Speaking of those arena statistics, I have a noob question I'd like some veterans to help me understand.
I personally "feel" like I do better in games when I have the coin, particularly with jade druid since the coin helps with getting more powerful cards out early when needed, or with driving auctioneer. However, this is obviously an unscientific feeling and I haven't kept statistics.
My question is: Why would the first player win so much more often in arena? Is a chance of getting a 1-drop down in the first round really that powerful? It seems to me that 2-drops are far more common, and if you don't put a 1-drop then the second player will coin out a 2-drop and leave you already behind. Is there something else at play here?
(Also a related question: If a 1-drop is so powerful, should you basically mulligan everything for a chance at getting one?)
Constructed is very different from Arena.
In Constructed, you have more combos and synergies that you can take advantage of as the 2nd player because the 2nd player also has one additional card to work with. In addition, you have more spells to come back from a deficit along with other recovery tools that you have specifically put into the deck. Control and combo decks do fine in Constructed going second... going first has advantage in aggro/tempo match ups in Constructed.
Guess what Arena is played as for the most part? Aggro and tempo for the most part. In a game of tempo, first player has massive advantage. In Arena you cannot count on synergies and combos so having that extra card doesn't mean as much. Also you are less likely to have recovery tools/answers to their tempo plays so once you are behind on board it snowballs out of control.
In your example of coining out a 2 drop... that's a risk that the player going second is taking. They are going for a one time tempo play at the start and if it gets answered they are not favored to win the match anymore. Imagine if the player going first does nothing on turn 1 and you coin out a 2 drop. They answer with Dark Bomb or Frostbolt, then you play another 2 drop. They are now on 3 mana crystals and will play a 3 drop that contests your 2 drop freely, you play your 3 drop, their 3 drop kills your 2 drop for free and they play a 4 drop. So you went all in as early as turn 2 and got punished which resulted in a snowball effect.
A person going first playing a solid 1 drop is heavily favored to win the game in Arena. There are statistics on all of this. In addition, 1 drops are very powerful for their cost and many 1 drops contest 2 drops. Let's they play a 2/1 1 mana minion (very average even mediocre 1 drop) and you are not one of those classes with a ping. You have a 2 mana 3/2 card that will die to a 1 drop. You are now in a terrible position because they got to play a 1 drop on curve to contest your 2 drop. Now imagine if they play a Trogg/Mana Wyrm/Chow/Mixtress/Flame Imp/Buccaneer or other 1 drops that can grow or combo with another card.
It's a snowball effect in Arena that is very hard to stop because of the limited options. That's why Blizzard wants to increase the amount of spells that are drafted, so that there is less of this player 1 snowball effect.
You should mulligan for 1 drops based on match ups. Most tempo/aggro decks always want a 1 drop. If you are playing a control deck against another control deck then you don't really want a 1 drop and you instead want your greed cards (the Kazakus, the Twilight Drakes, the Mountain Giants etc.). Sometimes in very specific match ups like say a Shaman vs Warrior, it's not uncommon for high level plays to mulligan away Tunnel Trogg in favor of a Totem Golem to avoid the turn 2 War Axe punish.
If I am playing Zoo, I am mulliganing HARD for 1 drops in almost every match up. Hell I would even drop certain 1 drops against certain match ups for better 1 drops because I have so many 1 drops. In other decks, if I am going first I REALLY want a 1 drop at start. If I am going second and if I have two solid two drops then I would probably want to coin one out and not need a 1 drop there. There's more nuances to this than just that but generally if you are playing aggro/tempo or playing control vs aggro/tempo... 1 drops are REALLY good on turn 1 so mulliganing for them (even all the way) is not usually wrong.
I just want to point out the stats are probably not nearly as slanted as kripp's "data" of a grand total of 38 games suggests.
https://hsreplay.net/articles/4/mulligan-luck-arena
The stats at large are damn near undeniable. Sure it's not as slanted as Kripp's own data but there's a gross difference between going first vs going second in Arena.
If you go first and drop a 1 drop against someone going second then you have a difference of 15% in win rate in some cases. That's 45%vs 60% in some cases. That's kinda outrageous.
If you go first and not even drop a 1 drop then you are still favored to win by about 6% more.