[MISC] A look at Weapon Performance



  • (to avoid the tainted word “balance” - at least in the topics name)

    As most discussion over weapon performance usually degenerates into unbased whining I will just introduce a formalism I will use to look at it from a not purely subjective point of view. This is a more theoretical approach aimed at judging the strength of a weapon. Feel free to use, hate, comment, add your own thoughts or ignore.

    I - Terminology

    A task is a single situation with:

    • a high probability of occuring
    • an indication if it is about to occur
    • a defined start and end

    Examples:

    • a duel between two Knights
    • a single skirmish between two groups
    • an Archer shooting at somebody from a distance
    • people defending the Pyre on Hillside

    Now we simply consider the set of all tasks or a specific subset. A Metagame is a set of the at one specific moment and/or for a specific group most important (= most likely to occur) tasks. As nobody is able to list all tasks every analysis can only be done on Metagames with as many tasks as possible.

    Weapons are rated by their performance in certain tasks in comparison to other (competing) weapons. Weapons can only be compared if every other parameter (skill, hitpoints etc.) stays the same. So we cannot compare weapons that can’t be wielded by the same class (like Shortsword and Warhammer). A weapon A performs better at a given task than a weapon B when switching A for B (given everthing else stays the same) increases the rate of sucess. The weapon performs best at a specific task if there is no weapon that performs better at this task.

    Examples:

    • The Flanged Mace performs better at dueling a Knight than the Hunting Knife.
    • The Longbow performs better at shooting a Vanguard on open ground than the Hunting Knife.
    • The Longbow does not perform better at shooting a Vanguard on open ground than the Flanged Mace (as these weapons cannot be compared directly).

    The last example seems a little weird but the point is to avoid too much influence from pure class balance (armor and special abilities). There is no point comparing a Longbow and a Flanged Mace as they do not compete at all on the weapon level. Now we can sort weapons by their performace at multiple tasks. Everything below depends on a chosen set of tasks T:

    Weapons are called exchangeable if they perform equally at all tasks in T. A weapon A is dominated by a weapon B if there is no task in T where A performs better but A and B are not exchangeable. We calla weapon is viable if it is not dominated by another weapon and redundant if it is exchangeable or not viable.

    Construction of a Competition Set C(T):
    0) start with an emty set

    1. pick a weapon A that performs best at a maximum number of tasks in T and add it to C(T)
    2. set T’ as the set of all tasks in T where A does not perform best
    3. pick a weapon B that performs best at a maximum number of tasks in T’ and add it to C(T)
    4. set T’’ as the set of all tasks in T’ where B does not perform best
    5. … (repeat until there is no task left)

    We can see:

    • If a weapon is not viable there is no Competition Set including this weapon.
    • If a weapon is redundant there is a Competition Set without it.
    • If two weapons are exchangeable each Competition Set includes no more than one of them.

    This potentially gives us different weapon types:

    A required weapon is included in every Competition Set. These are either niche weapons that excel at specific tasks or are just overall too strong. An endangered weapon is not included in any Competition Set but still viable. These are not outcompeted by a single weapon but in combination there is always a more effective choice. Finally a viable weapon that is not endangered (thus included in at least one Competition Set) is called competitive.

    And at last some more strict definitions for words too many people use both carelessly and cluelessly:

    A weapon is called underpowered if it is not competitive and overpowered if there is a Competition Set that only includes this single weapon.

    Which gives us interesting conclusions:
    a) If there is an overpowered weapon, every viable weapon is overpowered.
    b) If there is an overpowered weapon but no underpowered weapon, every weapon is redundant.
    c) If there are both a required weapon and an overpowered weapon, they are the same.
    d) If there is an endangered weapon, there is no overpowered weapon.
    … (Many other conclusions just by messing with the terms)

    I used this (arguably strange) approach to define the terms in a more objective way opposed to the very subjective “too strong”, “too weak” or even “clan used it in tournaments” (here the subjectivity comes from the specific clan member). But I feel it helps understanding instead of just perceiving “mimimimi” all the time.

    II - Damage Analysis

    Talking about damage is not easy. While you can talk about the Mauls overhead base damage or the number of strikes you need to kill a Knight if you hit his head a statement like “The Maul deals the most damage of all wieldable weapons.” is not really valid. There are a lot of factors that incluence your damage even when only considering a single attack type:

    (1) your Base Damage
    (2) your Attack Speed (splits into Windup, Release, Combo and Recovery)
    (3) your Damage Type
    (4) your opponents armor and where you hit him (Target)

    As weapons do not emit a continuous stream of damage but rather deliver strikes in discrete attacks we cannot assume that a modification of this factors changes the overall weapon performance in a rate proportional to the amount of change. Increasing Base Damage by 10% and decreasing Attack Speed by 10% can lead to a much stronger weapon but also to a much weaker one. And almost certainly it will not lead to a weapon that performs equally well. Still it might be benefitial to have a basic measurement of damage output that combines all of these factors to a single value.

