## Damage And Defense Calculations

By JarJarIsASith

2020-08-31

Players have had a lot of curiosity regarding damage and defense calculations on the Singularity - UO free shard. Due to this I have compiled a number of interesting facts regarding how all these calculations behave so you can make informed decisions on your character progression. As time goes on, I will continue to update this list with more information so we can be as comprehensive as possible. Many of these calculations are exactly the same as you might find on other servers using ServUO as the core engine, and some of these may deviate from the standard calculation mechanics you may find elsewhere.

# Physical Damage Calculations

Each time a player executes a physical attack with a bow or melee weapon there is a calculation that determines a damage amplification of the base amount that was rolled. There are four fundamental components to that calculation: Strength, Anatomy, Tactics and Lumberjacking. Lumberjacking only applies to weapons that are classified as axes in the game, which is pretty much everything that looks like an axe or has axe in the name (except Halberd and Bardiche, those are considered polearms, and also Pickaxe). Also note that each of these has a separate GM (100+) bonus that is a flat additional amount applied once the stat or skill reaches 100.0 or higher.

Here is how each of these four categories calculates the total percentage boost of the damage you will hit with:

**Strength:**

30% * Strength + (GM Bonus of 5)

**Anatomy:**

50% * Anatomy + (GM Bonus of 5)

**Tactics:**

62.5% * Tactics + (GM Bonus of 6.25)

**Lumberjacking:**

20% * Lumberjacking + (GM Bonus of 10)

These final values are then added together and multiplied against the weapon damage to compute the final resulting outcome, which will then pass through further damage boosts (slayer, class abilities, etc.) as well as the defensive mitigations of the target being attacked. A good way to understand how these calculations work is by comparing two different skill / stat setup examples: all at 100, and all at 120:

**Example 1**: Strength, Anatomy, Tactics all at 100: 35% + 55% + 68.75% = 158.75%

**Example 2**: Strength, Anatomy, Tactics all at 120: 41% + 65% + 81.25% = 187.25%

So this comparison of examples demonstrates that your damage can grow by close to around 18% by continuing to push your skills and stats after reaching a GM level in these. It is also worth understanding how impactful lumberjacking can be, since it will result in another 34% increase in damage, which is yet another roughly 18-20% overall increase in your multiplier.

If we then take this value we should be able to see what happens when we hit with for example, a Large Battle Axe or Ornate Axe at maximium stats and skills. This means we need to also add in Weapon Damage Increase, this will add another 100%. So our final result for this axe damage calculation on a hit for a maximum base roll of 20, yields: 20 x 421.25% = 84 damage. This number is what should be displayed in your characters stat detail sheet as the upper end value. There are more calculations after this for a wide variety of class features, as well as slayer damage and mitigations of the attacked target that all come into play for the final value.

# Magic Damage Calculations

When a player casts a spell there are a variety of calculations that get pushed through to determine the final value of the damage applied. Here we are trying to explain how we arrive at the initial damage that will be applied to a target. This value will not take into account the resistances and defensives of the target.

First, in order to calculate the damage you need to know the base damage of the spells, below is a short list of common spells and their damage ranges:

**Magic Arrow**: 11-14**Harm**: 18-22**Fireball**: 20-24**Lightning Bolt**: 24-27**Mind Blast**: 37-42 (this spell has a completely different calculation for PvP and when monsters cast it)**Energy Bolt**: 41-45**Explosion**: 41-45**Flamestrike**: 49-53**Chain Lightning**: 52-56 (multiplies by 2x for 2 or more targets hit)

So first, we take a random value in the range of damage that a spell can apply, for example Flamestrike might roll a 53 for the base of the damage. This number is then multiplied by bonuses from the following: Evaluate Intellect, Spell Damage Increase, and Slayer if applicable. We can see how these calulate below:

**Evaluate Intellect**: 30-138% - all spells come with a 30% "bonus" from this regardless of skill. Then, this percentage raises by 0.9% for every skill point gained, up to a maximum of 138% at 120 Evaluate Intellect skill. Due to the fact that this is multiplicative, Evaluate Intellect is probably the single most important thing to max first for having impactful spell damage.**Spell Damage Increase (SDI)**: there are three sub-sources for this increase: Intellect, Inscription, and Spell Damage Increase (SDI). Intellect gives 1% for every 10 Intellect. Inscription also gives 1% for every 20 but 100 skill or above grants a flat 10 increase to SDI. Spell Damage Increase is uncapped and comes from weapons and armor found in the game. These percentage bonuses are all added together then added to a 100% base before being applied.**Slayer**: This is the last multiplier that is computed and can be applied to this calculation from any weapon or spellbook in the game that has a slayer on it, so long as it is equipped and you are casting at a monster of the appropriate type. All slayers on the Singularity - UO free shard are super slayers, so they grant a bonus of 100% more damage.

