[Note: Well whaddaya know? The message forum has a character limit per post of 20,000 characters. And I hit it. That should tell you something about this message. Anyhow, since I can't post all of this message in one go, I'm cutting it into two bits. The 2nd part will be in the reply to this message.]
Preliminaries
The motivation for this post was, simply, to come up with a way to compare different weapons. We've all been faced with the choice of two weapons with differing speeds, damage ranges, and HAM costs, and it would be useful to have a way to compare them and determine which one is better for a given situation. With that in mind, and with pen, paper, and calculator in hand, I sat down and tried to come up with a useful method of comparison.
To warn you, this post is very long, and is filled with all manner of Math Geekery(tm). If you are the sort of person who likes to see the figures and the formulas and the reasons those particular formulas are used, then you may want to read the entire post at your leisure.
If, on the other hand, you're the sort of person that feels your eyes glaze over at the mere mention of the word "algebra," and assuming you trust me to know what I'm talking about, then feel free to skip over all of the following until you get to the next section. Everything between here and there will be simply me setting the foundation for my data and my conclusions, so that those who want to check my methodology can do so. The actual weapon comparisons will be in first reply to this message.
Before we go further, a recap of some basics:
Base Damage: The damage that appears in your "Battlespam" (i.e. the text which shows up in your Combat window). The minimum amount of Base Damage you can do with autofire will be the minimum damage rating of your weapon multiplied by 1.5. The maximum amount of Base Damage you can do with autofire will be the maximum damage rating of your weapon multiplied by 1.5. So if you have a weapon with a damage rating of 100-200, your base damage will range from (100 * 1.5) to (200 * 1.5), or 150-300.
Floaty Damage: The damage that appears over the heads of critters, NPCs, and PCs when you shoot them. This is the damage that is actually removed from the HAM bars of your target. 80% of the damage is applied to one HAM bar, and 10% is applied to each of the other two. So a 100-point shot to the Head would take off 80 points of Mind, 10 points of Health, and 10 points of Action. Floaty damage is obtained by multiplying the Base Damage by a Resistance and Armor Factor (RAF).
Resistance and Armor Factor (RAF): The effect of Armor Piercing (or lack thereof) and Damage Resistance. The RAF consists of an Armor Piercing Bonus (or Penalty), and a Resistance modifier.
Armor Piercing Bonus: [(1.25)^(AP-AR)] This is applied whenever the AP of the weapon is larger than the AR of the target.
Armor Piercing Penalty: [(0.50)^(AR-AP)] This is applied whenever the AR of the target is larger than the AP of the weapon.
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One of the convenient things about the SWG combat engine is that the damage distribution seems to be even. If you have a weapon with the following stats: 100-200 Damage; 3.5 Speed; 15/20/25 HAM; AP: Heavy, then you will have Base Damage values of 150-300 for autofire, and the chances of you hitting for any particular damage value from 150-300 will be the same for all values. Your chance of hitting for 188 points of Base Damage is the same as your chance for hitting for 234 points of Base Damage, which is the same as your chance of hitting for 150 points, which is the same as your chance of hitting for 300 points, etc.
This is convenient because, with an even distribution, you can easily find out your Average Base Damage Per Shot. Specifically: [(Weapon Min + Weapon Max)/2] * 1.5
So for our hypothetical weapon with damage 100-200, the Average Base Damage Per Shot is: [(100 + 200)/2] * 1.5 = 225
Next we need to factor in Armor Piercing. This will give us the Average AP Damage Per Shot To factor in the Armor Piercing rating of the weapon, simply take the Average Base Damage Per Shot of the weapon and multiply it by [(1.25)^N], where N takes on a numerical rating based on the following:
0 = No AP 1 = Light AP 2 = Medium AP 3 = Heavy AP
This represents the "base case" where you're firing against a critter with no armor. Returning to our hypothetical weapon, the Average AP Damage Per Shot is: [(100 + 200)/2] * 1.5 = 225 225 * (1.25)^3 = 439.5
With the Average AP Damage Per Shot in hand, one of the more obvious ways to compare weapons is via AP Damage Per Second.
And here's where it gets a little tricky.
