For those interested, here's an explanation of what the numbers of the supply map mean and how it (apparently) works, as of 1.3.3. This does not cover many things (i.e. ports, etc), but hopefully it can fill some gaps for the basic mechanics. I really didn't like the lack of explanations (and very confusing numbers in the supply map), so I did some testing to figure this stuff out. Sorry if it was posted somewhere already, I did not find an explanation like this when doing basic search. So, --
Part I: Definitions
There are several kinds of infrastructure values that are shown and/or play a role in calculations:
"State infra": the infra you actually build in a state, ranging from 0 to 10.
"Total infra": the sum of all state-infra in a province. It is the number displayed below the railroad image in the supply map, and is also referenced in the tooltip when you hover over the railroad image itself.
"Province-average infra": the average state-infra of all states in a province (the province being the whole chunk that gets highlighted when you click on supply map, e.g. the Moscow province consists of 4 states). This number is referenced in the tooltip when you hover over the railroad image when looking at the supply map (f4). This is the ONLY number that is important for supply calculations.
There are also a couple of supply/throughput values that play a significant role:
"Province own supply-throughput capacity": this is something like how much incoming supply can be handled by a province's own infra, and it appears to be directly a function of province-average-infra. If province-average-infra is X, the own-infra-supply appears to be given by f(X)=2*X^2. So for example, for average infra of 5, the own-infra-supply will be 2*5^2 = 50. When you mouse over the gas-canister image in the supply map, this own-infra-supply value appears as "Infrastructure" when you look at the capital, and as "local infrastructure" when you look at other provinces -- when those provinces cannot "handle" (i.e. pass along) the full supply that's coming into them (more on this later). This is confusing, because what is referred to as "infrastructure" in those tooltips is really "supply throughput that can be handled by province's own infra".
"Province total supply-throughput capacity": this is how much incoming supply a province can ACTUALLY handle in total. I don't know why this is needed as something different from "Province own supply throughput", but it is. Basically, the province's total throughput capacity is equal to its own throughput capacity plus an extra 25%. So if the own throughput capacity is 32, the total throughput capacity will be 32*1.25 = 40, etc.
Now, important thing -- the province's total throughput number is the mystery number that is displayed above the railroad image for a given province in the supply map. This is how much total incoming supply a province's infrastructure can handle (pass along and make available to units inside the province). It shows red when the province infra can't handle/pass along the incoming supply (more on this below). (It also shows red over the capital, but I'm not sure that itself means anything, perhaps just a bug).
Part II. Calculations
Now, on to how the calculations work.
The capital generates supply equal to its "own supply-throughput capacity", which is again 2*X^2, where X is the average infra of all states in the capital. (This capital-supply appears as its "infrastructure" when you hover over the gas-canister image of the capital in the supply map.)
Let's say the capital province A has avg.infra = 7, so its own throughput is 2*7^2 = 98, and this is what it will be pushing to all neighboring provinces. The "capital"/main supply, so to speak.
Now, there are two cases possible for some receiving province B downstream.
Case 1. Province B can handle the full incoming supply.
Visually, for such a province the number above the railroad image in the supply map will be white.
Easy case -- province B receives whatever a provider/previous province A can push, the max being the "own throughput capacity" of province A.
Case 2: Province B cannot handle the full incoming supply.
Visually, for such a province the number above the railroad image in the supply map will be red.
Let's say province B has average-infra = 5, so its own throughput is 2*5^2=50, and its total throughput (the number displayed above the railroad image in the supply map) is 125% of that, i.e. 50*1.25=62 (rounded) -- and this is less than what the previous/provider province is pushing (98).
In this case the supply mechanics "soften the blow" in the following way -- instead of calculating the total throughput capacity as "own + 25% of own", it calculates it as "own + 25% of provider". The logic being, I guess, if the infra of the provider-province A is stronger (can push more supply than the own infra of province B can handle), then let's "allow" province B to use 25% of the stonger province's infra to handle the incoming supply. (Pretty arbitrary if you ask me, but whatever...). In our case, the capital province A is pushing 98 (this is the own throughput capacity of the capital); the receiving province B can basically handle 62 (which is 125% of its own throughput capacity of 50); so, the "soften the blow" calculation kicks in and gives: 50 + 0.25*98 = 50 + 24.5 = 74.5. This will be the actual supply that comes into province B and is available to its units (plus any local supply from victory points, etc) -- and this will also be supply that province B will push on to the next province C. So A is pushing 98 to B, B can only handle 74.5, and that's what it's pushing to C.
Part III. Conclusions
(When speaking about images and tooltips, it all refers to the gas-canister and railroad icons shown for every province in the supply map (f4)).
