Per OP's request, I gave this its own thread: https://www.reddit.com/r/heroesofthestorm/comments/3sl0xg/yaptr_thread_the_math_behind_damage_scaling_it/
THE MATH: (warning huge nerdy post)
Damage has almost tripled at level 1. But that damage increase also came with not only an HP increase, but a healing increase. So it's not as simple as "3x the damage at level 1".
All this is based off the numbers from this spreadsheet: https://docs.google.com/spreadsheets/d/1VzuQvKT2vnOdnvQp9IHUVr-_M3KoXTKbTGQRXGMdrHI/edit
Let's just look at HP, between a simple tank (Muradin) and a burst assassin (Kael'Thas) at level 1:
Muradin's HP used to be 1040, now it is 2557.
Let's say KT comes at Muradin with both barrels: a Flamestrike, two Living Bombs, and 4 AA's (long enough for the bombs to explode):
Old scaling:
102 (FS) + (82+41)2 (Bombs) + 394 (AA) = 504 dmg
New scaling:
247 (FS) + (237+119)2 (Bombs) + 914 (AA) = 1323 dmg
In the old scaling, Muradin has 536 HP left (51%) and in the new scaling, he has 1234 HP left (48%).
The difference is real, but it's subtle. But now let's look at the one everyone's talking about, Thrall, who will use Chain Lightning, Feral Spirit, and Windfury for more AAs (being generous and giving him 6), over the same period of time (4s):
Old scaling:
67 (CL) + 50 (FS) + 55*6 (AA) = 447
New scaling:
185 (CL) + 159 (FS) + 179*6 (AA) = 1418
In the old scaling, Muradin would have 57% of his health left, but in the new one, he has 44.5%. That's 12.5% more damage from Thrall, which explains why he's so tough now.
Surprisingly, Muradin is actually one of the best case scenarios in terms of new scale HP. It gets even worse when you look at heroes whose level 1 HP has suffered due to the patch. Raynor is especially vulnerable, as his old Level 1 HP was 725, and now it is 1427 -- not even 2x as much.
Put it this way: if KT unleashes his full assault, in the old scaling, Raynor had just over 30% health at level 1; he doesn't even pop his Adrenaline Rush. In the new scaling, now he has 100HP left. If Thrall hits Raynor as described above, in the old realm he was even better off, down to just 35% health.
In the new scaling, Raynor is fucking dead. (~9HP left)
What's going on here, mathematically? Well, stats before had a base amount (value at level 1) which I'll call Base or B, and an amount that it went up per level, which I'll call Per-Level or PL. The bigger PL is compared to B, the better off that stat is at level 1 in the new scaling. Thrall is so powerful because his Auto Attack Base is 38, but his Per-Level is 17, which is 44% of his Base. That's the second-best ratio in the game (Valla's is higher). Auto Attack ratios (excluding Chen, Stitches, and Abathur, who really suffer at Level 1 here) are all above 25%. I haven't done the work of looking at ALL damage abilities, but a cursory glance shows they've got ratios of 20-30%.
However, if you look at HP, the best scaling hero was Stitches (or Azmodan), whose Base was 800, and Per-Level was 260 -- 32.5% of his HP. The worst (excluding Abathur) was Nova, who is at 18.6%.
Basically, HPs scale either as good as or worse in the new system than all other forms of damage. This tilts the balance of things in the early game towards assassins.
The flip side? "Glass cannon" assassins are now easier to kill at early levels. Everyone seems worried about the resurgence of Nova, but now she's just gotten the biggest Level 1 HP nerf outside of Abathur. If you look at the KT damage above, it seems like a lot, but then also realize that his HP has only increased by 206% -- which means that a mirror KT would take him down to 13% in new scaling compared to 32% in the old.
I actually came in here with the hypothesis that people were blowing it out of proportion, but no, the math basically represents what people are experiencing in PTR. My conclusions from just looking at the math and not having played it at all:
This will benefit assassins with larger health pools like Thrall or The Butcher; more fragile assassins will be riskier to be aggressive with.
This will only change early game (pre-10) balance. These skewed values approach the old scale very quickly. By level 10, the results will not be nearly as drastic. Thrall's AA, for example, will have gone from 3x the damage to just 1.2x, and Raynor's HP will be 1.12x his old value -- so the difference will be very slight.
Caveat: Don't take my word for it. If you spot something wrong, I'll change it, and my conclusions could be completely flawed!