Keep in mind that my highest iccup ranking is only B+, what I believe to be correct may very well be flawed in the eyes of a higher level player. I am only trying to help by sharing what has helped me to get this far. So here we go.
Also, ZvZ is not included because both economy and combat style are unique in that particular match up.
I believe that T and P have two important similarities:
1. Both T and P set up their economy before they maximize production. Starting with the first SCV or probe, T and P generally produce workers nonstop until they reach their desired production capacity. Z, on the other hand, must switch between drones and units, and his economy is trickier to develop.
2. Both T and P depend exclusively on special units for fighting power. T depends on siege tanks and vessels, while P depends on HT and reavers. Without these special units, T/P's army is very weak compared to the Z. I will discuss the implications later.
First, Z needs to set up his economy different from the T/P opponent:
Using TvZ FE into SK build as an example, T goes one rax, cc, academy, second rax, ebay, third rax, factory, startport, science facility + two more rax, second ebay, second starport and another two more rax for 7 rax in total. All the way up to the construction of the last two rax, T produces SCV non-stop, setting up his entire economy first, then simply non-stop army production until he runs out of resources. The only time T will add more economy is if he takes an early third base.
P goes the same way, setting up a full economy first, then produce at max capacity for the rest of the game.
Do you ever get that feeling that the T/P army just keep coming and coming and never gets any smaller no matter how much you kill? That's because they have already set up a full economy and they can produce at max capacity for as long as they have resources. Many Z fall behind in the mid game because they fail to set up their own economy to match that of the T/P opponent, the econ disadvantage lead to less units, and makes the T/P army appear stronger.
Every Z is told on first day "you must power drones in the early game, make as many as you can get away with, then switch to army to defend". And by watching VODs and reps, most Z gets his early BO down fairly easy. The problem occurs after the initial switch to unit production, inexperienced Z don't know what to do after they go through their memorized BO. Once into the mid game their econ management fall apart.
Take a hypothetical ZvP on destination for example: both FE, the Z goes the now standard 3 hatch lair into 5 hatch hydra/ling/lurker, and he does fine in the early-mid game, putting down a 6th hatch at a 4th expo, denying P from taking a third, etc... But as the game progresses he feels that the P gradually started to out produce him. He takes a look at the rep and sees that the P was pumping 9 gateways on 2 bases, and Z screams imbalance, "In the mid game, my 4 bases cannot match P's 2, his army is just stronger, may be that's how the game is designed?" Not true.
What the Z did wrong was that after he replicated the BO, he started to mass only units until he took the 4th expo. He feels that his econ is weak but the P is always attacking so he is pressured into making only units to survive, and finally when he gets some drones for his 4th base, the P is pumping 9 gateways, taking expos everywhere, and just started to out macro him. A close look reveals that despite having 4 bases, he didn't actually have the economy to maintain max production of all his hatcheries, ultimate, because he didn't make enough drones.
So when does Z make units and drones?
Timing is everything:
Drone timing is neither a magic timing that only high level players know, nor a random timing you hope to get lucky with. There is a simple rule that you must follow: you make enough units to meet defense timings, and all other time and resource is devoted to drones. That's it.
What the Z player needed to do, is go back to watch the rep again, and pause at every possible attack timing the P has. When does the first zealot comes out? If P attacks now with 1 zealot do I have 4 lings to defend? When does the second and third zealot comes out? Do I have enough units to defend that those attack timings? When does P gets the corsair out? Does my scourge come out in time? When P finishes +1 and leg speed and rolls out with 1 archon + 11 zealots, how many hydra/ling and sunken do I need to defend at that point?
After figuring out all those defense timings, and knowing how many units you need to defend, you can prepare for them, and devote all other resources to make drones. Now, instead of wondering in the dark if you made too many or too few drones, you know exactly what you are doing!
Listen to the Day[9] audio guide on building triggers, he basically tells you how to design your own BOs based on defense timings. For those lesser mortals who are content with just copying what the Koreans do, you can save a lot of time by watching their reps and write down the defense timings, instead of figuring them out yourselves through practice. Some people believe that takes the fun out of Starcraft, some people have just as much fun playing mapped out Korean builds, whatever suits you.
Let's go back to the ZvP game earlier, the Z player now builds lings based on the early zealot timings, adding sunkens accordingly, and reach a point where he has 45 supply (12 lings), with 39 drones, 6 on gas, 33 on minerals, hydra speed and +1 carapace and overlord speed have started. He makes his first group of hydras knowing that the P is morphing his first archon and has 5 zealots, with 3 more in the gateways. Z knows that after 1 more round of zealot production P will finish +1 attack and leg speed, and will push him with 1 archon and 11 zealots.
