Is there an optimal patrol travel length and suppression strength?

[4xForEver]

First by "patrol travel length" I mean count of star systems that a patrol fleet would go trough on it's patrol mission,
and "Suppression strength" is patrol fleet piracy suppression strength.

Here is an example of a 7 stars long trade route where the numbers represent "max piracy":

279
239
227
218
191
160
142

Our job here is to assign a patrol fleet to the route above, and the problem is whether to assign 1 or 2 or more patrol fleets and what would be optimal suppression strength of these (or single) fleet(s)?
The ultimate goal is to collect trade value and avoiding pirates popping out on that route.

Before you jump in consider there are 2 major problems that contribute to this issue as follows:
1. More fleets means faster max piracy cool downs because patrol fleet would return sooner to each of the systems due to shorter travel length.
2. The higher the suppression strength (than max piracy) faster will cool down be per system.

Precondition to solve this, results in 2 sub questions:

1. What is the optimal suppression strength relative to max piracy? (ex. I think if max piracy is 240, then optimal suppression strength is 280 or more or less?)
2. What is the optimal patrol travel length? (ex. I think 3-4 systems would be optimal, higher than this is counterproductive while lower is more expensive in terms of naval cap. and ship maintenance)

Therefore suppression strength is relative to travel length in addition to max piracy, but what is the optimal and how to develop some formula to let us calculate optimal?
Please consider sample route above to present your solution to the problem.

Btw. gateways are not a solution I'm looking for because that's late game tech.

EDIT:

Short version solution:

+8% patrol suppression strength increase is required per system.

For example above, a patrol route that covers 7 systems where max piracy of most affected systems is 279 "max piracy", would require 7 x 8 = 56% increase in suppression strength, which means this patrol fleet would need to be of 279 x 1,56 = 435,25 suppression strength or 44 corvettes.

Long version solution

 

[Strangedane]

The optimal patrol route is "none".
The upkeep spent on patrol ships will not be worth the tradevalue gained.

Snake your starbase from the center of your empire and end the snakes with trade stations.
Ignore all trade you cannot collect like this, until you get gates.

 

[4xForEver]

Thanks for reply.

The upkeep spent on patrol ships will not be worth the tradevalue gained.

How can this even remotely be true?

In my current game I'm collecting 2454 energy from trade without the use of any gateways yet. (approx. 90% is gateway free trade)
Approximate amount of energy that I spend on patrol ships in this game is 350 energy and 75 alloys (250 patrol corvettes x 1.5 energy = 375; x 0.3 alloys = 75)
Naval capacity is not an issues at all as well, easy to get it with strongholds.

As you can see I'm generating approx. profit of 1700 energy thanks to patrol fleets (excluding trade protection)

Gateway tech is is pretty much late one, are you saying until then we should ignore additional trade that can be protected by patrol fleets? this means I should ignore my 1700 energy because I still don't have gateways ready.

Snake your starbase from the center of your empire and end the snakes with trade stations.

Can you please expand on "trade stations"?
how would you apply this method to sample trade route in my OP? considering no gateway tech.

 

[GloatingSwine]

The upkeep spent on patrol ships will not be worth the tradevalue gained.

You can minimise that upkeep by patrolling with naked corvettes. Like literally naked, no weapons, defenses, tier 0/1 everything else. They still have 10 suppression value each.

 

[4xForEver]

You can minimise that upkeep by patrolling with naked corvettes. Like literally naked, no weapons, defenses, tier 0/1 everything else. They still have 10 suppression value each.

That's very helpful, I didn't think of this before but will consider.
One issue however is that this is a human cheat and I don't find it fun to cheat the AI.
Another advantage is that large patrol fleets are able to fight pirates so you don't have to bring your main fleets back from anywhere.

The optimal patrol route is "none".

I must also disagree with this as well.

If you put your patrol fleet to patrol a single system then it will be 100% effective.
Larger router diminishes this effectiveness but it never goes to 0% as long as suppression exceeds max piracy value.

I do still believe and have arguments that optimal length and suppression strength exists, I just wanted to hear if anyone else mastered these optimals.

