Vampi's Guide to
Weapon Evaluation

an Anarchy Online Player Guide

FINAL UPDATE 13-Sep-01

A big thank-you to Slicer from HackersQuest for finding the code actually used in the AO client that calculates the effect of your weapon initiatives on your attack speed. Another big thank-you to Tiran for reminding me about the damage formulas published in the Sybex guide. Thanks to Vehementi and others who have posted critical feedback about their observed slope of the Attack skill modifier. Super-special thanks to Velkoris for explaining what the client code found by Slicer really means (Slicer's interpretation was partly wrong), and also to Konril for some extensive AggDef slider testing that confirms Velkoris' interpretation.

Goodbye, My Friends

I will leave this guide and my PvP Guide up for some time, at least until I need the server space for things related to the next game I play. I give blanket license to anyone to take my spreadsheet and carry it forward, and to take the information in this document and carry it forward. I, however, will no longer be updated either of these guides or my spreadsheet.

CHECK THIS OUT!

Overview of the Variables That Affect Your Overall Damage Output

A weapon's listed values are only a small part of the story. The weapon's base statistics are heavily modified by several of your skills and some other factors:

What I Want You to Get Out of This Guide

The formulas in this guide (and in my corresponding spreadsheets) take all of the above variables into account, except for the last item about critical hits. By using these formulas/spreadsheets, you can more accurately determine the best weapon for you at any given time. In a nutshell, the main things I hope to show you are that:

For those of you that don't care to understand the formulas or read through this guide, I've built an Excel 97 spreadsheet that pretty much does it all for you. If you have Excel, download this and use it, and you'll have to read no farther.

For the rest of you, here's how to do it the "hard" way, by calculating this stuff yourself. It's really not that tough. Note that I have submitted all this info to CptFallout and Toshan so that they can update their weapon analyzer utilities, but I don't know whether they will or how long it will take them.

How this Guide is Organized

First, there's a disclaimer section where I list the gotchas:

Then I detail exactly how to calculate your actual damage output. This involves a lot of smaller calculations that can be organized into three large chunks:

The Big Disclaimer - READ THIS

Alright, before you get too excited about all this stuff, let me point out that these formulas and my spreadsheets are not yet perfect and do not tell the whole story. There are several additional factors that combine to determine your real, honest-to-goodness total damage output. But unfortunately, these additional factors are very difficult or impossible to represent in my formulas and spreadsheet, or else they apply equally to any weapon that you're comparing and therefore add no value to the comparison:

Beware The Attack Skill Curve

According to the Sybex guide, the damage modifier that's based on your Attack skill does not follow a constant slope at the "very high levels." At some point, the slope of this modifier flattens out quite a bit because Funcom wants characters at the very high levels to diversify their skills rather than constantly maxing out the weapon skills that make up their Attack skill. The Attack skill is based on your primary weapon skill and possibly other skills, depending on the weapon you're currently weilding (so it may change from weapon to weapon). You can find the Attack skill on your Status window:

So be aware that when you plug in numbers for a hypothetical level 150-200 character and some QL190 weapon, the damage output numbers you get from these formulas will NOT reflect actual damage observed in-game. The numbers provided by these formulas/spreadsheets should be fairly accurate for characters below 150 or so. As I gather reports of real-world data from higher level characters, I may be able to modify the formulas to approximate the curve of the Attack modifier.

And it gets uglier, I'm afraid. Reports coming in from various players are suggesting that the Sybex guide may be wrong. Instead of being a constant, straight slope until the "very high levels," the Attack skill modifier may be a be a true curve all the way, which means that as your Attack skill keeps increasing, the slope keeps flattening out for less and less effect.

If you want to help me figure out where the curve starts kicking in, and to what degree it changes the slope, I ask you to spend 20-30 minutes doing some tests for me, especially if you are a character over level 100:

  1. Grab a very low QL weapon from a basic store that is appropriate to your primary weapon skills.
  2. Grab a friend who's willing to let you shoot/hit them with that low level weapon for about 10-15 minutes.
  3. Grab a doc to continuously heal your friend while you're shooting/hitting him.
  4. Get yer butts to an arena or Mayhem zone.
  5. Using that very low QL weapon, shoot/hit your friend for about 10 minutes while the doc keeps him/her healed up and alive (yes, stop shooting if you're about to kill them). If you can log the damage to a text file, please do so.
  6. Email me the following info:

Only if enough people help out, especially high-level people, can we have a chance at figuring out what the Attack curve looks like. If we can nail down the general shape of the curve, then we can make these formulas/spreadsheets accurate. In the meantime, my formulas and spreadsheets allow you to tweak the slope of this curve when doing your own weapon evaluation. See the section Factoring In Your Attack Skill And Calculating Adjusted Damage for more info on how to do this.

