Introduction
I plan to write a few articles to avoid very huge longposts in which I will say about basic principes of optimal (from resources point of view) fleet building. TI4 is a comlex game so exatc mathematically describe it very hard, so I focus only on space combat. I want to underline it: this won't teach you how to win, but I hope it get you more deeper understanding of combat system that make your games better.
In general I will say about default ships and about combat effectivity of them, but sometimes I will discuss another uses. Value of every ship type depends on game situations, factions and from pilot and his playstyle. I can't physically say about every case, but you should understand that I try to consider general case. To do this, I will use the simplest mathematical operations, basic concepts of probability theory and a combat calculator.

Expected value and probability of an event
Since result of combat depend from dice for analys we should to use such concepts as expeted value and probability. Every ship has COMBAT characteristic. If the value rolled on the die is equal to or greater than the value of this characteristic, then event A will occur - the unit produces a hit. In another case event B occur - the unit misses (Fig. 1).

Fig. 1 Probability
Probability product of two independens event is product of this events probability. For example, if we want to assess hit ability for flagship which roll on 2 dices, we can use this rule for get Fig. 2.

Fig. 2 Probability product
Dispite on simplicity and clarity hit probability is hard to use in game for assess fleet power. Just take 1 warsun, 2 dreadnouts, 2 cariers and 16 fighters. Even if you could count probability of all events every round, this information can't get you any value. So for this it is convenient to use expected value. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. In simple word expected value is product probability of even and its value. In TI4 hit value allways (with exection of Jol-Nar flagship and few other cases) equal 1. So for one ship in TI expected hit value numerically equal to the probability of hits (see Fig. 3 right). From definition we can simple way count expected hit value for all fleet. For it we just can add all expected hit value of every ship in fleet (Fig. 3 left). Expected hit value is useful instrument for losses assess both players in one-two rounds but it doesn't allow to predict battle outcome.

Fig. 3 Expected hit value
The most effective unit (Fighter)
Fighter is the best unit in terms of cost/quality ratio. For just half resource we get unit which add one "HP" and 0.2 expected hit value per round. Let's compare ships characteristics with chatacteristics of fighters which we can buy for the same price (Table 1).

Table 1

Unit	Expected hits value	HP	Resources	Expected hits value (fighters)	HP (fighters)
War Sun	2.4	2	12	4.8	24
Dreadnout	0.6	2	4	1.6	8
Cruiser	0.4	1	2	0.8	4
Destroyer	0.4+0.2	1	1	0.4	2
For example, instead of dreadnout we can build 8 fighter for the same price. Superiority of fighters is clear excluding destroyers. But this table is not entirely fair cause we need ships which can transport fighters. This table says us important thing: if we want to improve our fleet power - the most optimized (from economic point of view) way is to fill your transport capacity if you have (but OFC we have production limitation, see later).
But let's make this table more fair. In the most cases you fighter will be located in carriers, so in first approximation we will consider only them. In one carrier can be placed 4 fighters. The total cost is 3 + 4*0.5 = 5 resources. The carrier has the same characteristics, as the fighter, so, we can count, that for 5 resources we have bought 5 fighter. So we can consider that 1 fighter's cost is 1 resources with "transport correction". With this correction table 1 will looks like:

Table 2

Unit	Expected hits value	HP	Resources	Expected hits value (fighters)	HP (fighters)
War Sun	2.4	2	12	2.4	12
Dreadnout	0.6	2	4	0.8	4
Cruiser	0.4	1	2	0.4	2
Destroyer	0.4+0.2	1	1	0.2	1
From table 2 we can see that fighers is not only fleet's "HP" but fleet's damage dealer. Even with transport correction they "win" every ship type for the same price with exception of destroyers. Real game cases is between table 1 and table 2, but it's clear that in general case to optimally improve you battle fleet power you need to focus on fighters. I hope, I was able to prove you, that "fighter screen" is important and best part of your fleet. There is one nuance with destroyers, but is subtheme of second part.
Fighters look imbalanced, but game has a few power limitation of them: carriers limit, capacity limit and production limit. This mechanics make other ships usefull too. Let's imagine that our docks have an infinite amount of production. In this case if we built 10 effective (with transpport correction) fighter for 10 resources from one side and another ships for the same price from second side (but with enought small destroyers amount) the fighters fleet will stronger (Fig. 4). But if our base has PRODUCTION 6 we lose part of resources and our fighters fleet will be weaker, cause obviously 1 vs 1 fighter weaker than any other ship (Fig. 5).

Fig. 4. Infinite production
Fig. 5 Limited production
Weigth of one unit
In the next parts of this seria post calculator often will outcome results where win/lose ratio is 55%/45% etc. Formally, this gives us an understanding of which fleet is stronger but in TI4 combat where you win even in 2 out of 3 cases very risky and expensive for you. Don't forget about it. But in real it is no problem and now I try to prove you it. The fact is that even one any unit has huge weight in combat. Let's take 2 the same fleets with 2 dreadnouts, 1 cruiser, 2 carrier and 8 fighters. Obviesly, the win probability will close to 50% for both fleets. How are you think, if defender get base with 2 fighers in capacity, how strong relation is changed? Result on Fig. 6. Draw your attention that right fleet no only win but in most cases save much more then 2 ships (in comporation of amount added fighters) and lose <25% of max fleet cost.

Fig. 6 Weight of one unit
How we can to explain this? Let's look on Fig. 7. All other things being equal, our two fighters will produce 0.4 hits each round (blue). And for each hit, the enemy fleet will deal less damage in the next round (blue), and this number will increase with the number of rounds. Moreover, in the next round these two fighters will again inflict their 0.4 hits and we will have a second chain in addition to the first (red). And this scenario will happen every round (green). Moreover, this process is constructive itself, since if the enemy’s fleet deals less damage, this means our fleet lives more rounds, which again allows us to deal more damage in order to survive even longer. The result is a snowball that, of course, although cannot grow indefinitely, will eventually reach a size large enough to feel its influence. Let's add to this that when the turn comes for our two extra fighters to get hit, their sacrifice will save the dreadnoughts and cruisers, which will continue to cause relatively large damage for some time.

Fig. 7 Snowball
For 7 combat rounds 2 fighters produce 2.8 hits + give 2 "HP" to fleet + reduce enemy hits on 1.8 and increase our damage on 0.25 hits. Total difference is close to 7 "pseudohits". One unit influense OFC is smaller in long combats but it decrease slowly, how we can see on Fig. 8.

Fig. 8 Weight of one unit in long combat
So from one side if you collide two fleet with close powerfull the first round with high probability define result of battle (who better roll on dice). But with another side you can protect youself from dice random just if you built 4 additional fighters for 2 resources. I guess "weigth of one unit" rule is one of basic TI4 combat system rules. For this reason you need assess condition of your fleet every round and retreat, even if you should have won. For this reason "Moral boost" is definetly good for midgame+, "Shields Holding" usefull even in huge fights and Sustain Hits continue to be useful at any game stage.

End of the first part
Thank you very much for reading this far. In the next part I will take a closer look at each individual ship type and compare it to the others. I will try to prove why the TI4 does not have a Rock-Paper-Scissors system, as some believe, and also find out whether destroyers are weak/strong.