How bases work - an indepth analysis
As a result of a small attempt, where I found out, that naval base level doesn't influence, I decided to look at the effect of airbases / naval bases.
So here for my findings, first the easy ones:
Naval Bases
Repairing
As I already stated, ships do repair at any friendly naval base, no matter if it's the home base and no matter the base level and how many ships are based or located at the base. Even if the base is bombed to level 0, they still have full repair speed. They will not repair at small ports or at sea.
Repair speed at a naval base depends solely on build time of the unit and the repair modifier from the repair techs (and of course on the reinforce_time value in misc.txt)
So the time to repair a naval unit at a base is (100-current_strength)/100 * build_time * reinforce_time * 1/(1+repair_modifier)
Org regain
Now here base level has an influence. Through experimentation I've come to this formula for daily naval organization regain. (contrary to land units whose org regain slows down as they approach the max, naval and air units have a constant org regain rate)
So a level 10 naval base gives 4.8 org per day on top of regular org recovery. Again, there is no influence of the number of ships at the base.
This can lead to 6 org per day at 30 morale up to 8.52 org per day at 100 morale (or 7.2 to 10.22 org per day with the minister)
But with the limited importance of naval morale, I'd say building more than 1 level of naval base for range extension isn't worth it.
Air Bases
Repairing
Repairs are pretty much the same as ships, again totally independent of the airbase.
Org regain
I've finally cracked the formula. Turns out Infra is counted twice, once as part of ESE and once directly. So here's my findings:
The formula for the ground based reorg also tells us that in low infra provinces airbase level hardly matters anymore. An airbase in a 20% infra province will only have (at best, meaning 100% TC) 12% the effect an airbase in a 100% province has.
This also means morale is all the more important in low infra provinces, providing for a base reorg of 0.72 at 60 morale (after the first half of doctrines) and 1.68 at 100 morale (after the second half) regardless of infrastructure.
Compared to that an airbase will only give you a max 0.37 / 0.49 org per day in a 20% infra province, compared to 3.12 / 4.08 org in a 100% infra province.
So on one side the effect of an airbase is really low, on the other hand you could argue that exactly in those situations every little bit counts. And with 30 morale, the 0.28 org per day is the only thing you get.
When placing a new airbase, always try to put it in as high an infra province as possible, at 0 infra an airbase doesn't help reorg at all, no matter it's level or your TC.
Land Units
Now those don't have bases, but they kind of fit in here anyway, as the numbers are similiar (and more importantly I figured them out too
)
Repairing
Like with the other units, repairs operate on an on/off basis. Neither infrastructure nor terrain type have an influence on repair speed. So your trooops will reinforce just as quickly in the Saharan Desert or the Pripyat Marshes as they would in the streets of Berlin.
Reorg
Now reorganization is really crazy. (And if I ever have the pleasure of meeting the guy who thought of this formula, I'll gladly strangle him )
Again, there's a few conclusions from this formula. TC overload doesn't hurt reorganization nearly as much as low infrastructure does. Conversely, if you're in a low infrastructure province, even the 25% ESE boost from offensive supply doesn't help a whole lot. (and nothing at all if you're in zero infrastructure)
In high infra or with low morale, the final quarter of reorganization takes more time than the first 75%.
If you're playing one of the mods, where not every backwater province has 60% infrastructure, this might be important to you: If you can move your units from a 20 to a 40 inf province to recover org, you might save weeks waiting to reorg, as the reorg speed is more than twice as fast up to 60 morale and still 85% faster at 100 morale.
This also applies to logistical strikes. If you can bomb down a 80% province to 20%, enemy troops' daily reorg will drop from 7.78 to 1.73 at morale 30, from 10.82 to 2.97 at morale 60 and from 14.90 to 4.6
Final Note on Repair cost
On a side note: I noticed that repair costs in ICdays are a lot less than what we commonly assumed, especially on lightly damaged divs. Daily IC cost is build_cost * reinforce_cost * (1-strength)
So let's assume a unit with build time of 40 days, and a cost of 10 IC with a strength of 75.
At full funding and without any repair tech, this will take 5 days (0.25*0.5*40 days) repairing 5 strength a day. And it will cost 2 IC on day 1 (0.25*0.8*10 IC), 1.6 IC on day 2, ... for a total cost of 6 ICdays compared to the traditional calculation of (40 days * 10 IC * 0.5 * 0.8 * 0.25) = 40 ICdays
As a result of a small attempt, where I found out, that naval base level doesn't influence, I decided to look at the effect of airbases / naval bases.
So here for my findings, first the easy ones:
Naval Bases
Repairing
As I already stated, ships do repair at any friendly naval base, no matter if it's the home base and no matter the base level and how many ships are based or located at the base. Even if the base is bombed to level 0, they still have full repair speed. They will not repair at small ports or at sea.
Repair speed at a naval base depends solely on build time of the unit and the repair modifier from the repair techs (and of course on the reinforce_time value in misc.txt)
So the time to repair a naval unit at a base is (100-current_strength)/100 * build_time * reinforce_time * 1/(1+repair_modifier)
Org regain
Now here base level has an influence. Through experimentation I've come to this formula for daily naval organization regain. (contrary to land units whose org regain slows down as they approach the max, naval and air units have a constant org regain rate)
- A base value of 0,024 per point of Morale over 30. This applies anywhere, even moving at sea
- A value of 1,2 + (0,012*(Morale-30))*ESE which applies while in port (small and big)
- A bonus of .48 for every level of Naval base
- the final modifier from a +20% org regain chief of staff, which comes on top of all those values.