Why These Formulas Do Not Factor In Critical Hits and Special Attacks

Your Attack value versus your opponent's corresponding evade value significantly affects your chance of scoring a critical hit, so at present I do not use the weapon's listed critical hit value (the number in parentheses after the min/max damage range). According to the Sybex guide, your chance of scoring a critical is always at least 3%, increasing by an additional 1% for every 10% by which your Attack value exceeds your opponent's evade value. So if your attack value were exactly twice that of your opponent's evade, then you have a 13% chance of scoring a critical on any given attack.

It's impossible to realistically factor in the critical hit value of your weapon (the number in parentheses) because there's no way to tell how often you'll crit (see the previous bullet for why).

So instead, use this basic rule of thumb for critical hits: if you get two weaps with the same damage output but one has a higher crit number, then obviously you'll want to use the one with the higher crit number.

Finally, with regard to special attacks, remember that faster-recycling specials such as Fling, or weapons with multiple specials will obviously put out more damage during the course of a fight than a weapon with only one special. Aimed Shot, for instance is often not usable at all when fighting mobs, but its alway available in PvP. It just gets too complicated to try and factor in the effect of specials with any precision.

So instead, use this basic rule of thumb for special attacks: for two weapons with roughly the same overall damage output, if one has more specials than the other, or a faster recycling special like fling, then you probably want the one with the most specials or faster specials.

Why These Formulas Do Not Factor In Miscellaneous Damage Modifiers

Small-percentage damage bonus modifiers, such as those provided by rings and merit board awards, obviously increase your average damage output. However, these kinds of modifiers equally affect every weapon you wield (of the appropriate damage type) so it's a non-issue for comparing weapons to each other. Hence, I don't include variables for these kinds of modifiers.

Dual-Weilding Is Currently Not Accounted For

With regard to dual-wielded weapons, you run into questions of which weapon affects the recharge rate and other questions that I don't want to touch with 10-foot-pole. So you dual-wielders remember that these numbers are NOT factoring in any special duel-wield considerations. If you think you have a handle on how dual-wield really works, email me with the info and I'll see what I can do.

Note: some emails have started trickling in, so with any luck I may be able to account for dual-wielded weapons within the next week or so. Keep that info coming!

ATTACK DAMAGE

Factoring In Your Minimum Damage Buff And Calculating Buffed Damage

The first modification you have to make to a weapon's listed damage stats is the effect of your profession's typical "minimum damage buff." These are the buffs that add a certain small amount of damage to every attack, in the range of +2 to +10 points of damage for each attack. It may not seem like a lot, but this number is factored into your weapon's base min/max damage stats before the damage is increased by your weapon skill. This can add up quickly.

Say you have a weapon with a damage range of 4-57. If you can cast a damage buff that adds +6 to each attack, then your weapon's actual damage range effectively becomes 10-63 when you are weilding it and buffed.

To calculate the buffed minimum, maximum, and average damage per hit of your weapon, use the weapon's listed damage range and apply the following formulas:

buffedMinDamage = listedMinDamage + buffValue
buffedMaxDamage = listedMaxDamage + buffValue
buffedAverageDamage = (buffedMinDamage + buffedMaxDamage) / 2

For example, using the listed damage range 4-57, then your buffed minimum damage would be 4 + 6 = 10. Your buffed maximum damage would be 57 + 6 = 63. Your buffed average damage would be (10 + 63) / 2 = 36.5

Factoring In Your Attack Skill And Calculating Adjusted Damage

Once you have the buffed min/max/average damage numbers that include your minimum damage buff, you next factor in the effect of your Attack skill. Your Attack skill is calculated from one or more weapon skills, depending on the weapon. For some weapons, your Attack skill may be the same as your primary weapon skill, because that's the only value used to calculate your Attack skill. You can see your Attack skill on your Status window when you have the weapon equipped:

According to the Sybex Guide, when your Attack skill is 1, you do the listed damage of the weapon (including the effect of your minimum damage buff). When your Attack skill is 33, your listed min/max/average damage values are all increased by 25%. At 198 Attack skill, your damage is multiplied by 150%, and so on.

