Which imbued wand deals more damage - Cobra Wand or Falcon Wand?

Question

You see a cobra wand (Range:4, magic level +2, critical hit chance 10%, critical extra damage +35%).
It can only be wielded properly by sorcerers of level 200 or higher.
It weighs 19.00 oz.

 You see a falcon wand (Range:5, magic level +3, protection fire +8%).
It can only be wielded properly by sorcerers of level 300 or higher.
It weighs 33.00 oz.

Recently I got lucky and looted cobra wand. I'm trying to figure out the price by comparing it to the falcon wand. 

With imbuements the items give:

• Cobra wand - +6 magic levels, 10% crit chance, 35% extra crit damage 
• Falcon wand - +3 magic levels, 10% crit chance, 50 extra crit damage, 8% fire protection

I am skipping mana leech as it's same for both, also skipping irrelevant details like range/  dmg. 

Obviously, you could put a magic level in falcon wand but most people don't do it as they prefer mana leech so please focus on a combination of items/ imbuments as above as I think it will be the standard setup for both items.

Falcon wand has an obvious advantage of 8% fire protection but did anyone did the math which is better - additional 3 magic levels of cobra wand or 15% higher crit damage of falcon wand?

I would like to see the answers with some math or solid explanations rather than purely opinions. 

Btw. there was a question asking to compare cobra and falcon items recently but the answers there regarding wands are not sufficient. 

Comments

Your question was already answered in this one:
https://www.tibiaqa.com/4833/cobra-items-are-better-than-falcons-items-yes-or-no-and-why?show=4833#q4833

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The user mentioned that the answer there is not sufficient + this question is a little more specific in what it asks for in the answer

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oh, right, didn't see last part. Apologices ;P

Answer 1

Fingercrossed for my maths to be right.

Let's take an example:

• ED 300
• Magic level 100
• Average SD damge (according to tibia-stats.com): 685
• How much damage would he deal depending of the wand he wears with 100 SDs?

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• Without Wand: 685x100= ~68500
• With Cobra Wand: (Range:4, magic level +2, critical hit chance 10%, critical extra damage +35%).
  • If you put mlvl on it, it would make this ED raise 106 mlvl: Average SD damage: 720
  • 10% aditional chance of 35% extra crit, means 10 hits of over 972
  • 100 SD would deal a damage over: 972x10+720x90= ~74520
• With Falcon Wand:  (Range:5, magic level +3, protection fire +8%).
  • If you put Critical on it, this ED would have 103 mlvl: Average SD damage: 703
  • 10% aditional chance of 50% exra crit, means 10 hits of over 1055
  • 100 SD would deal a damage over: 1055x10+703x90= ~73820

This is following your thought of people not using magic level in the falcon wand, which I think is not true in many cases where they try to make the maximum damage.

• If we do the maths using mlvl on the falcon wand this is the result:
  • The ED would have 107mlvl: Average SD damage 726
  • 10% aditional chance of 50% exra crit, means 10 hits of over 1089
  • 100 SD would deal a damage over: 1089x10+726x90= ~76230

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Conclusion: Cobra wand is kinda better as long as you don't use mlvl on the falcon wand, not counting the fire protection of the falcon wand too.

Comments

I have done some calculations on my own and it seems that Cobra Wand is slightly better in terms of damage as well (nothing big like 1dmg more average on avalanche and 10 on hell's core).

Thanks for putting time into those calculations.

Answer 2

The best is:  Falcon Wand.

In number do you gonna deal more damage with 15% more on crit damage than with 3 more magic levels. Also the fire protection is really useful.

Answer 3

I consider Sorcerers must deal the highest damage possible, so Falcon Wand is the best option, and you have an extra of 8% fire protection which help a lot in most of hunting grounds.