I think the key is that via "more damage" or larger range of damage, you get the swingy factor, because via hit or miss to do 12 or 0 damage or hit or miss and do 1d12 to zero damage is kind of similar effect.
This concept came up during a cofee break at work with some co-workers.
They were talking about sports and being from India, american sports aren't the same as what they have there. Namely cricket and soccer, where despite the skill of the team, the outcome can shift greatly.
What these guys were unknowingly talking about is "swinginess" in an athletic game.
Consider soccer, where the score does not go up very high. Games of 1-0 being common. If you liken the score to hit points, and scoring to be damage, it's pretty much the same problem.
When it only takes a few hits (your HP divided by the average damage) to take you out, that's a very swingy game. First, it only takes a few rounds to take you out anyway, and one bit of bad luck and it's even faster.
Whereas, when you can take lots of hits (lots of HP versus minimal damage per round), the fight lasts longer. This means you can consider other alternatives to simply trading blows to give you an advantage. This is certainly where 4e seems to have done, by making "basic" combat have high HP and low damage output. Then the cool abilities and spells shift that, which is where the strategy and opportunity comes in.
If you can only last a few rounds, there's not much room for tactics. Given that the typical 3e fight was 6 rounds...