However, be aware that Funcom has built a curve into this Attack skill modifier, so that "very high level" characters (quoted from the Sybex guide) will get less and less value out of increasing their Attack skill. Funcom wants "very high level" characters to be diversifying their skill sets rather than trying to completely maximize their Attack skill. So at some currently unknown point, the slope of this skill increase starts flattening out. The bottom line is that if you try to plug in numbers for a hypothetical level 200 character with an Attack skill level of 1000 using a QL200 weapon, the following formulas will NOT be accurate. At a guess, I'm presuming the following formulas are accurate at least for Attack skill levels 1-700. At Attack skill levels 700-1000 the curve probably starts kicking in.

To calculate your adjusted minimum, maximum, and average damage, use the weapon's buffed damage numbers and apply the following formulas:

adjustedMinDamage = (buffedMinDamage * (yourWeaponSkill * (.25 / 33))) + buffedMinDamage
adjustedMaxDamage = (buffedMaxDamage * (yourWeaponSkill * (.25 / 33))) + buffedMaxDamage
adjustedAverageDamage = (adjustedMinDamage + adjustedMaxDamage) / 2

For example, using a buffed damage damage range of 10-63 and a weapon skill of 250, then your adjusted minimum damage would be
(10 * (250 * (.25 / 33))) + 10 = 29. Your adjusted maximum damage would be (63 * (250 * (.25 / 33))) + 63 = 182. Your adjusted average damage would be (29 + 182) / 2 = 105.5, which is significantly higher than either the listed or buffed average damage. So as you can see, your primary weapon skill has a huge effect on your raw damage numbers, and you should keep it maxed if possible.

Okay I'm gonna throw a curve at you now. Several players have reported that even their not-so-high-level characters are not getting real-world observations in-game that match the slope of the Attack skill curve at +25% damage per every 33 skill points. Instead, they are reporting that flatter slopes are yeilding damage output that matches what they see in-game. If you want to flatten out the slope in your own calculations, then replace the value 33 in the above-listed formulas with some higher value.

A slope that several players have reported as being more accurate for them uses the value 132. My personal observations do not agree with this--the Sybex-published slope seems to closely match what I have personally observed in-game so far, but my char is only level 41. Perhaps these other players are high enough level that the curve is starting to kick in.

TIP
Any way you slice it, my spreadsheets now allow you to specify the slope of the Attack skill modifier. You can replace the default value of 33 in the spreadsheet with higher and higher values until a known weapon you are familiar with is generating values that seem to agree with what you observe in-game. Then you can use that slope for evaluating other weapons with a fair degree of confidence. As you level up and put more IP into things that increase your Attack skill, you will have to recalibrate the slope for yourself.

Factoring in the AC of Your Opponent

For every successful hit you score on your opponent, their AC soaks up a portion of the damage, to the tune of absorbing 10 points of damage for every 100 AC they have. However, your attack will never hit for less than your adjusted minimum damage.

The effect of AC is the last thing you factor in when figuring out the actual damage output of your weapon.

The formula for calculating AC-adjusted minimum, maximum, and average damage is this:

acAdjustedMinDamage = adjustedMinDamage - (opponentAC / 10)
acAdjustedMaxDamage = adjustedMaxDamage - (opponentAC / 10)
acAdjustedAverageDamage = (acAdjustedMinDamage + acAdjustedMaxDamage) / 2

For example, if you score a 200-point hit against a mob with an AC of 1100, then your AC-adjusted damage would be 200 - (1100 / 10) = 90.

Important: Your AC-adjusted minimum damage cannot ever be less than your adjusted minimum damage from the previous section.

The Myth of "Bigger Damage Crashes the AC Barrier"

I've seen arguments that a very slow, but huge damage weapon (like a sledgehammer) is actually much more effective than a faster, lower-damage weapon even if the two weapons have the same average damage output according to these formulas. The argument seems convincing at first, and it goes like this (This is a direct quote from someone posting on the FunCom general forum):

A sledgehammer doing 17.5 damage / second is far more useful than a 3rd level ninja sword doing 17.5 damage / second.

