I believe the attacker gets some extra bonus for attacking, I'm not sure what the multiplier is though.

plus i think that there are some other random numbers thrown in there for the heck of it just to make things interesting.

Plus there's the Luck factor. Does your race have Luck? (I think there is only one option for luck, +25%.) Maybe the Drengin don't but you do? How easily are you winning these battles? Do you just have 50 or 100 or so soldiers left afterwards, or are you winning by large margins? Also, what is the happiness of the planets you are attacking? If I recall correctly, planet morale plays into how well the planet will fight (I know that the "Information Warfare" option will get plenty of soldiers to defect if you use it, but it seems you're using traditional warfare).

Also, what level are you playing on? Is it possible that on beginner levels, the defense is crippled for the AI players?

There's nothing random about the ground invasions. If the invasion is 25v5, you kill 5x as many troops as you lose. So your 1000 troops can kill up to 4999 troops and win. All of the soldiering and tech numbers just modify the single random roll you make to determine the outcome of the fight.

Now how are the advantage numbers determined? I have no idea.

it mostly depends on how lucky (not the in game bonus, just plain old human luck) you are when you click the invade button. In the situation you are describing you could get anything from about even odds to about 5:1, which you did. Attackers do get a fairly significant advantage, I believe this is a design desicion to make it actually possible to conquer planets without having to decimate your own population.

Send in your debug file or update your video drivers, or both, quick

There's nothing random about the ground invasions. If the invasion is 25v5, you kill 5x as many troops as you lose. So your 1000 troops can kill up to 4999 troops and win. All of the soldiering and tech numbers just modify the single random roll you make to determine the outcome of the fight. Now how are the advantage numbers determined? I have no idea

I'm not sure that that is true.

I lost a planet to the Dread Lords in the campaign once. The Dread Lords suffered no losses.

I reloaded a save that I had made the turn before invasion and did let them invade again. This time I actually defended the planet successfully. I don't have hard numbers, but there appeared to be a random element beyond the ratio generator.

The random bit appears to be when you press space to stop the numbers changing.

It would be nice to know what exactly is going on here, so -- at the very least -- one might be able to re-evaluate the worth of the soldiering ability, amongst other things.

It's called, "Allowing a 1,000 population invasion to kill 5,000." Without it, you'd be getting closer to 1:1 ratios, which would make the already difficult planetary invasions even moreso.

I've seen questions on race abilities and bonuses before that ultimately boiled down to: "Yes the X civ does get a 20% morale bonus vs. the other civs - you just can't see it on the screen becasue of incomplete disclosure." I think this situation is similar.

When you attack a planet, the screen displays your soldiering bonus and tech advantage. I'm not sure how the tech advantage weighs in, but the soldiering bonus appears to have a direct correlation to the "advantage factor". (The advantage factor usually shows up as something like (Attacker advantage:0, Defender advantage 2".) I think there is a problem with lack of documentation on the screen here. It is my understanding that the attacker gets an automatic +5 to their advantage factor for air superiority. I believe (but don't know) that a +5 in advantage factor translates into the equivalent a roughly +50% soldiering bonus. The probem is that this information is not provided on the screen.

This "air superiority" advntage is likely much of what you are witnessing when you seem to always have the "die rolls" go in your favor. I am willing to bet that as the defender's advantage (as disclosed on the screen) gets closer and closer to 5 above the attacker's advantage (as disclosed on the screen), you will find that the "die rolls" seem to come out closer and closer to 1:1.

As for luck (and by "luck", I mean the luck factor actually coded into the game, not the luck of hitting the spacebar) - my understanding is that it plays a minimal factor in the results, basically tweaking the actually battle results slightly to the attacker or defender.