So a level 10 naval base gives 4.8 org per day on top of regular org recovery. Again, there is no influence of the number of ships at the base.
This can lead to 6 org per day at 30 morale up to 8.52 org per day at 100 morale (or 7.2 to 10.22 org per day with the minister)
But with the limited importance of naval morale, I'd say building more than 1 level of naval base for range extension isn't worth it.
Air Bases
Repairing
Repairs are pretty much the same as ships, again totally independent of the airbase.
Org regain
I've finally cracked the formula. Turns out Infra is counted twice, once as part of ESE and once directly. So here's my findings:
- As with naval units, org regain is constant
- There is a base level of org regain, that only depends on morale. Its value is 0.024*(morale-30). That's the org regain a plane also gets while flying.
- The second part of org regain only occurs when landed. Its value is (2.4+0.024*(morale-30))*ESE*Infra. This value is then multiplied with the overcrowding factor.
- An overcrowded airbase will slow down the ground part of reorganization of all planes by the ratio of overcrowding. Even planes in the air and those with full org count towards overcrowding. So 6 airplanes at a level 5 airbase will only get 5/6 of the second part.
- There is no benefit in having an airbase larger than the number of planes based there.
- Again, the org regain chief of staff will add a 20% to the final value.
The formula for the ground based reorg also tells us that in low infra provinces airbase level hardly matters anymore. An airbase in a 20% infra province will only have (at best, meaning 100% TC) 12% the effect an airbase in a 100% province has.
This also means morale is all the more important in low infra provinces, providing for a base reorg of 0.72 at 60 morale (after the first half of doctrines) and 1.68 at 100 morale (after the second half) regardless of infrastructure.
Compared to that an airbase will only give you a max 0.37 / 0.49 org per day in a 20% infra province, compared to 3.12 / 4.08 org in a 100% infra province.
So on one side the effect of an airbase is really low, on the other hand you could argue that exactly in those situations every little bit counts. And with 30 morale, the 0.28 org per day is the only thing you get.
When placing a new airbase, always try to put it in as high an infra province as possible, at 0 infra an airbase doesn't help reorg at all, no matter it's level or your TC.
Land Units
Now those don't have bases, but they kind of fit in here anyway, as the numbers are similiar (and more importantly I figured them out too
)Repairing
Like with the other units, repairs operate on an on/off basis. Neither infrastructure nor terrain type have an influence on repair speed. So your trooops will reinforce just as quickly in the Saharan Desert or the Pripyat Marshes as they would in the streets of Berlin.
Reorg
Now reorganization is really crazy. (And if I ever have the pleasure of meeting the guy who thought of this formula, I'll gladly strangle him
)- Again, there's an easy part: Base reorg is 0.024*(morale-30)
- Then there's the terrain factor:
- If province infrastructure is 60 or higher, it's 8.64*(1+(morale-30)/100)*ESE
- If province infrastructure is below 60, that value is again multiplied with a factor of (infra/60)
- Finally the value is multiplied with a factor depending on current organization of the division: Up to 25% of maximum org the factor is 1, from 25 to 50% it's 2/3, from 50 to 75% it's 1/3 and if you're above 75% of maximum org the factor is 1/6.
- When moving, there's always a drain of -0.48 (at least for human players, the AI always recovers org)
- As always, the org regain chief of staff will add a 20% to the final value.
Again, there's a few conclusions from this formula. TC overload doesn't hurt reorganization nearly as much as low infrastructure does. Conversely, if you're in a low infrastructure province, even the 25% ESE boost from offensive supply doesn't help a whole lot. (and nothing at all if you're in zero infrastructure)
In high infra or with low morale, the final quarter of reorganization takes more time than the first 75%.
If you're playing one of the mods, where not every backwater province has 60% infrastructure, this might be important to you: If you can move your units from a 20 to a 40 inf province to recover org, you might save weeks waiting to reorg, as the reorg speed is more than twice as fast up to 60 morale and still 85% faster at 100 morale.
This also applies to logistical strikes. If you can bomb down a 80% province to 20%, enemy troops' daily reorg will drop from 7.78 to 1.73 at morale 30, from 10.82 to 2.97 at morale 60 and from 14.90 to 4.6
Final Note on Repair cost
On a side note: I noticed that repair costs in ICdays are a lot less than what we commonly assumed, especially on lightly damaged divs. Daily IC cost is build_cost * reinforce_cost * (1-strength)
So let's assume a unit with build time of 40 days, and a cost of 10 IC with a strength of 75.
At full funding and without any repair tech, this will take 5 days (0.25*0.5*40 days) repairing 5 strength a day. And it will cost 2 IC on day 1 (0.25*0.8*10 IC), 1.6 IC on day 2, ... for a total cost of 6 ICdays compared to the traditional calculation of (40 days * 10 IC * 0.5 * 0.8 * 0.25) = 40 ICdays
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