Starcraft 2: Marine vs Marauder

Solution 1:

You're almost on the right track, but some of your math is a little off.

First I'm going to define effective DPS:

100 * Damage / (Attack Cooldown * (Minerals + Gas * 2.5))

Next let's look at the Marine and the Marauder:

Marine:   100 * 6 / (0.86 * 50)               = 13.95  
Marauder: 100 * 10 / (1.5 * (100 + 25 * 2.5)) =  4.10

So the Marine has about 3.5 times as much effective dps.
For the Marauder to win out against the Marine you'd need at least 3.5 times as much HP.

The Marauder to Marine ratio is 125 / 45 = 2.7

Ultimately, the opinion on TeamLiquid has almost nothing to do with this calculus and everything to do with real world experience. In real world scenarios groups of Marines beat out Groups of Marauders, not only because the Effective DPS ratio is higher than the Hit Point ratio, but also because Marines take up less space; this means that more Marines will be able to attack at the same time. Ultimately that math trumps just about any theory crafting you and I could perform.

Note, that in Marauder vs Marine, Marines only do 5 damage, which reduces their effective dps to 11.6, and the dps ratio to 2.8. While this still gives the advantage to the Marines, it is paltry compared to the size advantage.

Solution 2:

The top post is excellent, but a few more things that are missed here.

1) Marines build faster. This has very large ramifications, especially when considering the ability to replenish an army.

2) Gas is worth more per unit then minerals.

3) It is easier (cost wise) to inject tanks and other supporting units in to a marine army, while you will have to cut more in the way of marauders (due to gas restrictions) in order to get the same effect.

Solution 3:

This answer just adds further points to tzenes and windfinder.

You have to consider that Marauder have projectiles and Marines do instant damage. This might seem insignificant, but it adds up.

For the arguments sake I assume you do not have the shield upgrade, this would also work otherwise.

While missile attacks can "overkill" an unit, thus wasting DPS, instant attacks just "kill" the unit. e.g. 10 Marauders shoot at the same time at 1 Marine dealing 100 damage, but you need only 45 damage to kill the Marine, thus you loose 55 damage.

On the other hand 30 marines shoot at 1 Marauder, dealing 126 damage with 9 doing nothing (potentially shooting at another Marauder). They just waste 1/126 damage.

This might seem insignificant, but Marauders shoot slow and you cannot effectively prevent them from doing this. So basically Marines profit from focus fire, but Marauders do not and focus fire is very beneficial in a battle.

Even if you are able to micro Marauders perfectly, you lose at least 5/50 damage (10%), because Marines have only 45 health.

If this is not enough it gets worse with upgrades. Assuming you could build 3 Marines instead of 1 Marauder resource wise at +1 upgrades 30 Marines deal +30 damage, while 10 Marauders deal only +10. It gets even worse für +2 and +3 upgrades.