Z feels that 2 groups of hydras + lings and sunken should be plenty to defend, but taking account of the P's walking time across the map, he knows that he can make 1 more round of drones and still have just enough hydras when the P arrives, so with 5 hatcheries he makes 5 drones (15% boost to his 33 drones on minerals), and then he adds a second group of hydras. If Z did not get P's attack timing down, he may have unnecessarily made the second group of hydras first, and missed out 15% of his economy for several rounds of production.
If you read my previous guide on Z econ management, you should know that it takes 6 drones on minerals (it's more like 5.5, but I'm sticking to the higher number) + 1 drone on gas to maintain constant hydra production of 1 hatchery. With 33 drones on minerals and 6 on gas, Z barely has enough money for constant hydra, barely any gas for upgrades, and no money to expo again. With 38 drones on minerals, now Z has enough to maintain hydra production and take a third gas and add a 6th hatch at his 4th expo.
Back to timing, with 3 groups of hydras and some lings on the map, lurker research almost done, Z feels that he can defend the bridges if he dodges storm correctly, (remember, destination is used for the example here). So he adds another round of 5 drones, and when he got his first lurkers, with 4 groups of hydra/ling, he added another round of 5 drones. So now he has 43 drones on minerals and 9 on gas, which should comfortable support 7 hatch lurker/hydra/ling + upgrades, which is on par with 9 gateways' production speed. So if at this point P has less than 9 gateways, he will be the one who gets out produced.
So as much as economy goes, Z's mid game production should not be weaker than the P player. If you feel that you keep getting out produced in the mid game, you probably did not add enough drones, or added them too late because you didn't know your defense timing and made too many units early on.
But what about psy storms? Even if Z keeps up the production in numbers, it still seems that his mid game army is weaker...
Rules of engagement:
Referring back to my initial claim that T and P armies depend exclusively on special units for fighting power. This is of course assuming that you have equal production speed. If Z is out macroed, that is an economic issue, not combat.
So what does it mean? All Z strategies and tactics are designed to counter these units.
Since I just rhetorically asked about psy storms, let's use that same ZvP game for example. Try to picture the relative armies in your head, P has 1 archon + 13 zealots + 6 dragoons + 4 HT, Z has 36 hydras + 12 zerglings, who is stronger? It all depends on storms, right? How much max damage can 6-8 psy storms do? That's something a Z never wants to find out.
Now picture again, with the 4 HT removed from the P army, lets say they morphed into 2 archons, now we have 3 archons + 13 zealots + 6 dragoons vs 36 hydras + 12 zerglings, easy fight for the zerg no?
What the above exercise should illustrate, is that without psy storms, P army is always weaker on equal production. Notice I said storms, not HT, because an HT without energy is as useless as a neutral creature on the map. What this means for the Z player is that to win battle, he must either 1. assassinate the HTs or force them into archons, or 2. deplete the energy of those HTs before engagement.
Before we go into how Z should fight, lets analyze how P fights first, knowing your enemy is the key to win combat. Assume that the above zeal/archon/goon/HT army is sitting in a ball in an open area, Z with his hydra/ling army starts the attack with a nice flank from 3 sides, left right and bottom, the P will do 1. storm the incoming Z, 2. fall back, 3. storm the chasing Z, whose spread out flank is starting to cluster as it gives chase, 4. fall back again, 5. storm the remaining Z, and 6. morph the energy depleted HT into archons, and finish off the left over Z with his units. If you said, "hmm, all the major damage in that battle is done with psy storms", you are right. If Z gives up the attack half way and falls back, he loses all those units for nothing, the HTs will recharge their energy and Z must spend resources to replace his lost units.
Now, same fight, but P is the one attacking, Z army is spread out in a small arc. The armies engage, 1 HT is mis-placed and got in front of the army, Z snipes the HT and dodges the desperate storm, the rest of the HT catches on, Z sees that the HTs are in range, and falls back accordingly, a couple storms go off catching only tails of the retreating Z army. Since everything moves faster than HT, Z engages again when the HTs are out of range, and promptly retreats again when HT gets close, dodging yet another round of storms. P has lost many zealots and the archon, and with only 3 storms left he wisely decided to retreat and regroup with his reinforcements.
So Z must rely on defensive advantage and dodge storms, sounds easy? Yes, but to be honest, it's usually not enough...in actual game, storm dodging is extremely difficult to execute when you have to keep up the macro and reinforce your army. It is possible to fight mid game wit hydra/ling, but most Z will recommend otherwise. To fight HT, you need either mutas or lurkers.
1. Way of the mutas:
Many Z players falsely believe that mutas are only useful for offense, to disrupt enemy bases. What they don't realize is that mutas are very effective in eliminating HTs on the map. Sniping HTs off is obviously desirable, but just forcing them into archons is usually good enough.
Player who keeps track of the Korean pros may have noticed the popularity of a muta/hydra build. Z goes his normal 3 hatch lair into 5 hatch, but gets delayed mutas for defense together with some sunkens, then follow up with mass hydra to put pressure on P's third base, some times ending the game right there.