 

[GloatingSwine]

I don't think there's a single optimal length because how frequently your patrol fleet passes through a system isn't just down to the route length but also your sublight speed. The faster your ships are the more often they can cycle the same number of systems, or the more systems they can cycle in the same amount of time.

And starbases are still a large part of your answer. A single starhold in the middle of you putative 7 system trade route with 6 hangars would provide a base of 84 trade protection at a 6 system range, covering the entire route and beyond, and if you're not being cheesy to flatten the ship upkeep is probably cheaper than an equivalent number of patrol corvettes (and has no alloys upkeep).

The opportunity cost of using a single starbase that way is pretty low for most of the game. Pretty much no matter what you're doing moar starbases is good for it.

 

[Stardance]

Its complicated. GloatingSwine has it right.

Take for example your 7 system trade route. The max piracy of 279. That is likely the max piracy for the entire route, you just see fluctuations in the numbers because of the patrol, starbase protections, growth of the piracy, and possibly merging routes - without a screenshot it is hard to say.

So for that 7 system trade route you would need 28 corvettes (280 protection) because you have to exceed the max piracy in order for the piracy growth to become negative - otherwise a patrol with lower numbers will just decrease the speed of growth. Some people have discussed whether the maintenance is worth it, but also consider fleet cap - that's nearly 30 fleet that could be helping you defend/conquer/expand. And the piracy isn't static, it grows as your population grows, and there is no notification when your patrol can't manage the cap anymore.

Further, if you have piracy, ANY piracy, even on a patrolled route, a pirate fleet can pop up. While they aren't hard to defeat, it can disrupt reinforcement routes for a real war, colony/science/construction pathing, and just generally be annoying. They also tend to be stronger than the fleet patrolling, so you have to stop the patrol as well until you get enough fleet over there.

Using starbases to provide the necessary trade protection is cheaper (no impact on fleet cap) a lot cleaner, and you don't get pirates spawning. You do still have to watch the piracy growth, but it is easier to plan and manage.

I usually use dedicated patrols as a transition period until the starbase network I am building can manage the piracy on their own. Each starbase has inherent protection built in, and with 6 hangars and some platforms, its roughly 90 protection per base. Two bases, that's 180. Three bases, that's 270. Build a few extra platforms and you are good.

Clever placement of collector bases (dedicated to collecting trade) and protection bases can drastically reduce those piracy maximums to manageable levels. You try and keep your major collector bases as close to your capital as you can manage to shorten the piracy route and reduce the number of systems affected by piracy. I've written other posts on that so I won't go into too much detail here, but it is doable. I do a rough estimate of 50 piracy per normal planet that requires protection and plan my bases accordingly. Obviously it will exceed those numbers in late game, but you get the option to stop growing that planet and resettle to an ecumenopolis in your center, or other strategies like gateways.

For those thinking it is a waste of starbases, I've regularly been under my starbase limit since adopting this strategy, and I use strongholds/fortresses on planets to boost fleet cap. Plus it is nice to actually build starbases that have at least some defense value, thematically. It works.

If you do figure out the math for patrols, I'd be interested. Just from general experience I think a 7 system route would require two fleets of 30 corvettes to manage effectively. 7 systems is fairly long without any starbase support.

 

[4xForEver]

I don't think there's a single optimal length because how frequently your patrol fleet passes through a system isn't just down to the route length but also your sublight speed.

Friend, you said more than what you believed to say!

I see clear advantage in this in combination with your argument "You can minimise that upkeep by patrolling with naked corvettes"

Traveling from system to system is almost instant for which sublight speed doesn't matter, therefore patrol corvettes should be equipped such that sublight speed is minimum, because in doing so it will curbe more of piracy per system.

