I think the dice will affect the game as much as you let them. This is both from a tactics perspective--some people will try to focus and target lock constantly to mitigate bad rolls while others may try other actions hoping for dice--and especially from a mental perspective:

In one game in my Kessel Run tournament, I was rolling pretty hot and my opponent was not getting some of the rolls he needed. He moaned and got angry and played incredibly quickly, perhaps making some mistakes. But my great attack rolls that he kept complaining about were because I had a target lock for all my ships each turn to spend on rerolling, or at least a focus to change otherwise bad rolls into good. He essentially gave up after a few turns and went through the motions until I wiped him out. This shows both me controlling the amount of luck in the game with my target locks and the luck in the game controlling him mentally with frustration.

Of course, there was also a game I played where my opponent scooped after turn 2 because I rolled 1 miss on my first 17 dice. Though even with that I don't think he was completely lost and would argue that he could have engaged me better initially, reducing the amount of good attacks I could make and upping his.

Anyway, I like using dice, it provides a constant source of excitement (and a good excuse for when I lose).

Now that I have several more games under my belt, I think I have a decent grasp. 

I've played about 20 games against 12 different people; so far I've lost only once. I've played about 14 games as the Empire and 6 as the Rebels. My only loss was in an Empire vs Empire match. Though I freely admit luck plays a huge factor, I can't attribute this record purely to luck…

Luck plays a factor in 100% of the games. That said, your build gives you lots of opportunities to bend the luck in your favor and mitigate the impact of bad luck. Here are some build tips for increasing the odds of luck going your way:

• Ships with shields significantly reduce your risk of taking lethal crits.
• Combos like Concussion Missiles + Squad Leader to allow focus + target lock increase your odds of scoring hits.
• Focus on offense over defense; there are greater odds of scoring hits than evades.
• Generate as many attack rolls as possible; the more often you roll, the more likely to succeed.
• Builds that grant additional ATK dice are more successful.
• Secondary weapons at long range give you a mathamatical advantage.

Build without skill and experience can't negate the luck factor. You need to learn the maneuver dials to increase you odds of getting favorable position while denying your opponent shots. You need to be able to get hurt ships out of the line of fire or into positions where your opponent can't utilize their most effective weapons. 

I don't believe in arbitrary percentage breakdowns of luck v build v skill. The game's primary mechanic is based on die rolls; that means luck. The pilots and equipment at your disposal can be used to bend the luck curves. And skill + experience help you recognize the best actions in a given moment to grant you the best odds while possibly denying your opponent shots. Without a good build the game is mainly luck. Without experience and skill your build will not effectively mitigate luck.

I have to disagree with everyone who says that this game doesn't involve a lot of luck. For one thing it is a dice game which always means you can be unlucky with rolls. Secondly, this game relies more on luck than just about any other TT game I've played. (including 40K, Fantasy, Anima Tactics, and Infinity) 

I think Infinity and Anima Tactics recquire far more skill in tactics than this game does. Luck plays a signifcantly smaller factor in those games than it does this one. I have seen multiple games of X-wing where one player has out manuevered his opponent most of the game and either lost or nearly lost because of bad luck. Very rarely does something like that happen in AT or Infinity. (for reference those games use D8's and D20's respectively)

Even 40K and Fantasy rely less on luck. Though I think this is because the luck evens out over the course of a game(in general). This is because you are making dozens more dice rolls. The more you roll, the better chances you have to change your luck.

Now that said, I do love this game and think that if you maneuver well and build a good squad you significantly increase your chances to win. There is definitely a lot of strategy and tactics that can be had in this game and trying to predict your opponents movements is one of the best parts of the game. But to say that luck plays a minimal part in this game is simply not the case.