They've stated the coin makes is what makes 1st to 2nd pick close to even in win rate and I believe them. It certainly makes it very very attractive when you get something like Wyrm/Arcane turn 1, but also a lot of times it's not enough on it's own to catch you up to the 1 mana deficit you are always facing going second.
I've only started to use some program that does image recognition and automatically parses stats, but I'm fairly sure my win rate going second in arena is quite a bit higher than going first. I find it's A LOT harder to get fucked out of a good hand when you go second since you can coin a higher cost card one turn earlier AND get an additional card to mulligan. It's very rare I get an unplayable hand when going second. If you go first and mulligan into 3 5+ cost cards, there's a good chance the game is over right away, unless your opponent also has the same shit hand or you draw the right cards every turn for the next 3 turns.
The lack of consistency in arena is annoying though, both in terms of making a good deck and in terms of balance between 2 decks. When some guy plays Sylvanas and Tyrion, there is only so much you can do. Getting topdecked by a second pyroblast is just soul crushing. It just feels really bullshitty when your deck has 1 rare and 29commons. Not that all epics and legendaries are good, but some of the best class cards are epics.
But anyway that's how it is. I've come to the conclusion that I'm probably not losing games because I drafted wrong, but either because I got fucked on draws, my opponent got very lucky on draws or because I messed up. Can't do much about the first 2 cases so I've been frapsing my games to check when I'm messing up and try to fix it this way, thinking more about what's coming next turn, taking better trades and so on. Most of the losses seem to be to RNG though(and some of the wins are also due to RNG) which is a bit annoying.
I've also come to hate Mirror Images. Might not be too good in constructed because of the consistency of the decks but mirror images in arena is a fucking pain to work through if you don't have the right cards at the right time. Worst being, 2 mirror images. Generally can't fucking do shit until turn 5 or so, mage just kills all your shit with spells and keep playing mobs behind the taunts, they don't do anything but stall but that's enough when you can't actually trade. By the time you've worked through the mirror images and the board, you're 15health behind and the game is pretty much over already since you're gonna eat fireballs. Such an annoying card.