighter but lower speed/cost engines). Up to, say, speed 6 or 8, the value of adding more speed far outweighs the cost. However, as you get close to the maximum speed, the costs become significant. Premium freighters don't pay off (except perhaps for very long trade routes).
- If cargo space is taken up by life support or sensors, you will be forced to accept a less efficient engine configuration. Sensors and life support have a total cost greater than the direct cost of these modules.
- For the data I used, the difference between a ship stuffed with the most efficient engines and a ship that tried to strike a balance was very small--3 bc total difference. There are many things to like about 13 speed instead of 9 speed, and for a cost difference so small, it may be the preferred model. Perhaps the strongest conclusion that I can make about freighter design is to avoid the extremes: keep your speed at or above what you can get by filling it with your cheapest engines, but about 2 or more points below the maximum attainable speed. For small maps or low production cities, stay near the bottom of this range; for large maps, stay near the top.
----------
A quick footnote about the assumptions made in this post:
1. The value of money is constant with respect to time, that is, 1 bc now is worth the same to you as 1 bc next turn. This is rarely completely true; for example, whenever you buy with a payment plan you're effectively stating that 1 credit now is worth many credits later (probably because right now you're broke and need a warship).
2. A freighter will go straight to its destination and do nothing else during its lifespan, like explore, say, or get attacked and die.
3. There is no opportunity cost to devoting production to a freighter beyond the direct production cost. This isn't strictly true, as building a ship, in addition to the bc you have to put towards production, also occupies your production capacity when you could be building something else of value. This opportunity cost will be significant in cases where you have more money than production capacity, and not significant in cases where you have more production capacity than money. Recognizing this additional cost has the effect of making cheaper freighters more attractive, as they do not occupy your precious production capacity for as long.
4. Trade route values grow slowly enough that I can treat the value of the first few turns as a constant
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