Your basic supply originates in the capital and can be found as the number listed as "infrastructure" in the gas-canister tooltip of the capital. It's 2*X^2 of the average infra in the capital province's states.
This is how much the capital is pushing everywhere. To increase it, build up infrastructure in any state of the capital province.
When looking at other provinces, if the number above the railroad image is red, it means the province can't handle (pass along) the full incoming supply, so it will accept and pass through a reduced amount. To resolve this, build up this province's infrastructure (any state -- only the average matters).
You don't necessarily need to build up infra in every province to handle max supply coming from the capital. If the capital is pushing 100, and your current province can only handle 50, but the units in the province only need 20, well you're ok. In the end what matters are the numbers on the gas-canister image -- how much the troops use vs. how much is available in total.
Now if your units are starving in a province (e.g. gas-canister reads 70/29, with 70 displayed red), here's what to do:
If the number above the railroad image is red, then, like already mentioned, your province can't handle the full incoming supply. So build up this province's infra until there's enough for your units.
If you've build it up to where the number above the railroad image is white, but its still not enough, then the problem is upstream -- either an upstream province has a bottleneck (this will be shown in the current province's gas-canister tooltip, and the problem province will have a red number above its railroad image), or the capital is not generating enough supply (the tooltip will then reference your capital infrastructure as the bottleneck). Once you've identified where the bottleneck is, build infra there. For the capital, probably a good idea to get that out of the way early. (As an example, for me, playing SOV in single-player, level 7 avg. infra in the capital province (this, again, is shown in the tooltip when you mouse over the railroad image) is enough to handle the early war with GER.)
With experience, you'll be able to see how much max supply your units need (perhaps in specific provinces), and build infrastructure in advance accordingly. E.g. let's say your max unit supply-needs tend to reach 90 in some province. So next time you play, you can build up infra in capital to level 7, giving 98 (2*7^2) "capital" supply. Then all the provinces along the way to your "critical province" need to be built up to about 6.3 average infra (giving them total throughput of 1.25*6.3^2 = 99). Obviously, you can increase those numbers to give yourself extra room if needed.
Finally, here are the numbers as reference -- for a given avg. infra level, how much supply the capital generates, and how much throughput a receiving province can handle.
Avg infra => Capital supply => Max throughput
-----------------------------------------------------------
2 => 8 => 10
3 => 18 => 22
4 => 32 => 40
5 => 50 => 62
6 => 72 => 90
7 => 98 => 122
8 => 128 => 160
9 => 162 => 202
10 => 200 => 250
Part I: Definitions
There are several kinds of infrastructure values that are shown and/or play a role in calculations:
"State infra": the infra you actually build in a state, ranging from 0 to 10.
"Total infra": the sum of all state-infra in a province. It is the number displayed below the railroad image in the supply map, and is also referenced in the tooltip when you hover over the railroad image itself.
"Province-average infra": the average state-infra of all states in a province (the province being the whole chunk that gets highlighted when you click on supply map, e.g. the Moscow province consists of 4 states). This number is referenced in the tooltip when you hover over the railroad image when looking at the supply map (f4). This is the ONLY number that is important for supply calculations.
There are also a couple of supply/throughput values that play a significant role:
"Province own supply-throughput capacity": this is something like how much incoming supply can be handled by a province's own infra, and it appears to be directly a function of province-average-infra. If province-average-infra is X, the own-infra-supply appears to be given by f(X)=2*X^2. So for example, for average infra of 5, the own-infra-supply will be 2*5^2 = 50. When you mouse over the gas-canister image in the supply map, this own-infra-supply value appears as "Infrastructure" when you look at the capital, and as "local infrastructure" when you look at other provinces -- when those provinces cannot "handle" (i.e. pass along) the full supply that's coming into them (more on this later). This is confusing, because what is referred to as "infrastructure" in those tooltips is really "supply throughput that can be handled by province's own infra".
"Province total supply-throughput capacity": this is how much incoming supply a province can ACTUALLY handle in total. I don't know why this is needed as something different from "Province own supply throughput", but it is. Basically, the province's total throughput capacity is equal to its own throughput capacity plus an extra 25%. So if the own throughput capacity is 32, the total throughput capacity will be 32*1.25 = 40, etc.
Now, important thing -- the province's total throughput number is the mystery number that is displayed above the railroad image for a given province in the supply map. This is how much total incoming supply a province's infrastructure can handle (pass along and make available to units inside the province). It shows red when the province infra can't handle/pass along the incoming supply (more on this below). (It also shows red over the capital, but I'm not sure that itself means anything, perhaps just a bug).
Part II. Calculations
Now, on to how the calculations work.