How significant is this indeed depends on patrol route length because in longer route all other systems grow in piracy, therefore their cumulative piracy growth must be lower than current system piracy lowering, for which to be true, the patrol fleet suppression must exceed max piracy for some percentage, ex. 40% more than max piracy of the highest max piracy system in whole route. (not cumulative but system with most max piracy is determinant)

And starbases are still a large part of your answer. A single starhold in the middle of you putative 7 system trade route with 6 hangars would provide a base of 84 trade protection at a 6 system range

Indeed, I agree because that protection may apply to multiple patrol fleets because it spans 6 system range in all direction, therefore all affected patrol fleets would be smaller reducing their upkeep and indirectly increasing our naval capacity.

Most optimal approach would be to build minimum amount of starholds under condition that all of them should cover whole empire or more precisely all trade routes.

and if you're not being cheesy to flatten the ship upkeep is probably cheaper than an equivalent number of patrol corvettes

No, I see advantage in both of them combined, as long as cheat against the AI is excluded, for example lower sublight speed is good and normal while removing weapons is wrong.
You gave me some hints that will help me better analyze optimals. thank you.

 

[GloatingSwine]

Using starbases to provide the necessary trade protection is cheaper (no impact on fleet cap) a lot cleaner, and you don't get pirates spawning. You do still have to watch the piracy growth, but it is easier to plan and manage.

Now I wouldn't say it has no impact on fleet cap, because it does. It has an opportunity cost of 36 (43 with Supremacy tradition) because those hangars could be anchorages (which increase naval cap without requiring a job so you can free up those soldiers to do more techrushing and make more alloys).

However, for most of the game you can expand your fleet cap much faster than you can pay upkeep to fill it, so you'll have a few more left over that don't need to be anchorages to keep you in the fleets game.

I generally find the options to increase starbase cap are all pretty good too. Grasp the Void and Unyielding will give you an extra 9 between them (and reduce their upkeep), and that's 90-144 food with no farmers, and later on 324-454 fleet capacity when you can throw your trade through gateways and turn them all into anchorages.

 

[4xForEver]

So for that 7 system trade route you would need 28 corvettes (280 protection) because you have to exceed the max piracy in order for the piracy growth to become negative - otherwise a patrol with lower numbers will just decrease the speed of growth. Some people have discussed whether the maintenance is worth it, but also consider fleet cap - that's nearly 30 fleet that could be helping you defend/conquer/expand. And the piracy isn't static, it grows as your population grows, and there is no notification when your patrol can't manage the cap anymore.

Correct, in my example 279 is the highest max piracy of a route, therefore 28 corvettes is a minimum (but not optimal) for 2 reasons:
1. max piracy cap may grow over time.
2. higher suppression is needed which depends further on next 2 reasons
--- A) The speed of suppression per system (current piracy lowering)
--- B) The length of a route because all other system in a route grow in piracy (cumulative growth)

Further, if you have piracy, ANY piracy, even on a patrolled route, a pirate fleet can pop up. While they aren't hard to defeat, it can disrupt reinforcement routes for a real war, colony/science/construction pathing, and just generally be annoying. They also tend to be stronger than the fleet patrolling, so you have to stop the patrol as well until you get enough fleet over there.

I disagree because on such high trade value route your patrol fleets will be much stronger than pirate fleet, so you don't even have to worry about pirates even if they appear.
Because you can simply set your patrol fleet to "aggressive" mode and it will deal with pirates as soon as it returns to that system.
Sit back and watch your super patrol deal with them automatically.

I usually use dedicated patrols as a transition period until the starbase network I am building can manage the piracy on their own. Each starbase has inherent protection built in, and with 6 hangars and some platforms, its roughly 90 protection per base. Two bases, that's 180. Three bases, that's 270. Build a few extra platforms and you are good.

I did not know protection is cumulative lol!
One issues however is this means we need more starholds which reduces amount of anochoage focus starbases, which isn't good.

"Transition period" also means we have to wait for gateway tech which is very late game event, until then a lot of energy could be harvested.
In early game patroling is not that expensive or hard but grows as the game progresses, but that's not IMO valid reason to wait until late game and ignore additional trade.

If you do figure out the math for patrols, I'd be interested. Just from general experience I think a 7 system route would require two fleets of 30 corvettes to manage effectively. 7 systems is fairly long without any starbase support.