The idea of the build is not to do economic damage to the probe line, (of course do it if you could), but rather to force all the initial HTs into archons, so that when mass hydras are out, Z can over power the zealot/archon army. Indeed, without psy storms, it is very difficult for P to deal with mass hydra. If you are a muta fan, definitely give this build a try, but if your muta micro is sub par, don't panic, there is option 2.
2. Way of the lurkers:
With mutas, the raw power of the archons can pose big problems early on. Timing attacks delivered right when you make your switch into hydras are extremely powerful, and requires good micro from Z to defend. But if you can't micro mutas well, lurkers work just fine, though in completely different style.
Whereas muta/hydra seeks to eliminate HTs and build a stronger mass hydra army to control the map. Lurker builds are defensive in nature aimed to out macro the P. Remember that to deal with HTs the second option is to deplete their energy? Storm dodging with hydra/ling is indeed difficult, but if you have lurkers then it is a whole different story.
Set up the lurker field so that 1 storm hits only 1 lurker. The correct way to play lurker defense is to always keep a small hydra/ling army on the field to take hits for the lurkers, but keep your main army in the back to avoid storms. Let the lurkers absorb the psy storms. A field of 6 lurkers can easily absorb 6 psy storms before P can clean up everything on it. But the real fight begins after P clearing the lurker field! P is still feeling happy that he broke through the lurkers with relative ease, but now he is in a situation where he has used up most of his psy storms, and many units are damaged and lost their shields. Z must take this window and engage with everything he has, surround if possible, to not give P any breathing room to recharge his HT energy or shields. The depleted HTs cannot do anything in this fight, and they must be picked off even if part of the P army escapes.
What if I want to attack?
Well, if you want to play aggressive in the mid game, you have to use mutas to eliminate existing HTs or at least force them into archons. If you have chosen the more defensive lurker strategy, they you do NOT want to attack. Attack is not always necessary, simple as that.
But if I don't attack P will expo everywhere and get too big? Not true.
Before the popularity of the current aggressive muta/hydra build, ZvP is always played under the tradition assumption that it is the P's job to kill Z, not the other way around. Consider that Z can add 5-7 drones every single round of production, if P doesn't attack, Z will get huge much much faster than P can. So if you are worried about P playing turtle, just grow like crazy and get big before he does, that is Z's racial advantage. Usually lurker builds transition much faster into hive for cracklings and defilers, in comparison to muta builds that are more aggressive in the mid game. Drop upgrade is usually researched after hive. What Z wants to do in the mid game is pure defense, and get huge extremely fast. By doing that, you essentially force the P to attack your lurker fields, or he will simply be out macroed.
As to P taking expos, understand that you don't need to launch a major offensive to stop him from taking expos! First you need to have at least one ling at every P expo for both scouting and harassing the probe that tries to build stuff. As the game progresses, keeping 3-5 lings near his expos can quickly kill the probe and delay the expo. When crackling finishes, the sheer mobility of zergling raids become very difficult for P to deal with. And when defiler comes out, zergling raids become simply devastating. 2 swarms to cover the cannons, +2 cracklings can ignore everything and take down the nexus in just a few seconds. Of course when drop finishes you know what do. All this time you are growing your economy and massing units, right?
To sum up, deal with the HTs and the rest of Ps army is trash.
Same goes for reavers, just focusing on shuttle and reaver sniping.
And the Terrans?
Same concepts apply, except muta/hydra doesn't work. With exception to risky drop builds, ZvP can only be play defensively.
The first T push is generally the most dangerous one, because the size of that army is disproportionally larger than his production capacity. What does it mean? It means that if you kept up your economic growth to math T's production capacity, his horded up army will be disproportionally larger than your production capacity the same way it is larger than his.
Therefore, you cannot engage when his army leaves base. You must delay him as much as possible, and not allow any reinforcements to join up, and mean while horde up an army as big as his before he breaks your front door. If T got his timing right, your defilers will not come out for the first push, you must defend it with brute force.
Sounds hard? Not really. Remember that the only units dangerous to you are the tanks and that first vessel? To defend, you don't need to do perfect surrounds and kill his entire army, all you need to do is taking out those siege tanks to buy time for defilers.
Don't panic when T is pounding on your sunkens, that's what those sunkens are for anyway. Let them die to buy time. When you engage, T usually keeps his m&m slightly behind his tanks to avoid getting cornered by lurkers on all sides. Some Z makes the mistake of going in too deep and ends up losing the fight even with superior numbers. The correct thing to do is to attack from both sides, borrow the outside lurkers just in range of the his marines, which is as far away as possible from tanks, and borrow the inside lurkers just in range of his siege tanks, which is as far away as possible from the marines. As long as you take out those tanks, his siege is over. Don't worry if the marines get away, the fact that you lose minimum units in that fight will help you more than those marines can help him. And of course kill that first vessel when you engage.
I'm not going to cover late game because this is a mid game guide. So, that's it. gg