Special Upgrades: Red or Blue
The question that made this blog a reality. I saw a friend of mine telling another that blue upgrade stones were better if your weapon had low damage. When I confronted him about it, he told me that a friend told him about it.
Most people will already know the answer to this question, but I feel that this is a good place to start and go into depth about why it is so.
In terms of physical damage weaponry, red upgrade stones will add a percentage of your damage onto the critical multiplier you already have, and blue upgrade stones will increase the damage of a weapon by a set amount. When used with a wand, it will increase your magic attack, while cylinders will gain special buffs depending on the type used.
For more information, check out the wiki article on Special Upgrading your weapon.
We are going to be looking into the life of Milletian, a sufficiently veteran player. Some things you need to know about him are that he:
has rank 1 in every skill he uses.
lands critical hits 30% of the time regardless of whatever enemy he faces.
has 80% Balance and 100% Magic Balance regardless of weapon used.
wants to maximize his average damage.
has infinite funds to support his damage obsession.
spends the remainder of his money on fashionable clothing in order to stand out when he AFKs in Dunbarton.
Milletian is standing in front of the Upgrade Anvil. The only thing on his mind is to maximize his average damage. To this end, he has the choice between red or blue.
First, we need to find all the required information. We will assume that the wiki is correct in all cases. While this isn't necessarily true, it gives us a good ground for understand.
The necessary information are the formula for critical hit and the modifiers for both Red and Blue upgrades.
The simplified formula for critical hit is:
CritDamage = Damage + (MaxDamage * CritModifier)
Because of 80% Balance, 1.25 * Damage ≥ MaxDamage ≥ Damage. This leaves a large range for MaxDamage, which is all we can do unless specific stats are added in. For now, let's assume that:
MaxDamage = 1.15 * Damage
This means that the formula for crit is now:
CritDamage = Damage + (1.15 * Damage * CritModifier)
In order to find average damage per hit, we're taking the fact that Milletian will crit 30% of the time. He will crit thrice in ten hits, so the formula for his average damage is:
AverageDamage = 0.3 * CritDamage + 0.7 * Damage
AverageDamage = 0.3 * [Damage + (1.15 * Damage * CritModifier)] + 0.7 * Damage
Now we can start calculating damage.
For Red Upgrade Stones, we add to the crit modifier:
0.3 * [Damage + (1.15 * Damage * 1.92)] + 0.7 * Damage
For Blue Upgrade Stones, we replace Damage with Damage + 27.8, as 27.8 is the damage added by Blue Upgrade Stones after balance:
0.3 * [(Damage + 27.8) + (1.15 * (Damage + 27.8) * 1.5)] + 0.7 * (Damage + 27.8)
Now, in order to see when one surpasses the other, we set them equal to each other and solve for damage, which comes out at 291. As long as your Damage After Balance is greater than 291 while wielding a single sword, provided the Max Damage is accurate, it is better to use Red Upgrade Stones.
Applying the same formula for the other weapons, you get:
Axe - 278
1H - 291
2H - 307
Merlin's Knuckles - 454
While these numbers are not unreachable, they are quite steep for the average player. Therefore, when you consider the costs of Red or Blue, it's generally a better idea to use Blue stones at lower levels unless you are preparing your end game gear in advance.
But we have yet to talk about wands. Again, we need to look at the formulas for damage, but this time, we look at a simplified version of Magic Damage:
Base Damage + (Spell Constant * Magic Attack)
What we notice here is that Magic Attack works on a Spell Constant, which will affect the damage in different ways depending on what spell we want to calculate.
For example, with Icebolt:
Icebolt is affected less by Magic Attack than Firebolt. Knowing this, we'll want to apply the same idea shown above in the physical damage section.
Red: (80 + (MagicAttack * 0.4) * (0.7 + (0.3 * 3.12))
Blue: (80 + ((MagicAttack + 84) * 0.4) * (0.7 + (0.3 * 2.5))
When applied to different skills, in order to benefit more from Red Upgrades than Blue Upgrades, you'll need:
Icebolt: 454 Magic Attack
Firebolt: 415 Magic Attack
Lightning Bolt: 404 Magic Attack
Ice Spear: 483 Magic Attack
Fireball: 454 Magic Attack
Thunder: 464 Magic Attack
Hailstorm: 561 Magic Attack
Meteor Strike: 114 Magic Attack
Lightning Rod: 616 Magic Attack
Shockwave: 574 Magic Attack
When you use a wand that’s aligned with the spell element you use, it raises the base damage, reducing the amount of Magic Attack you use, going down to almost 360 for Firebolt.
Most of these are near unreachable or not worth reaching, aside from Meteor Strike, whose base damages are high enough to warrant Red Upgrade Stones.
In conclusion, we learn that Red Upgrade Stones are for Physical Damage dealers who have more than around 300 Damage, and Blue Upgrade Stones are for mages who don't use Meteor every four seconds.
As for what mages are using Meteor every four seconds, that's a whole different question.