I'm all in to figure this out and will share my finding in this thread if no solution is found.

 

[Stardance]

Now I wouldn't say it has no impact on fleet cap, because it does. It has an opportunity cost of 36 (43 with Supremacy tradition) because those hangars could be anchorages (which increase naval cap without requiring a job so you can free up those soldiers to do more techrushing and make more alloys).

However, for most of the game you can expand your fleet cap much faster than you can pay upkeep to fill it, so you'll have a few more left over that don't need to be anchorages to keep you in the fleets game.

I generally find the options to increase starbase cap are all pretty good too. Grasp the Void and Unyielding will give you an extra 9 between them (and reduce their upkeep), and that's 90-144 food with no farmers, and later on 324-454 fleet capacity when you can throw your trade through gateways and turn them all into anchorages.

Fully agree.

 

[Stardance]

"Transition period" also means we have to wait for gateway tech which is very late game event, until then a lot of energy could be harvested.
In early game patroling is not that expensive or hard but grows as the game progresses, but that's not IMO valid reason to wait until late game and ignore additional trade.


I'm all in to figure this out and will share my finding in this thread if no solution is found.

Just to clarify, that particular transition period is for when you unlock the ability to have 6 hangars for maximum protection range (also maximum collection range of 8 for a collection focused base). So it isn't *that* long to keep using patrols.

Best of luck on your calculations!

 

[4xForEver]

Just to clarify, that particular transition period is for when you unlock the ability to have 6 hangars for maximum protection range (also maximum collection range of 8 for a collection focused base). So it isn't *that* long to keep using patrols.

Best of luck on your calculations!

Ah OK, but starholds are not enough to keep piracy at zero, purpose of starholds is to reduce "piracy effects" rather than suppressing piracy completely, we still need patrols to get trade beyond default protection, until gateways are in place.

Best of luck on your calculations!

As for my calculation I have performed a test and come to conclusion as follows:

Short version:

+8% patrol suppression strength increase is required per system.

For example, a patrol fleet that covers 7 systems where max piracy of most affected systems is 100 "max piracy", would require 7 x 8 = 56% increase in suppression strength, which means this patrol fleet would need to be of 100 x 1,56 = 156 suppression strength or 16 corvettes!

Long version:

I used following test data:

Trade route (travel) length: 6 systems
Max piracy system: 280
Patrol fleet suppression strength: 360 (36 corvettes)
One of the systems is protected with a star base (therefore 5 systems only need protection, but patrol fleet handles all 6!)

System layout of this trade route is as follows:
First column is "current piracy effects", second column is increase in piracy during 30 day period, and 3rd column is change:

221,63 - 223,96 = 2,33
98 - 100 = 2
96, 36 - 98,29 = 1,93
185,63 - 187, 31 = 1,68
159, 64 - 161,31 = 1,87

Cumulative current piracy growth is therefore a sum of 3rd column which results in:
9,81

piracy suppression of 360 suppression patrol fleet (36 corvettes) during that same period of 30 day time is:
13,28

13,28 must be reduced for 1 system that is already protected therefore:
5/6 = 0,83
13.28 x 0,83 = 11,02

This means 360 patrol fleet against max 280 max piracy route was able to reduce approx. following amount of piracy for the whole route:
11,02 - 9,81 =1,21

1,21 is therefore reduction in piracy for 360 fleet against 280 piracy trade route!

360 suppression is grater than 280 piracy for the following percentage:
360 / 280 -1 = 28%

Therefore 28% stronger patrol fleet gives us 1,21 overall suppression for that route.

Following is the amount of time needed to reduce piracy to zero:
221,63 / 1,21 = 183,16 game months
183,16 / 12 = 15 game years!

