Wtf? In game battles include no luck. Every field trainer can be beaten eaisily, maybe except Steven. Then again, the Gym Dumbass and the Weak 4 require no skill at all, as ALL of them have all Pokemon of the same tpe each. The only trainers that could be hard and are more clever than other in-game trainers are in the BF. But again, they can be beaten eaisily. The only trainers that could be hard to beat are the Frontier Brains, but they're not clever enough to be able to switch their Pokemon or EV train.
But competive play is another story. Unless you are battling someone who doesn't know about EVs, IVs, natures and all that stuff, it's still not the question of luck, but a question of skill and knowledge about Pokemon. The only thing that involves luck in competive battles is the start, and if your moves hit. Unless you know the person well and know what Pokemon s/he will be using, you need to be ready for a switch.
Conclusion:
In-game play requires no skill and luck outside the BF. You can beat any trainer with all Pokes un-ev trained with sucky natures and 0 IVs everyhere if ti's not the BF.
The BF is the only in-game place where you need some skill.
And Competive is where it all becomes harder, because you battle other people who also EV train and IV/nature/ability breed.