The capital generates supply equal to its "own supply-throughput capacity", which is again 2*X^2, where X is the average infra of all states in the capital. (This capital-supply appears as its "infrastructure" when you hover over the gas-canister image of the capital in the supply map.)
Let's say the capital province A has avg.infra = 7, so its own throughput is 2*7^2 = 98, and this is what it will be pushing to all neighboring provinces. The "capital"/main supply, so to speak.
Now, there are two cases possible for some receiving province B downstream.
Case 1. Province B can handle the full incoming supply.
Visually, for such a province the number above the railroad image in the supply map will be white.
Easy case -- province B receives whatever a provider/previous province A can push, the max being the "own throughput capacity" of province A.
Case 2: Province B cannot handle the full incoming supply.
Visually, for such a province the number above the railroad image in the supply map will be red.
Let's say province B has average-infra = 5, so its own throughput is 2*5^2=50, and its total throughput (the number displayed above the railroad image in the supply map) is 125% of that, i.e. 50*1.25=62 (rounded) -- and this is less than what the previous/provider province is pushing (98).
In this case the supply mechanics "soften the blow" in the following way -- instead of calculating the total throughput capacity as "own + 25% of own", it calculates it as "own + 25% of provider". The logic being, I guess, if the infra of the provider-province A is stronger (can push more supply than the own infra of province B can handle), then let's "allow" province B to use 25% of the stonger province's infra to handle the incoming supply. (Pretty arbitrary if you ask me, but whatever...). In our case, the capital province A is pushing 98 (this is the own throughput capacity of the capital); the receiving province B can basically handle 62 (which is 125% of its own throughput capacity of 50); so, the "soften the blow" calculation kicks in and gives: 50 + 0.25*98 = 50 + 24.5 = 74.5. This will be the actual supply that comes into province B and is available to its units (plus any local supply from victory points, etc) -- and this will also be supply that province B will push on to the next province C. So A is pushing 98 to B, B can only handle 74.5, and that's what it's pushing to C.
Part III. Conclusions
(When speaking about images and tooltips, it all refers to the gas-canister and railroad icons shown for every province in the supply map (f4)).
Your basic supply originates in the capital and can be found as the number listed as "infrastructure" in the gas-canister tooltip of the capital. It's 2*X^2 of the average infra in the capital province's states.
This is how much the capital is pushing everywhere. To increase it, build up infrastructure in any state of the capital province.
When looking at other provinces, if the number above the railroad image is red, it means the province can't handle (pass along) the full incoming supply, so it will accept and pass through a reduced amount. To resolve this, build up this province's infrastructure (any state -- only the average matters).
You don't necessarily need to build up infra in every province to handle max supply coming from the capital. If the capital is pushing 100, and your current province can only handle 50, but the units in the province only need 20, well you're ok. In the end what matters are the numbers on the gas-canister image -- how much the troops use vs. how much is available in total.
Now if your units are starving in a province (e.g. gas-canister reads 70/29, with 70 displayed red), here's what to do:
If the number above the railroad image is red, then, like already mentioned, your province can't handle the full incoming supply. So build up this province's infra until there's enough for your units.
If you've build it up to where the number above the railroad image is white, but its still not enough, then the problem is upstream -- either an upstream province has a bottleneck (this will be shown in the current province's gas-canister tooltip, and the problem province will have a red number above its railroad image), or the capital is not generating enough supply (the tooltip will then reference your capital infrastructure as the bottleneck). Once you've identified where the bottleneck is, build infra there. For the capital, probably a good idea to get that out of the way early. (As an example, for me, playing SOV in single-player, level 7 avg. infra in the capital province (this, again, is shown in the tooltip when you mouse over the railroad image) is enough to handle the early war with GER.)
With experience, you'll be able to see how much max supply your units need (perhaps in specific provinces), and build infrastructure in advance accordingly. E.g. let's say your max unit supply-needs tend to reach 90 in some province. So next time you play, you can build up infra in capital to level 7, giving 98 (2*7^2) "capital" supply. Then all the provinces along the way to your "critical province" need to be built up to about 6.3 average infra (giving them total throughput of 1.25*6.3^2 = 99). Obviously, you can increase those numbers to give yourself extra room if needed.
Finally, here are the numbers as reference -- for a given avg. infra level, how much supply the capital generates, and how much throughput a receiving province can handle.
Avg infra => Capital supply => Max throughput
-----------------------------------------------------------
2 => 8 => 10
3 => 18 => 22
4 => 32 => 40
5 => 50 => 62
6 => 72 => 90
7 => 98 => 122
8 => 128 => 160
9 => 162 => 202
10 => 200 => 250
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