Why? AC.

Let's say you are fighting a mob with 800 hp and 300 ac. The sledgehammer, doing 17.5 damage / second, will kill the mob faster than the 3rd level ninja sword doing 17.5 damage per second. Why? The faster, lower damage weapon has more armor class to overcome.

Let's say we had two theoretical weapons. One fast one (10-200, 0.5 / 0.5), and one slow one (10-2000, 5.0 / 5.0). The average for the small weapon, not taking initiative into account, is 105 / second, and the big slow weapon is 100.5. Let's round the numbers to 100 / second for each. It's been stated that every 10 points of AC reduces the maximum damage of an incoming attack by 1 point.

If you had a slow weapon that hit once every 10 seconds for an average of 1000 points of damage, you would effectively do 970 points of damage (1000 - (300 ac / 10)) * 1 = 970 damage every 10 seconds. If you had a fast weapon that hit 10 times every 10 seconds, doing an average of 100 points of damage a hit, you would effectively do (100 - (300 ac / 10)) * 10 = 700.

Okay that sounds reasonable, doesn't it?

In reality, however, you'd never have two weapons of the same Quality Level with numbers like these. FunCom is not that stupid. In reality, you'll find that among weapons with roughly the same QL, the actual numbers on the big hitting, slow weaps versus the lighter-hitting, fast weaps are much more balanced. For what it's worth, my damage output calculations DO take AC into account, and you can trust the resulting numbers for damage per second (DPS).

Important: Be aware, however, that as of the 12.4x patches, and probably the 12.5 patch as well, there is an EXPLOIT that can be used with the big-hitting, slow weapons like Sledgehammers that allows the player to cut out the recharge cycle, and unfortunately, the attack animation for some weapons like these are much faster than the weapon's normal recharge time. This exploit effectively doubles or triples the damage output of these weapons. Hopefully FunCom will be fixing this exploit soon, because some Enforcers with sledgehammers are really tearing up PvP with this exploit.

ATTACK FREQUENCY

Factoring in Your Combat Initiatives And Your AggDef Slider

There's been a lot of speculation on the boards about whether or not Ranged Init or Melee Init are worth a damn. Some people have argued that your initiatives and evades don't really matter, because everyone just puts their AggDef slider at full Aggressive.

Wrong.

Also, there has been a lot of misunderstanding about the effect of your AggDef slider. The conventional wisdom for quite some time now has been that at full Agressive, it speeds up your attack/recharge times by 1 second each, and at full Defensive, it slows down your attack/recharge times by 1 second each.

Wrong.

Fortunately for all of us, a guy named Slicer found the actual client code that calculates your attack speed. The real numbers are much more promising, and demonstrate that:

The Controversy Over the Actual Formula

IMPORTANT UPDATE (August 22) - In all the previous versions of this guide and my spreadsheets (before today's update), I was using Slicer's interpretation of the client code that he found. Unfortunately, one part of Slicer's explanation was wrong. Velkoris has properly interpreted the way the code works, and Konril has confirmed Velkoris' interpretation through some extensive testing. The bottom line is that I used to say that pushing the AggDef slider to Full Aggressive would increase your weapon's attack and recharge speeds by 1 second each. This was incorrect. The real story is that Full Agressive is your base speed, moving the slider to the neutral position decreases your attack/recharge speeds by 1 second, and moving the slider to Full Defensive decreases your attack/recharge speeds by 2 seconds!

Be aware that there is currently some controversy over whether Slicer's formula is the "real" formula. This controversy centers around an earlier post to the various boards relating a supposed conversation with a FunCom designer, in which that designer quotes some different numbers than what Slicer found in the client code.

The argument hinges on whether Slicer's formula applies only to the client-side animation of attacks, rather than the server-side calculation of attacks. To further complicate matters, one poster has postulated that server timing seems to run at 2x the speed of "real time," so he thinks that Slicer's numbers may actually be in agreement with the seemingly faster numbers attributed to the FunCom designer.

In my formulas, and in my spreadsheets, I am going to use Slicer's numbers, since I personally trust actual code over supposed statements by a supposed designer. I'll also note that I have personally observed Slicer's numbers to seem very accurate, based on the calculated optimum position of my AggDef slider. When I set the slider to the optimum position indicated by Slicer's formula, I notice no further observable speed improvment by subsequently pushing the slider to full Aggressive.

