I ran some interesting tests with these two skills of the Arcane Soldier. At the time of the test, he was level 26. Flame Strike was on skill level 10 and Ice Strike on level 3. I played on hardcore.
I used a weapon with 18 damage and no weapon enchantment. I usually delivered 3 hits and counted the numbers. Then I changed the weapon to 14 damage + added damage against humans. And delivered 3 hits again.
Ice Strike
Wyvern
Physical damage: 23 / 21 / 24 ----> 19 / 19 / 19
Frost damage: 24 / 19 / 22 ----> 25 / 14 / 18
Freeze time: 12 / 9 / 11 ----> 12 / 7 / 9
Burglar
Physical damage: 26 / 28 / 28 ----> 34 / 32 / 36
Frost damage: 23 / 24 / 22 ----> 30 / 25 / 28
Freeze time: 23 / 24 / 22 ----> 30 / 25 / 28
Thief
Physical damage: 28 / 28 / 28 ----> 36 / 33 / 33
Frost damage: 22 / 24 / 24 ----> 34 / 17 / 26
Freeze time: 18 / 22 / 19 ----> 19 / 14 / 21
The numbers are definitely weird. The freeze time seems to be based on the actual frost damage when you look at the Burglar numbers and is definitely way too high. Is there some bug with the decimal places? E.g. 30 sec should be 3.0 sec instead?
Flame Strike
Burglar
Physical damage: 28 / 26 ----> 34 / 35 / 36
Flame and burning damage: 23 / 21 ----> 19 / 14 / 17
The tooltip states 8 - 16 fire damage. As you can see the flame damage decreased when equipping the lower damage weapon. From the tooltip it is not stated that the flame damage should increase with the base weapon damage. Is this a bug? Was that the reason why Flame Strike got nerfed in the recent patch?