First we ignore the damage to the controller. That is an attempt to balance it and we will evaluate it after we see what we are to balance.
Second this does only damage so one way to get a better view is to see how it scales for that you should open up Excel.
Turn | Attacks per Turn | Total Attacks(end of turn) |
1 | 1 | 1 |
2 | 2 | 3 |
3 | 3 | 6 |
4 | 4 | 10 |
T | T | T(T-1)/2 |
So now we know 2 things:
1) That its damage grows in a similar manner to Lava Golem(or other Atk growers) but at a different rate(starts at +4|+2).
2) Since it is increasing attacks and not attack it has multiplicative synergy with attack buffs like Blessing or Shard of Patience.
Now while that is brewing in your head let's talk interaction: Lobotomy / Liquid Shadow / "Target creature gains Venom"
Since the skill is activated(has an activation cost) it is automatically an active skill. This means it can be lobotomized/replaced with Vampire(another active skill) from Liquid Shadow. However you can choose whether the extra attacks remain(are a status effect) or are also removed(are part of the skill). The attacks remaining results in multiplicative synergies. When you balance the interaction with Blessing then these might also become able to be balanced, but for now let's remember there is the option to have these synergies not exist. You can, if needed, have lobotomy remove the extra attacks.
Now back to the balancing. Since we are comparing it to growers as a lower bound on its strength, then it would make sense to use their costs system as a minimum estimate for the costs we would need. This apparently means that we should have an activation cost and probably a non trivial one. Next compare a Blessing + Hastening Knight deck to a Lava Golem deck and to a Hastening Knight deck.
Interesting to note, since the more powerful usage of Hastening Knight has a detectable different(has higher attack) we might be able to use that to balance the card. What would happen if instead of dealing damage to us each attack, it attacks us for its first attack each turn(thus the drawback scales with the more powerful usage)?