However, as many players have pointed out, there are several weapons in game whose listed attack and recharge speeds are faster than the lower limits exposed by Slicer's formula. So these players logically argue that these faster numbers are indicative that the numbers attributed to the FunCom designer are actually the "real" numbers behind the initiative formula.

Here's what I have to say about that particular argument, though: my theory is that these weapons exist to enable you to set your AggDef slider more towards the Full Defensive value! Think about it--if the true lower limit is 1/1--if that's that fastest attack/recharge cycle you can actually get, then by giving players weapons with listed attack/recharge values less than 1 second each, they are allowing you to move your AggDef slider into the green. In other words, those weapons with listed attack/recharge values lower than 1/1 are specifically meant to be weapons that you can wield while keeping your evades high!

But that's just my theory, and I'm sure that some of you will disagree, so both in my formulas here, and in my spreadsheets, I'll leave it up to you to decide which set of numbers you want to use. In the spreadsheet, I provide several variables that you can set yourself with the set of numbers you believe most. I suggest you experiment with both sets of numbers, then go in-game and set your AggDef bar at the two different positions that will be optimum, according to which set of numbers you plug in. See for yourself which AggDef position seems to be better, and from that point on, use the set of numbers that yeilded the best observable results to you. And email me with your feedback so we can get a feel for which set of numbers may actually be the true ones.

The FunCom Designer's Numbers

The numbers attributed to the FunCom designer were tossed around the boards for some time before Slicer posted his finding. This was the gospel for some time:

Note: As of August 22, we now know conclusively that the AggDef slider does NOT work in the manner attributed to the FunCom designer. Konril did a lot of testing that shows conclusively that the AggDef slider works as described in the client code found by Slicer. This is further evidence that these numbers attributed to the FunCom designer are probably not accurate.

Slicer's Numbers

What Slicer's client hacking revealed is that combat initiatives and the AggDef slider work like this:

The Formula using Slicer's Numbers

Attack Speed
The formula to calculate your weapon's initiative- and AggDef-adjusted attack speed is this:

adjustedAttackSpeed = MAX [((listedAttackSpeed + 1) - (yourCombatInitiative / 600)) - (aggdefSlider / 100) , 1 ]

Where aggdefSlider = +100 for full aggressive, -100 for full defensive, and 0 for the neutral position.

And where you choose the maximum of either the calculated number or 1, whichever is higher.

For example, if your weap's listed attack speed is 1.0, your associated initiative is 400, and your aggDef slider is at full Aggressive then your weap's adjusted attack speed would be MAX [ ((1 + 1) - (400 / 600)) - (100 / 100) , 1 ] = MAX [ 0.34 , 1 ] = 1

One more example. If your weap's listed attack speed is 1.0, your associated initiative is 400, but this time you set your aggdefSlider at half Defensive then your weap's adjusted attack speed would be MAX [ ((1 + 1) - (400 / 600)) - (-50 / 100) , 1 ] = MAX [ 1.84 , 1 ] = 1.84

Recharge Speed
The formula to calculate your weapon's initiative- and AggDef-adjusted recharge speed is this:

adjustedAttackSpeed = MAX [((listedAttackSpeed + 1) - (yourCombatInitiative / 300)) - (aggdefSlider / 100) , 1 ]

For example, if your weap's listed recharge speed is 2.5, your associated initiative is 400, and your aggDef slider is at the neutral position then your weap's adjusted recharge speed would be MAX [ ((2.5 +1) - (400 / 600)) - (0 / 100) , 1 ] = MAX [ 2.84 , 1] = 2.84

The Formula using the FunCom Designer's Numbers

If you prefer to use the FunCom designer's numbers, the formula to calculate both your weapon's initiative- and AggDef-adjusted attack and recharge speeds is this:

adjustedSpeed = MAX [(listedAttackSpeed - (yourCombatInitiative / 1000)) - (aggdefSlider / 100) , 0.5 ]

For example, if your weap's listed attack speed is 1.5, your associated initiative is 400, and your aggDef slider is at full Aggressive then your weap's adjusted attack speed would be MAX [ (1.5 - (400 /1000)) - (100 / 100) , 0.5 ] = MAX [ 0.1 , 0.5 ] = 0.5

Determining the Optimum AggDef Slider Position

As the previous section shows, your AggDef slider affects your weapon's adjusted attack and recharge speeds. The effect of the AggDef bar is cumulative with the effect of your combat initiative, however, so after factoring in the effects of both your combat initiative and your AggDef slider, you can often end up with actual attack/recharge speeds that are much faster than the minimum possible speeds.

