In my latest game, I was the second to weakest military force in the game. I just trounced the top military power. I went from last place to first place over the course of a few months.
How? First of all, I'd spent time building up my alliances: I cozied up to a couple of the mid-level powers by giving them free stuff. and generally kissing buttock. I developed my planets. I built up a good infrastructure and fortified my constructors. I flipped one of my smaller factory planets to a research planet and started researching soil enhancement so I could turn my crappy planets into decent ones. Then I took on a minor race and stole their PQ 15 planet. Lo and behold, the frogs had researched Plasma II: that's at least two ranks higher than any other weapon system in the game. I used my new plasma weapons to build some fighters and conquer the second-suckiest race in the galaxy.
This got the attention of the Tech Cheese (the big dogs, custom race with mondo research bonuses) and they immediately attacked me. My allies jumped in, and TC wound up on a four-front war with me and my allies. Right away, I found out that my Medium-class frigates were no match for Tech Cheese Battleships, so I sold my plasma technology to the Arceans in exchange for Superior Hulls (I think that's the one, the one between Medium and Large Building).
Still, it looked like I was about to be pwned, especially when two of my allies signed peace treaties with the Cheese. I was able to bribe one into resuming hostilities, the other wanted nothing more to do with it. However, I was able to bribe the Drath into attacking the Cheese by exchanging my now obsolete Laser technology, and some cash too. I got a lucky break when a major event popped up that increased my tax revenue something sick. I got a second lucky break when a galactic event increased reproduction rates: my planets were some of the few that had room to grow, and grow they did. I got a third when the Tech Cheese, sick of fighting a four-front war, sued for peace. I took it right away.
Instead of resting on my laurels, I prepared to go back to war. I ordered my tax rate lowered so I had 100% approval, maxxed out production, and switched to 100% research to grab Large Hulls right away: it took me 9 weeks. I then started provoking the enemy into declaring war again by massing my fleets on his border: the Cheese declared war again, and my allies jumped back into the fight.
My first generation battleships turned out to be swiss cheese against the Tech Cheese Battleships: the enemy had a three-to-one kil ratio, and even their Medium frigates could kill my Large Battleships in a one on one fight. I then redirected research to advanced Plasma weapons and abandoned Point Defense on my Larges, focusing on putting as many guns as possible. In the meantime, the Arceans attacked an outlying Tech Cheese world: they died, but they killed the Battleships and my fleet of Mediums was in place to mop up the survivors and invade, capturing the Tech Cheese Research, Industrial, and Manufacturing Capitals (I kid you not, they built all three on the same planet

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My upgraded "World Slayer 2" was nowhere near as strong as the TC's battleships, but I had two advantages: first, the enemy battleships were all using Point Defense, which was useless against my Plasmas. Secondly, with my six factory worlds working at focused military production, I could churn out a World Slayer about every turn. It turned into a battle of attrition: the enemy battleships still had a 1.5 to 1 kill ratio, but they were up against multiple pairs of World Slayers each battle. They would kill one fleet and immediately get attacked by a second, then a third. Meanwhile, my few surviving Mediums and Smalls were running around behind enemy lines wreaking havoc, destroying mining bases, shooting down freighters, running away when the enemy Battleships drew near. My spies were dispatched to the TC homeworld to take out their factories and prevent them from building new ships. When the Tech Cheese and the Torians signed a peace treaty, I bribed the Torians into resuming hostilities.
I then took over their homeworld and used the starport to build more World Slayers. The remaining assault shuttles swept through the rest of the TC worlds and soon eliminated all resistance. In the end, the TC dispatched a fleet into my territory to attack my resource bases. Those resource basees were in the middle of my industrial worlds. It was the matter of a couple mouse clicks to fast-buy a couple World Slayers and send them in: they died, but they reduced the fleet to a single wounded battleship, and the next two ships off the line finished the job one week after the last TC world fell and the Battleship became a pirate vessel.
In the end, the Tech Cheese's graph went from a mountain peak to a valley faster than you could say "PWNED." Three factors helped me win:
1. I had strong allies who could help me shoulder some of the burden.
2. I had a much higher production base and could field more ships.
3. I was lucky. More than that, I took full advantage of the luck I was given.
So if your numbers are low compared to the AI at the beginning, don't think of it as an indication that you necessarily suck. Imagine, instead, how much more awesome it will be when you take them out. The game is pretty good about lucky breaks, bad or good, changing the scope of the game, which pisses some players off pretty badly