Therefore 28% increase in suppression will take 15 years for reduction, however next problem is to determine whether 280 max piracy effect wouldn't surpass 360 during 15 year period?
Most likely it will much sooner so my approximation would be to increase the suppression percentage to +50% of the max piracy system as probable optimal:
280 x 1,5 = 420

420 patrol fleet would reduce 20 piracy per month instead of 13,28 (360 fleet) (I tested this separately)

Therefore 50% optimal would reduce piracy to zero in following amount of game years:
20 x 0,83 = 16,6
20 - 16,6 = 3,4
221,63 / 3,4 = 65,18 game months
65,18 / 12 = 5,4 game years

Therefore finally we have 28% stronger patrol fleet which will take 15 years to reduce piracy, or we could have 50% stronger patrol fleet to do the same for 5,4 years instead, which is much faster and realistic relative to piracy cap and trade growth over time.
Trade likely won't grow by 50% in 5 years in a stable empire so I think +50% is optimal suppression strength.

As for optimal travel length this depends on cumulative growth relative to suppression.
In addition minor information worth taking into account for travel length is higher suppression fleets will curbe piracy faster in non-linear way! for example:

360 suppression fleet will curbe 13,28 piracy per system
500 suppression fleet will curbe 20,00 piracy per system

Which is not linear suppression! and as such our optimal suppression percentage is then also relative to cumulative piracy growth or patrol travel length.

I'll make a shortcut and calculate it as follows,
3,4 is suppression gain for 6 system route in this example for +50% optimal suppression strength increase.

How does this value change if we reduce patrol route to, say, 3 systems and keep +50% suppression strength increase?
6 systems = 9,81 cumulative piracy growth
therefore 3 systems is half of that which is 4,9 cumulative piracy growth
and therefore suppression gain is double which is:
3,4 x 2 = 6,8

4,9 is larger and much closer to 3,4 so suppression will work much faster as well, but we need equal change which is:
221,63 / 6,8 = 32,59 game months or
32,59 / 12 = 2,17 game years

2,17 relative to 5,4 game years is 50% faster suppression time therefore this reduction is linear!
Because the reduction is linear this leads to conclusion:

0.5 / 6 = 0,08 (50% / 6 systems) or 8% suppression increase is required per system, therefore:

7 systems trade route requires:
7 x 8% = +56% suppression strength

For my trade route in OP max piracy system is 279
Therefore it will take:
280 x (0.08 x 7 + 1) = 436,8 suppression which is:
436,8 / 10 = 44 corvettes

Therefore for the trade route in my OP it would take 44 corvettes over min 5,4 years to deal with piracy and reduce it to zero.

44 corvettes corvettes require 66 energy to maintain but in return we protect 750 trade value (5248 / 7) worth of energy in this example.

If you guys think my calculation or test is wrong please let me know, I'm going to test it it my current game and if this works then patrols are more powerful than what is current belief.

 

[GloatingSwine]

Ah OK, but starholds are not enough to keep piracy at zero, purpose of starholds is to reduce "piracy effects" rather than suppressing piracy completely, we still need patrols to get trade beyond default protection, until gateways are in place.

Remember they can overlap, and they count as permanent presence in the systems they extend their protection range to.

So to suppress 280 piracy you need ~3 overlapping starholds with 6 hangars apiece, which will provide a constant background of 257 trade protection in their overlap zone for the cost of 30 energy (18 with Unyielding and Expansion traditions).

So unless you can consistently fill an extra 100 fleet capacity it's cheaper and more convenient to just slap down some trade protection bastions.

 

[fusei]

Ah OK, but starholds are not enough to keep piracy at zero, purpose of starholds is to reduce "piracy effects" rather than suppressing piracy completely, we still need patrols to get trade beyond default protection, until gateways are in place.



As for my calculation I have performed a test and come to conclusion as follows:

Short version:

+8% patrol suppression strength increase is required per system.

For example, a patrol fleet that covers 7 systems where max piracy of most affected systems is 100 "max piracy", would require 7 x 8 = 56% increase in suppression strength, which means this patrol fleet would need to be of 100 x 1,56 = 156 suppression strength or 16 corvettes!

Long version:

I used following test data:

Trade route (travel) length: 6 systems
Max piracy system: 280
Patrol fleet suppression strength: 360 (36 corvettes)
One of the systems is protected with a star base (therefore 5 systems only need protection, but patrol fleet handles all 6!)