The AggDef slider gives you more speed by reducing the effective value of your evade skills. The trade-off is more frequent attacks at the cost of fewer successful evades and more criticals scored on you.

So the important thing to understand is that you don't want to set your AggDef slider any higher than necessary to achieve the minimum possible attack/recharge speeds. Otherwise, you're throwing away your evasive skills for nothing.

To Determine the Optimum AggDef Slider Position for a Given Weapon

  1. First, decide whether you want to use Slicer's numbers or the FunCom designer's numbers for the fastest possible attack/recharge speeds. In other words, decide whether you're shooting for an AggDef setting that will yeild 1/1 attack/recharge speed, or 0.5/0.5 attack/recharge speed.

  2. Choose the slower of your adjusted attack or recharge speeds. Use the following formula on it:

optimumAggdefSetting = - MIN [ slowestInitSpeed , targetInitSpeed ]* 100

For example, if your weap's slowest initiative-adjusted speed is the recharge speed, weighing in at 1.83 seconds) and your target recharge speed is 1 second (meaning you're using Slicer's numbers), then your optimum AggDef setting would be MIN [ 1.83 , 1 ] * 100 = 100

Remember, a positive value indicates pushing the slider towards full Agressive. In this case, the 100 value indicates putting the AggDef slider at full Agressive. A value of 50 would indicate putting the slider halfway between the neutral position and full Aggressive. A value of 0 would indicate putting the slider at the neutral position. A negative value would indicate putting the slider at a corresponding percentage towards full Defensive.

Putting the AggDef slider at the optimum position gives you the greatest frequency of attacks possible without sacrificing any more evasive skills than necessary.

Putting It All Together To Calculate Your Actual Damage Output

Once you have your AC-adjusted min/max/average damage numbers and your adjusted attack and recharge speeds, you can calculate exactly how much damage a given weapon will put out per second.

There are two formulas I'm going to list: one is for ranged weapons and one is for melee weapons. I'm not going to dissect each formula for you, but here is the basic overview:

The Formula For Calculating Actual RANGED Damage Output

Plug the numbers from the preceeding sections into the following formula:

actualDamPerSecond = (clipSize * acAdjustedAverageDamage) / (((adjustedAttackSpeed + adjustedRechargeSpeed) * clipSize) + 3)

So, for example, take a QL62 Stigma with the following stats. With this weapon, you are fighting an opponent with a Projectile AC of 800. The weapon's base stats are shown first, and the adjusted stats that factor in a minimum damage buff of 6, Rifle skill of 256, and a ranged initiative of 161. Note that I am using Slicer's numbers for the AggDef-adjusted attack and recharge speeds. Also note that using Slicer's numbers, my Optimum AggDef slider position calculates to be +96, which maxes out the attack frequency of this rifle given your ranged init of 161.

Using these numbers, your actual damage output per second would be (125 * 152.5) / (((1+1) * 125) + 3) = 75.35

(Note that my spreadsheet calculates a DPS figure of 75.45 when given these stats. This is due to greater precision behind the various spreadsheet calculations before rounding to two decimal places.)

The Formula For Calculating Actual Melee Damage Output

Plug the numbers from the preceeding sections into the following formula:

actualDamPerSecond = acAdjustedAverageDamage / (adjustedAttackSpeed + adjustedRechargeSpeed)

So, for example, take a QL60 Sledgehammer with the following stats. With this weapon, you are fighting an opponent with a Melee AC of 800. The weapon's base stats are shown first, and the adjusted stats that factor in a minimum damage buff of 6, 2HB skill of 220, and a melee initiative of 147. Note that I am using Slicer's numbers for the AggDef-adjusted attack and recharge speeds. Also note that using Slicer's numbers, my Optimum AggDef slider position calculates to be +100, which maxes out the attack frequency of this blade given your melee init of 147.

Using these numbers, your actual damage output per second would be 371 / (1.54 + 5.51) = 52.62