It's for this game www.PocketSpaceEmpire.com (I have also made tons of post about it in the past if you recall :)), anyway it's less important and you could treat is as a generic question.

Note that the game is focusing on grand strategic level (no tactics, no moving ships around, etc) so the combat need be only as complex as to affect the strategic layer (what ships to build, what composition of fleet to send vs a certain alien race, how many to send, which upgrades to install). The combat is presented only in an observer mode (optional), so the player can see and learn how it all works together, not to issue tactical orders.

The combat is fully automated (the player's involvement in on the strategic level (which fleet to send where) and fleet composition. Combat is ressolved in phases (1-9), if both sides survive all phases (rare) the battle in inconclusive and can start again next turn (unless one side retreats).

You have:

- 3 classes of medium ships (escort ships): corvette, frigate, destroyer

- 2 classes of big ships (capital ships): cruiser, battleship

- beam guns (all ships have those)

- fighters that are carried by some ships (usually big ships have those)

- torpedoes (sort of missiles but torpedoes fit the theme better :D) that are carried by various ships

Combat is stacks based (all ships of the same hull type stack together and fire together). At the moment it's simple, each stack chooses a random enemy stack and fires at it with all beam weapons. Then they reduce the stack HP/kill ships (all attacks are simultaneous, so it does not matter in what order they fire). Then casualties are removed and a next phase of firing starts.

There are also tons of global abilities (like each escort ship provide a "Protect capital ship" value and this value is compared to the number of capital ships and then based on it capital ships get some defensive bonus, so it encourages a good ratio of escort to capital ships; some ships have "Tactical Net" installed and it counts how many ships have it installed, if most of them do then all ships get a nice bonus due to better coordination in combat; capital ships have "Command bridge" and the number of command bridges to total number of ships results in an accuracy bonus).

Question: How to make combat calculations? How it all should work together? How to make an interesting decision regarding what kind of ships to include in a fleet?

Especially fighters and torpedoes, these have no effect yet and these should work somehow different than beam weapons.

Feel free to invent arbitrary rules if needed :)

You have important characters who are part of the military in your Empire, right? I don't remember how fleshed out your character system is, but assuming they are given personalities, traits, and some form of political importance (IE, you as the Emperor would want to keep them happy, use them, get their support for things, etc) then you can tie together the political and strategic elements in ways that also occurred in the real world.

Think of some of the non-military reasons that ships get built, and decisions are made between building another battleship or switching to aircraft carriers (or some other general strategy): politics and economics. In Imperial Japan they continued to invest in battleships even after it was fairly clear the aircraft carrier had made them obsolete because politically powerful admirals pushed to keep building them. Here in the United States even as we speak we are building weapons and ships and all sorts of military projects not because the military wants or can use them or because they'd be effective, but because those military projects provide some jobs to certain regions and lots of profits to certain powerful people.

So say one of your military leader guys has the trait: "Favors Strike Craft." Every time you increase the rate of production on Strike Craft (fighters and bombers) this guy is more likely to support your other decisions. And, because you've got all these Strike Craft lying around, you start using them in your fleets more. This affects what else you build - no need to build anti-strike craft cruisers when you have so many fighters. You'll need more fast carriers if you want to deliver strike craft around the galaxy quickly. Etc etc. Soon enough, because of one influential character, your entire military strategy is shaped - and that's without even considering whether or not it was the best choice militarily.

It's interesting but I would primarily need a mundane combat calculations system. Like how those ships, fighters, torpedoes work and deal damage to each other. Only once it's done I could do more sophisticated things.

I was thinking about something like this (there are many holes in how it should work, so a very generic one):

Combat procedure:

1) Ships launch all fighters

2) Phases (repeat 9 times)

2.1) Ships (each stack) launch torpedoes (up to the number of torpedoe tubes, skip if no torpedoes left, typically most ships have those sufficient for 3-5 phases)

2.2) Torpedoes choose targets (they attach to the target stack)

2.3) Fighters attack enemy fighters (how?)

2.4) Ships (each stack) chooses a target enemy stack and fires beam weapons

2.5) Fighters attack incoming torpedoes (how?)