System layout of this trade route is as follows:
First column is "current piracy effects", second column is increase in piracy during 30 day period, and 3rd column is change:

221,63 - 223,96 = 2,33
98 - 100 = 2
96, 36 - 98,29 = 1,93
185,63 - 187, 31 = 1,68
159, 64 - 161,31 = 1,87

Cumulative current piracy growth is therefore a sum of 3rd column which results in:
9,81

piracy suppression of 360 suppression patrol fleet (36 corvettes) during that same period of 30 day time is:
13,28

13,28 must be reduced for 1 system that is already protected therefore:
5/6 = 0,83
13.28 x 0,83 = 11,02

This means 360 patrol fleet against max 280 max piracy route was able to reduce approx. following amount of piracy for the whole route:
11,02 - 9,81 =1,21

1,21 is therefore reduction in piracy for 360 fleet against 280 piracy trade route!

360 suppression is grater than 280 piracy for the following percentage:
360 / 280 -1 = 28%

Therefore 28% stronger patrol fleet gives us 1,21 overall suppression for that route.

Following is the amount of time needed to reduce piracy to zero:
221,63 / 1,21 = 183,16 game months
183,16 / 12 = 15 game years!

Therefore 28% increase in suppression will take 15 years for reduction, however next problem is to determine whether 280 max piracy effect wouldn't surpass 360 during 15 year period?
Most likely it will much sooner so my approximation would be to increase the suppression percentage to +50% of the max piracy system as probable optimal:
280 x 1,5 = 420

420 patrol fleet would reduce 20 piracy per month instead of 13,28 (360 fleet) (I tested this separately)

Therefore 50% optimal would reduce piracy to zero in following amount of game years:
20 x 0,83 = 16,6
20 - 16,6 = 3,4
221,63 / 3,4 = 65,18 game months
65,18 / 12 = 5,4 game years

Therefore finally we have 28% stronger patrol fleet which will take 15 years to reduce piracy, or we could have 50% stronger patrol fleet to do the same for 5,4 years instead, which is much faster and realistic relative to piracy cap and trade growth over time.
Trade likely won't grow by 50% in 5 years in a stable empire so I think +50% is optimal suppression strength.

As for optimal travel length this depends on cumulative growth relative to suppression.
In addition minor information worth taking into account for travel length is higher suppression fleets will curbe piracy faster in non-linear way! for example:

360 suppression fleet will curbe 13,28 piracy per system
500 suppression fleet will curbe 20,00 piracy per system

Which is not linear suppression! and as such our optimal suppression percentage is then also relative to cumulative piracy growth or patrol travel length.

I'll make a shortcut and calculate it as follows,
3,4 is suppression gain for 6 system route in this example for +50% optimal suppression strength increase.

How does this value change if we reduce patrol route to, say, 3 systems and keep +50% suppression strength increase?
6 systems = 9,81 cumulative piracy growth
therefore 3 systems is half of that which is 4,9 cumulative piracy growth
and therefore suppression gain is double which is:
3,4 x 2 = 6,8

4,9 is larger and much closer to 3,4 so suppression will work much faster as well, but we need equal change which is:
221,63 / 6,8 = 32,59 game months or
32,59 / 12 = 2,17 game years

2,17 relative to 5,4 game years is 50% faster suppression time therefore this reduction is linear!
Because the reduction is linear this leads to conclusion:

0.5 / 6 = 0,08 (50% / 6 systems) or 8% suppression increase is required per system, therefore:

7 systems trade route requires:
7 x 8% = +56% suppression strength

For my trade route in OP max piracy system is 279
Therefore it will take:
280 x (0.08 x 7 + 1) = 436,8 suppression which is:
436,8 / 10 = 44 corvettes

Therefore for the trade route in my OP it would take 44 corvettes over min 5,4 years to deal with piracy and reduce it to zero.

44 corvettes corvettes require 66 energy to maintain but in return we protect 750 trade value (5248 / 7) worth of energy in this example.