Continuing with our Flamestrike example we can now very accurately calculate our pre-mitigated damage if we had for example, 125 Int, 120 Inscription, and 120 Eval Int as well as a Slayer weapon: 53 x 138% x 222% x 200% = 324 damage. This will of course be mitigated down to something substantially smaller once it goes through defensive calculations, but still you can see that there is some serious DPS potential once your character comes closer to final form.

# Proc Damage Calculations

Many weapons in the game come with special "procs" that compute a second attack against an enemy when an attack lands. These various procs have a special calculation of their own, but first we need to take a look at each possible proc to understand the base damage that is behind each type of proc:

**Magic Arrow**: 11-14**Harm**: 18-22**Fireball**: 20-24**Lightning Bolt**: 24-27**Explosion**: 41-45

As you can see, the base damage is exactly the same as each spell they are modelled after. The logic for these calculations varies slightly from what we have for normal spell damage calculations:

**Evaluate Intellect**: 102% - all procs calculate as if the wielder had exactly 80 skill in Evaluate Intellect, regardless of their actual skill.**Spell Damage Increase (SDI)**: there are three sub-sources for this increase: Intellect, Inscription, and Spell Damage Increase (SDI). Intellect gives 1% for every 10 Intellect. Inscription also gives 1% for every 20 but 100 skill or above grants a flat 10 increase to SDI. Spell Damage Increase is uncapped and comes from weapons and armor found in the game. These percentage bonuses are all added together then added to a 100% base before being applied.**Slayer**: this does not factor in to proc damage calculations.

You can see that this equation is much simpler, and for all intensive purposes, we can summarize that this calculation is based entirely on the amount of Spell Damage Increase a player has equipped. We can review a sample calculation for an Explosion proc of 45 damage for a player who has 100 SDI, as well as 100 int and 100 inscription. Basically, the calculation is simply 45 * 2.2 = 99 damage. Which will also have to pass through the monsters mitigations once again, but you can see that this proc can pack some serious punch.

# Defend Attack Skill Calculations

On the Singularity - UO free shard, in order to land a physical melee or ranged attack against a player, you first must overcome a skill check that is calculated as a combination of your "offensive" weapon skill and their "defensive" weapon skill. The first step in this calculation is for the game to decide what defensive or offensive skill is to be used. The skill "choosing" calculation is exactly the same for both defenders and attackers, and it is based on the weapon they are wield at the time of the attack.

There are only exceptions for this if the weapon has either a Use Best Weapon ability or a Mage Weapon ability. If it has Use Best Weapon, then the highest of your weapon skills will be chosen from Fencing, Swordsmanship or Mace Fighting (Wrestling is completely ignored here). If it is a Mage Weapon then Magery skill will be used and all other skills will be ignored. Otherwise, the weapon skill of the weapon you are currently wielding will be used unless your wrestling skill is higher, in which case wrestling will be used for the defensive calculation.

Now that both skills have been chosen, we can determine if the attack lands successfully with the following calculation: (((Attacker Weapon Skill) + 20.0) * (100 + (Attacker Hit Chance))) / ((((Defender Weapon Skill) + 20.0) * (100 + (Defender Defend Chance))) * 2)

For example, if I am attacking an Ogre Lord who has 120 Wrestling, and I have a Mace and Mace Fighting of 120 and I also have 45% Hit Chance increase, then the chance I am able to land the attack will be: (120.0 + 20.0) * (145) / (120.0 + 20) * 100 * 2 = 20,300 / 28,120 = 72.19% chance to hit.

Another good example that is very easy to calculate is when two players are fighting and both have 45 Hit Chance Increase, 45 Defend Chance and 120 Weapon Skill. In this case there is a flat 50% chance for them to land attacks against one another.

Note, that there are a few things unique to the Singularity - UO free shard however. The above examples and explanations are how the base ServUO package calculates these values. Here in the Singularity - UO free shard there are a few key differences with how these equations work:

- The Hit Chance cap and Defend Chance caps are 70, not 45, and values beyond 45 have diminising returns of 2 for 1. Note that this impacts PvP calculations, but due to diminishing returns the impact is very small, players with even skill and one having 70 attack versus another with 45 defend will result in a 54% chance to hit rather than 50%.
- Player versus monster calculations will cap the defending monsters defend skill at 95.0, this results in a maximum possible attack chance of 95% for players, and this was done to balance melee in PvE combat.
- Monster versus monster calculations will cap the defending monsters defend skill at 120.0, this was also done to ensure that tamers and summoned units are not adversely impacted by high end monsters.
- Monster attacking skill however is uncapped, resulting in monsters that may have a very high chance to land attacks.
- In PvP all physical attacks are given a +5% modifier to land.

Please remember that this page will be updated as we move forward, if there is something you'd like to understand with calculations that isn't here or is incomplete, please send a request to me on discord or through the contact page and I will try to get it updated asap.

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