Balancing Heroes

I've come across the agonizing challenge of balancing heroes.
You see, i have four ranks of hero 'power'. Lieutenant, Commander, Racial Leader, Ledgendary.
Lieutenants are the base and are built in a 1:5, units it can kill without risking death. Commanders are twice at powerful, racial leaders are three times as powerful, and ledgendaries are six times stronger.
But you see, the problem in making them balanced is that a 1:10 ratio is not twice as strong as a 1:5 ration, because of a think I call exponential power gain. (Each unit added increases damage exponetially)
Example:
If you have 5 units attacking you, they deal 10 DPS each, and takes 2 seconds to kill each, the total damage dealth to you is.
50+50+40+40+30+30+20+20+10+10=300 total damage
If you have 10 units, all same stats, and you deal the same damage
100+100+90+90+80+80+70+70+60+60+50+50+40+40+30+30+20+20+10+10= 1100 total damage. You see the change?

What do you think is more efficient, using double the ratio (1:10) or just adjusting to resist double the total damage or a 1:5 ratio?

I think that as long as heroes from one rank can clearly beat heroes from another rank going solo against each other, then you have accomplished your goal well. How much ownage you want the hero of the higher rank to have would determine how wide you make the gap.

1100/20 is 55 dps resisted,
2 * 300/10 = 60 dps resisted.

I would choose being able to resist 20 units just because the dps gap (55-30) is smaller. If I was using a ranking system like yours (which sounds pretty cool, btw) I would think that 5-7 dps difference would be enough to clearly differentiate ranks. But that's pretty much an artistic vision thing, maybe you want each rank to be able to DOMINATE the lower ones instead of just beat them. In my opinion, it is better if numbers have *some* chance of beating quality. This allows for players to pursue either a numbers strategy or a quality strategy. If you make either too powerful, players are basically shuttled into choosing whichever is better.

Please learn the difference between polinomials and exponentials - it is very important.

More powerful units should be less powerful for the cost to be balanced, to account for the greater long term efficiency.

Sorry, I was just trying to imply it wasn't a linear relationship.
Let me clear this up, you don't pick heroes, each player has certain named heroes that are balanced according to rank. All the heroes are already balanced, its just a question of how i should balance them to the units.

don't make the ones directly above too much better then the one directly below, other wise it ends up being pretty shitty and u have to run when ever u see a stronger enemy. reminds me of dota and other AoS... course this all depends on the moves they have. maybe a lower level "hero killer" could beat a higher level "unit killer" but it should probably be close.

== a real balancing hero xD (omg rofl)

lol? what is that any way, Estonian?