Random thoughts:
- Yes, you won't beat dredge. Either go >= 6 or 7 sideboard cards or 0.
- Is Pyromancer good? Seems you have very few ways to trigger him. I think if you're going to play Pyromancer, you should be thrilled to cast him T1 off a mox if you draw him, but I don't imagine that'll be true here. Consider cutting him for more disruptive cards or mana.
- Have you considered Abrupt Decay and/or maindeck Claim? You seem very soft to Oath.
- No Mox Pearl? Turn 1 Bob seems to be one of your best plays.
- Skullclamp seems pretty bad, given how weak Pyromancer seems to me.
- 21 mana sources seems super low, without Gush. Try to push that to 23 or 24 at least.
I agree with most of these suggestions. As a more effective replacement for Pyromancer, Tarmogoyf is the go to beater. I actually think it is an insanely good card in the metagame right now. I would cut the snapcasters. It is very often just a clunky card, and while its not bad, abrupt decays would definitely be better in that slot. Decay hits key cards from almost every deck in the format. I would also try to cram in 2 thought seize. It gives you information and is disruptive. A mana drain or two also wouldn't hurt. Good luck!