If you guys think my calculation or test is wrong please let me know, I'm going to test it it my current game and if this works then patrols are more powerful than what is current belief.

I think there is an error that you assume that a patrolling fleet will protect all systems on its route at all times, but it will only protect the system it is currently in. That means the very minimum of suppression you need is the sum of max. piracy along the route. Considering this you can simply station a separate fleet in each system if you don't mind the micro and unless you're protecting a low value route where rounding up to the next 10 is an issue. The advantage is that you don't have to worry about uneven distribution of max. piracy / time spend in the system, but as I said it involves some micro and I usually use one bigger fleet on patrol, if I can't cover the route with starbases / hangars.

 

[4xForEver]

Remember they can overlap, and they count as permanent presence in the systems they extend their protection range to.

So to suppress 280 piracy you need ~3 overlapping starholds with 6 hangars apiece, which will provide a constant background of 257 trade protection in their overlap zone for the cost of 30 energy

I find this interesting because if those 3 star bases are used as anchorage this would give us 108 naval cap.

For 108 naval cap we can build 108 corvettes which grants 1080 piracy suppression.
That amount of piracy suppression is enough to deal with almost 4 times more of said piracy (4 x 280 = 1120) or 4+ routes instead of 1 or 2.

Only downside would be energy upkeep which is 160 compared to 30, but that's not a big deal.
However upside is that:
1. you now also have a fleet that is mobile.
2. it can be split across multiple routes as needed.

I think also overlapping starholds is not always possible for maximum gain, it depends on how star bases and hyper lanes are laid out.
Overlaping starholds overlap only in certain places but never across all 6 lanes.
Another ex. I don't prefer to build starbases in systems without colony so that limits me on how to overlap starholds.

I'm not saying that patrol fleets are superior, both have their use but it depends on situation, sometimes a combo will do, other times patrol only is best, and sometimes only starholds would be most appropriate.

I think there is an error that you assume that a patrolling fleet will protect all systems on its route at all times, but it will only protect the system it is currently in. That means the very minimum of suppression you need is the sum of max. piracy along the route.

Yes, to take max piracy of most affected system and apply it to all systems in route is reasonable and easier to calculate in game.
I don't assume patrol fleet would protect all systems, there will always be some piracy, but with large enough patrol fleet this should be minimal.

-----------

I'm still testing my calculation in game and so far the only thing that appears to be wrong is that +8% per system may not be enough for routes that are already highly affected by piracy because piracy reduction highly depends on "over suppression" of patrol fleet.
Higher over suppression curbs piracy almost exponentially faster, so some magic percentage like 20% should be fixed minimum in addition to +8% per system.

For example 3 systems = 3 x 8% + 20% = +44% over suppression for faster piracy cool down.

 

[fusei]

A problem you also have to consider is the time your patrol fleet spends in a system, this can vary especially at the ends where the fleet will usually spend half the time in comparison to systems in the middle of the route.

 

[4xForEver]

A problem you also have to consider is the time your patrol fleet spends in a system, this can vary especially at the ends where the fleet will usually spend half the time in comparison to systems in the middle of the route.

Ah man, now this likely answers why I see higher "current piracy" at the ends of patrol route!

If that's indeed so, it should be labeled as a bug

 

[fusei]

Ah man, now this likely answers why I see higher "current piracy" at the ends of patrol route!

If that's indeed so, it should be labeled as a bug

It is a consequence of how patrol routes are set up. At the end the fleet will fly to the center and back, while on the same route a system in the middle will be crossed twice and even there you can end up with under coverage when the used hyper lane entry points are close together. The problem at the ends can be mitigated by including an additional system at each end, which means you waste time on systems you don't care about, but those you do care about are covered more evenly.

 

[4xForEver]

I have one question:

Suppose you cover your whole empire (trade routes) with starbase protection, it doesn't matter how much, what matter is that at least 1 point of protection is in place everywhere.

Then doesn't this mean "Piracy effects" will never reach "Max piracy", and consequently you'll never see pirates popping out?
Because that starbase protection should cap Piracy effects below max piracy.