    For this we first neclect Attack Speed and focus on the other three. The most common (and in my opinion also most useful) thing to look at are Hits to Kill. For every single attack you now got 4 (number of classes) * 3 (number of hitboxes) numbers. Using these one can derive damage modifiers for each Damage Type. The Method: applying modifiers until the average performance (Hits to Kill) of each Damage Type with Base Damage values between 20 and 130 is roughly the same.

    The final modifiers are:
    Swing - 109%
    Pierce - 95%
    Blunt - 97%
    SwingBlunt - 102%
    PierceBlunt - 96%

    By multiplication with the Base Damage we get something now called Effective Base Damage (EBD) that gives us an expected amount of damage this attack will do. The higher the Effective Base Damage the more powerful the particular attack is.

    To include Attack Speed one can just consider the fastest way of delivering a single attack type: a combo of three strikes. If the attack is unable to combo we just use three times the time for a single attack. Now divide the total damage output (assumng only a single attack type was used) by the time needed to deal it and recover. The result: a value for the expected Damage Per Second (DPS) that gives us a basic measurement of attack strength.

    DPS = 3*(BaseDamage)*(DamageTypeModifier)/(TimeForTripleAttack)

    Examples:

    • Maul Overhead: ~136 EBD and ~77 DPS (highest EBD of all non-siege weapons)
    • Short Spears (Thrown): ~110 EBD and the same DPS (you can throw one each second, highest DPS of all non-siege weapons)
    • Cudgel Slash: ~46 EBD and ~45,5 DPS (45 Blunt Damage)
    • Shortsword Overhead: ~41 EBD and ~43 DPS (45 Swing Damage)
    • Thrusting Dagger Stab: ~47 EDB and ~56,5 DPS (45 Pierce Damage)


  • What you do now is use sprint in short bursts, much like you would do before and use your new speed boost (thanks TB :? ) to abuse the range on your weapons. Be wary though, people seeing you suddenly sprint forward can prompt the enemy to throw a pre-emptive attack your way. Counter this by simply using superior speed and foresight to backstep out of the attack and then throwing an attack their way while they are in recovery or even the windup of their next attack (always aim to flinch - more on this later), or simply parry and use the continued momentum to hit them with a riposte.



  • Excellent post !

    Now you explained and set the base, could we speak more precisely about the actual balance of the weapons ?



  • For this we need a metagame that reflects ingame reality (strange combination of words). I think it might be sufficient to get one metagame for each class. I made some topics for this (see signature).

    The second thing needed is a consensus which weapons perform best at the listed tasks. For this some tasks (something like “dueling”) should be split into multiple tasks (like “dueling a Vanguard”) to get this done without getting too specific (like “dueling a Vanguard using the Claymore with a fachugging and feintspamming playstyle that doesn’t include kicks or jump attacks”). Just to sort out the “ifs”.



  • The mathematician in me is extremely happy to see the OP’s post.

    Edit: I will review the OP’s logic when I have a bit more time.



  • I’m no theory crafter, but I have a thought about this post.

    DPS or EBD vs. Health of enemy or target, does the effective life span of a knight make the effectiveness of some weapons different than the effective lifespan of an archer? Take for example the bardiche which requires only one swing to an archers critical zone to cause an instant fatality, where in the case of a knight it would require 2 strikes in a critical zone or 1 strike in critical and 2 in the extremities like hands. IN BASIC, damage or dps does not have equal value across classes because of overdamage or “wasted damage” and required # of hits (in some cases like shortsword vs knight, 3 head, or vanguard, 1 head & 1 body strike)

    This is slightly convoluted, I’m not sure how to explain exactly what I mean.



  • The idea behind EBD is to compare weapons with different damage types. Everbody will agree that two weapons with same reach, same timings, same utility (stamina drain, knockback), same base damage and same damage type are equally strong.

    Now EBD combines damage type and base damage by rating damage types by factoring in the hits to kill for each class and body region. So two weapons with same reach, timings, utility and EBD should be equally strong overall even though they might perform differently in specific situations. For example the Zweihänder and the Grand Mace both have an EBD of ~83 on their slash meaning the overall damage output is balanced. In specific cases the Zweihänder slash performs better against light classes being able to oneshot Archers while the Grand Mace slash is better when fighting heavy classes being able to twoshot a Knight (only damage was compared).

    DPS fails at doing the same as it only factors in the damage aspect of timings while ignoring the utility aspect (like flinching). It can be used to rate the damage output of weapons but if you want to rate the whole weapon you need to take a second closer look at the timings.

    “Wasted” damage can still have its uses as you can combine different attacks with kicks, fall damage and damage from other fighters. Of course dealing 50 instead of 49 damage to your target is stronger than dealing 52 instead of 50 damage but thats already reflected in the hits to kill that got factored in while calculating EBD.



  • @Evil:

    The idea behind EBD is to compare weapons with different damage types. Everbody will agree that two weapons with same reach, same timings, same utility (stamina drain, knockback), same base damage and same damage type are equally strong.

    Now EBD combines damage type and base damage by rating damage types by factoring in the hits to kill for each class and body region. So two weapons with same reach, timings, utility and EBD should be equally strong overall even though they might perform differently in specific situations.

    Sweet, thanks for the explanation, it makes more sense to me now.


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