2.6) Ships (each stack) use Point Defence weapons to fire to incoming torpedoes

2.7) Torpedoes deal damage to ships (stack it targetted)

2.8) Fighters attack ships (how?), ships (each stack) use Point Defence weapons to fire to incoming torpedoes

2.9) Damage is applied to ships and kills are applied

3) Combat ends

Weapons effectiveness:

- beam weapons (ships) deal X-Y damage, heavy ships can ignore Z damage (therefore heavy armoured battleships might be totally immune to low damage beam weapons); big ships have typically higher damage beam weapons than small ships

- torpedoes deal damage equal to 1/3 of target's max HP, regardless of target's HP (therefore these are the most efficient vs big ships)

- fighters fight each other and have bombs which deal 10 damage each but ignore all shields and protections and resistances (so unstoppable 10 damage per fighter that passes through)

But if gameplay is focusing on grand strategic level, how is allowed to make decisiones about the upgrades installation? Is that the installation is done at building site (major work), and not just prior to any combat (repair or maintenance work)?
Also, there is the believing that grand strategy is even greater at the abstract level than "strategy" alone but that's too much overkill for a game to be fun, so you're on the right path here

Prior to combat.

It's more about "in what kind of ship types/upgrades I should invest" and then "where my fleets should station/whom should attack". All mundane things (sending ships to repairs, replacement of destroyed ships) is automated or abstracted.

The whole weapons, fighters, torpedoes are here to allow rich content to manipulate on strategic level (should I invest in fighters? should I make a dedicated fleet and station it on borders with race X or a more generic one which I could use against everyone?). Possibly also change those over time (like on turn X there is a major discovery (all races) making fighters less efficient and torpedoes more efficient).

On the building side they player decide what types of ships (hull types & hull sizes) are in a fleet and which technologies are researched (bonuses to certain weapons/ship classes).

I'm looking for a combat system (also alien races ships composition/patterns & weak/strong points) that could convey it.

always use the simplest possible simulation model that yields sufficiently correct results.

at the simplest level, each type of unit has one stat: combat strength.

to resolve one turn of combat, you add up the total strength of both sides, add some randomness, and that determines losses for each side, which are then applied at random to different ships.

so you add up the strength of both sides, figure out the odds, roll a die, and consult the combat table, which expresses losses as a percentage of total fleet strength most likely.

so if your fleet has total strength of 100, and 30% losses, you eliminate 30 strength points worth of ships at random.

with correctly balanced values for unit strength, something as simple as this could work. the unit strength would take into account all capabilities of the ship: weapons, armor, speed, maneuverability, special weapons, crew training, etc.

this would be a combat system similar to those seen in table top wargames games like blitkrieg and thrid reich by avalon hill.

Norman's method should work, it's a little wonky, in that it won't represent any rock / paper / scissor dynamics. Someone could theoretically find the cheapest ship with the highest combat strength and always auto resolve combat, and they would win out over someone who has a more expensive but more well rounded force.

then take it to the next level.

ships have 2 stats: combat strength, and speed/maneuverability.

or the next level:

attack, defense, range, and movement.

but no matter how simple or complex the model, balance will be required to prevent min-maxing from creating a dominant strategy - IE just building the ship with the best strength to cost ratio. but then you end up with all ships having the same cost/benefit ratio. Ie all choices become meaningless. perhaps have stronger ships cost progressively more, as they make it easier to bring a lot of force to bear at a single point - easier than gathering up a whole squadron of smaller ships to do the same job.

one of the big difficulties is the hands off nature of the game. to make fleet selection meaningful, you need in-depth combat rules. but the combat is hands off, its just the emperor watching the war on closed circuit tv from a surveilance satellite basically. and the emperor is not expected to know the nuances of plasma cannon usage in space combat. but they are expected to make informed meaningful decision as to what to build. its hard to add that gameplay feature and keep things high level.

maybe the imperial admiralty and not the emperor should be deciding what ships to build. maybe the emperor should just say "take this system" or "take that sector", and the admiralty should do the rest.

if you do go for more stats ("combat and movement" stats or "atk, def, rng, move" stats), you get the possibility of unit specialization (rock paper scissors), but then you have to model combat more in-depth. even just 2d atk and move with all weapon ranges the same, and you have the beginnings of a wargame on your hands. you'll either have to run it to determine the outcome, or fake the results with contrived rules.