Short answer
Low Blow is always at least as good as Savage Blow, and under certain conditions, it outperforms Savage Blow. Savage Blow can never be better than Low Blow.
Long answer
We can explain mathematically why this is the case.
Description of Low Blow, Savage Blow and Powerful Strike
Powerful Strike: Powerful Strike is an imbuement that can be applied to weapons. When applied, it raises critical hit damage by 50% and critical hit chance by 10%.
Low Blow: Adds 4% / 8% / 9% critical hit chance to attacks with critical hit weapons.
Savage Blow: Adds 20% / 40% / 44% critical extra damage to attacks with Critical Hit weapons.
Mathematical Model with Powerful Strike only (no charms)
Assuming our weapon is imbued with Powerful Strike, every 100 hits we have 10 hits dealing 50% more damage (critical). This can be written as
y = (100 * x) + (10 * x/100*50)
Where x is the base damage caused by the hit and y will be the total damage caused in 100 hits.
(100 * x) are the normal 100 hits.
(10 * x/100*50) are the 10 critical hit.
These are summed to calculate the total damage of 100 hits.
However, since we're only going to discuss critical hits, we can leave the normal hits out of the equation, leaving us with:
y = (10 * x/100*50)
Which can be simplified to:
y = 5x
This will be our original equation used in our comparisons below.
Model with Powerful Strike and Low Blow
Applying the values from Low Blow (levels 1, 2 and 3) to our original equation, we have:
| Low Blow 1 | Low Blow 2 | Low Blow 3 |
|---|
| y = (14 * x/100*50) | y = (18 * x/100*50) | y = (19 * x/100*50) |
| y = 7x | y = 9x | y = 9.5x |
Model with Powerful Strike and Savage Blow
Applying the values from Savage Blow (levels 1, 2 and 3) to our original equation, we have:
| Savage Blow 1 | Savage Blow 2 | Savage Blow 3 |
|---|
| y = (10 * x/100*70) | y = (10 * x/100*90) | y = (10 * x/100*94) |
| y = 7x | y = 9x | y = 9.4x |
Comparing the results
Comparing the simplified equations, we can clearly see that Low Blow and Savage Blow are equivalent on level 1 and 2, but Low Blow outperforms Savage Blow on level 3.
The outperforming of Low Blow on level 3 can easily be spotted if we look at the increase in both charms' effects from level 2 to level 3:
Low Blow: from level 2 (8%) to level 3 (9%), we have an increase of 12.5% in its prior effect.
Savage Blow: from level 2 (40%) to level 3 (44%), we have an increase of 10% of its prior effect.
We clearly see that Low Blow gets a bigger increase in its effect. We now understand why Low Blow outperforms Savage Blow on level 3.
The trick: increased critical extra damage from equipments
Tibia has equipments that increase critical extra damage, such as the new inferniarch items or the Soul War items. Let's take soulbleeder as example.
Soulbleeder adds 10% to the critical extra damage. In order to see how using a soulbleeder would affect our calculations, we have to update our equations and simplify them again.
Updating our equations to add 10% to the critical extra damage:
| Low Blow 1 | Low Blow 2 | Low Blow 3 |
|---|
| y = (14 * x/100*60) | y = (18 * x/100*60) | y = (19 * x/100*60) |
| y = 8.4x | y = 10.8x | y = 11.4x |
| Savage Blow 1 | Savage Blow 2 | Savage Blow 3 |
|---|
| y = (10 * x/100*70) | y = (10 * x/100*90) | y = (10 * x/100*94) |
| y = 8x | y = 10x | y = 10.4x |
Comparing the results yet again
We now see that Low Blow outperforms Savage Blow on every level when using equipment that increases critical extra damage. And, surprisingly, Low Blow level 2 becomes better than Savage Blow level 3!
But why does this happen?
The reason lies in scaling. Every percentage point added to critical extra damage will be multiplied by 14, 18 or 19 if using Low Blow, whilst being multiplied only by 10 if using Savage Blow. This means that Low Blow scales better with additional critical extra damage coming from equipments.
Conclusion
Low Blow outperforms Savage Blow on level 3 no matter the equipment, and Low Blow outperforms Savage Blow on every level if using equipments that grant critical extra damage. Otherwise, both charms are equivalent.
This is a graph of all levels of LB and SB with 10% critical extra damage applied.
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