If there's one thing I like about League of Legends, it's that nobody randoms in that game. The option is there, but nobody ever randoms. In fact, I have roughly 700 total games played in League, and I do not remember a single occasion where a player had consciously randomed. I've seen people random by accident, as they were afk, but never by will.
And you know why? Because there's literally no advantages to randoming in League. You see, in DotA, when you random, you get extra 200 gold or so. That's as much as 33% more starting gold. The advantage of this is so great that a lot of players get hooked on randoming.
I've heard a lot of players say, "I'll still random even if they don't give me the extra gold" and that is an utter, and an absolute bullshit. The expected value of randoming is now effectively lower than picking a hero, and therefore any player with a half-a-brain should be opting to pick. And you see this in League.
Sure, there are always going to be those that will random for whatever (stupid) reasons they have. That equity is always there, never a complete zero. I'm sure there are those who random in League as well. However, it will be significantly lower if random gold is taken out. And it's well shown and proven in League imo, as really no one ever randoms in that game. Whereas in DotA, the equity of randoming per game is probably.. easily ~20%. That's at a rate of 1/5. And it's probably true. I've always had at least 1 randomer per game.
Although, I have to say, another reason why random is less frequent in League is because the backlash of randoming is way greater in League than it is in DotA. And that's because the game is hugely limited compared to DotA. There's only so much you can do regardless of how godlike you are at the game. And because of this, the picks matter so much more than DotA. You can be the greatest player in the world, but there's only so much you can achieve with say, Evelyn or Sivir.
Whereas in DotA, an excellent player has a huge advantage over mediocre players. And that edge is so big that it can neutralize the picks element of the game at times. It's true, if you are good enough, you can just run all over your opponents. There's more room to express your edge. However, this only works up to a certain level. There is a point where picks start to matter. At which point, the value of randoming then drops significantly. The proof of this would be the tournament scene. If randoming was so damn great, pros would random in tournaments. But they don't, because it's simply not worth it. You don't see it in other games either (fighting games for one).
As far as ARTS genre goes, I believe League has taken the right step to discourage players from randoming by making it -EV vs. picking. Whereas in DotA, there's an incentive to randoming due to random gold. In a genre of a game where picks are an important element of the game, it's completely asinine that this incentive even exists, encouraging players to random.