Should I group together or spread out tanks in siege mode?

Short Answer

Spread your siege tanks out.

Long Answer

Clumping is, in essence, situational.

When Clumping is Bad

In most cases, it is not safe to clump your units together with each other or with your buildings. There are two main reasons for not clumping your units.

Splash attacks & AOE attacks damage more of your units at once if they are clumped.

Consider some examples:

• Nuke: If everything is clumped up, you just lost everything.
• Mutalisk: A large clump of units is subject to the bounce attack, resulting in more damage per attack to your units.
• Banelings: A baneling that explodes into a group of units damages more of them.
• Blinding Cloud

Addressing your specific example:

If I group my siege tanks together they cover less area and once melee units get to them they all become helpless together; but on the other hand if I spread them around they're easier to surround and their friendly fire is really devestating.

You have two outcomes:

• Clumped together: You do no damage to enemy units. Your units die, the opposing army incurs minimal loss.
• Spread out: You do damage to both enemy and friendly units. Your units die, but the opposing army is smaller after the skirmish.

In the end, you're better off with the second outcome.

Enemy units have a higher effective DPS against your units if they are clumped because they spend more time attacking and less time walking between units.

Without going into a numbers game, this should still intuitively make sense. If you have three siege tanks all lined up together and they get rushed by zerglings, they can essentially turn and attack the next take as each one dies. If you are spread out along a ridge, the zerglings have to rub between the tanks. That results in less time where you are attacked and more time where the opponent is attacked.

When Clumping is Good

Clumping should be treated as the exception, not the rule. At the moment, I can think of one instance where clumping would be an advantage, and it doesn't actually apply in the case of siege tanks:

If you find yourself in a situation where your ranged army is going up against a pure melee army with no splash or AoE attacks, clumping can work to your advantage.

• Units in the core of the clump are safe from attack.
• All of your units can still attack the opponents melee units (provided they have no minimum range) even though the melee units will not all have access to the clump.

Since siege tanks have a minimum range, the benefit to clumping is essentially nullified. I describe why above when addressing the specific example given in the original question.

tzenes & Shaun really made the point clear, but I wanted to add a couple more benefits to spreading that I think help support their answers:

1. Siege tanks almost always get focus-fired by the opponent. The risk for your opponent in focus-firing is that his units spend time traveling to the target instead of attacking the nearest. This increases your benefit of putting physical distance between tanks. The time the enemy spends traveling is usually more than the time the enemy is attacking.

2. If you group 3 siege tanks, it will be obvious to the enemy how many you have and where they are, and he can take an appropriate decision. By spreading them, he has no idea how many you have, and it's much harder for him to evaluate positioning. Imagine the image below represents the area your tanks can do damage. In the clumped example, your enemy will know exactly where to go to avoid damage:
   

3. Kind of obvious, but you cover more ground, preventing counter-attacks and limiting the enemy's positioning options. On Xel'Naga Caverns, you can control the entire center by spreading your tanks. Clumping would leave you more vulnerable to counter-attack.

4. Leap-frog behavior in a siege line. Usually through a battle, there is a geographic push and pull. The center of the battle will move back and forth. If the battle goes out of range of your tanks, they become useless. If the tanks are clumped, you would need to move them ALL in order to change the center of battle, which means no siege tanks at all during the relocation. If they are spread out, you can leap-frog them around which:

   1. Gives you more options regarding positioning
   2. Decreases risk. You will only be moving 1-2 tanks at a time. If you make a bad decision with 1 tank, it's much better than making a bad decision with all of them.
   3. Maybe it's easier. For some reason to me it is just easier to move 1 tank rather than move all of them. You can even queue up the entire relocation - unsiege, shift+move, shift+siege. Yea I realize you can do that just as easily with many tanks, but for some reason to me it's easier with only 1. Maybe it's that they are big units whose position is so important that queuing up a move command is dangerous, or maybe it's because the impact on the "siege cloud" is small so the decreased risk makes it easier to do. YMMV.

SPREAD!!!

Let's think about this for a second.

If I'm fighting against Siege Tanks (with whatever unit), and I kill the first Siege Tank, then I have to walk to where ever the next Siege Tank is. If they're together, that's a short distance (thus few attacks), if that's a long distance, then that is more time thus more attacks.

But I can understand your concern about friendly fire, seeing as if they're all helpless together they get 0 damage... but consider the following: Should they be worthless, or should you sacrifice some of them to hurt the enemy?

Consider the following:

You're running BioMech with a strong Siege Line backed by Marines against a Muta/Ling/Baneling army. The Banelings roll in and you back out your Marines, only to leave your Siege line vulnerable to Cracklings. Now, sure your Marines will be back in a second to back up your Siege Tanks, but Cracklings do a lot of damage, and odds are there might not be any Siege Tanks left. If they're spread out, that's more time those Cracklings spend in transit (thus more likely you'll keep some Siege Tanks). Sure you'll lose some of your Siege Tanks, but the more space between them the more of those high gas units you'll be able to keep around.

If you have more than 5 tanks, clumping can be more advantageous than spreading because more tanks are attacking the same target when they come in range and with that many tanks this means targets will die instantly before doing any damage, this is good vs bioball and gateway units and spell casters because they won't be able to get in range without taking heavy losses, especially when you block with your mobile units.

Unlike SC1, SC2 tank AI is very fast at knowing when a unit is dead so they don't waste shots. This was one idea that was brought up about nerfing the tank on the forums, to reintroduce the old AI but blizzard opted to reduce the damage-- thus more tanks in the same place means shot's aren't wasted as compared to SC1 and you're still doing massive damage at a far range and with splash damage.

Chances are, if they try to close the gap vs tanks and waste aoe on the tanks as opposed to your infantry, your army will come out on top. That's the idea.