Each weapon has a Base Weapon Speed. Our hypothetical 100-200 damage weapon has a Base Weapon Speed of 3.5. That means that, in autofire mode, and assuming reasonable latency conditions, the weapon will fire once every 3.5 seconds.
But.
Each specific weapon track has a corresponding "Speed" skill. If you train Novice Rifleman, you receive +5 Rifle Speed, +5 Pistol Speed, and +5 Carbine Speed. As you go up each track, your weapon specific Speed skill increases. By the time you reach the Novice level of one of the three specialized weapon professions (Novice Rifleman, Novice Pistoleer, or Novice Carbineer), your Speed skill for your specific weapon will be +30. (And if you're a Master Marksman as well, it'll be +35.)
This is important because your Actual Firing Rate is affected by your Weapon Speed skill thusly: (Base Weapon Speed) * [1 - (Weapon Speed Skill/100)]
This means (among other things) that you can't calculate an AP Damage Per Second rating simply by dividing Average AP Damage Per Shot by the Base Weapon Speed.
Fortunately, however, the purpose of this exercise is NOT to calculate Damage Per Second. Remember: We're just looking for a number we can use to compare weapon effectiveness. And, as it turns out, dividing Average AP Damage Per Shot by the Base Weapon Speed will -- with one particularly crucial caveat which I will detail below -- give us a very useful number for weapon comparison. I call this number the Effectiveness Rating. The complete formula for the Effectiveness Rating is:
Crucial Caveat(tm): There is a 1.0 second speed cap on all weapons. This means that for many weapons, there will come a point where you are shooting that weapon as fast as you will ever shoot it, and no amount of Speed skill increase will allow you to fire any faster. At that point, other weapons which have a lower Effectiveness Rating will slowly become more effective, relative to the weapon at the 1.0 speed cap, and may even surpass the original weapon's effectiveness with increased Weapon Speed Skill.
To illustrate this point, compare two hypothetical weapons: a 150-250 damage, 1.3 speed weapon with no armor piercing, and a 150-400 damage, 5.0 speed weapon, also with no armor piercing.
The Effectiveness Rating for the first weapon is: {[(150+250)/2] * 1.5}/1.3 = 230.8
The Effectiveness Rating for the second weapon is: {[(150+400)/2] * 1.5}/5.0 = 82.5
According to this, the first weapon is clearly superior. It will throw out more damage in less time than the second weapon.
However, the first weapon will hit the 1.0 second speed cap when the user's Weapon Speed Skill hits 23.1. Which effectively means that the user will hit the cap when he trains his 4th box in the Marksman Weapon Track (i.e. Rifle Specialist, Pistol Specialist, Carbineer Specialist), since that would put his Weapon Speed Skill at +25. So once he's trained that 4th box, he's firing that weapon as fast as he's ever going to fire it. The adjusted Effectiveness Rating for the first weapon once it hits the 1.0 speed cap is: {[(150+250)/2] * 1.5}/1.0 = 300
By contrast, the user of the 2nd weapon won't hit the 1.0 speed cap until she reaches a Weapon Speed Skill of +80. But at that point the adjusted Effectiveness Rating for the 2nd weapon will be: {[(150+400)/2] * 1.5}/1.0 = 412.5
Note that at this point, the 2nd weapon is actually outperforming the 1st.
If you're curious, the performance of the 2nd weapon equalled the performance of the 1st weapon when the Weapon Speed Skill of the user of the 2nd weapon hit +72.5.
If you're REALLY curious, if you have two weapons, and the 1st weapon (A) has a higher Effectiveness Rating than the 2nd; and (B) is already at the 1.0 second speed cap, you can calculate the Weapon Speed Skill needed to make the performance of the 2nd weapon equal the performance of the first via the following formula: Weapon Speed Skill = (100) * {1 - (Min2 + Max2)/[(Min1 + Max1) * Base Weapon Speed]}
where Min1 is the minimum listed damage for the 1st weapon, Min2 is the minimum listed damage for the 2nd weapon, etc., and where Base Weapon Speed is the speed of the 2nd weapon.
Anyhow, the upshot of all this fascinating math is this:
A weapon with a higher Effectiveness Rating will outperform a weapon with a lower Effectiveness Rating, provided:
1) The Armor Rating of the target critter is equal to or lower than the Armor Piercing Rating for both weapons. 2) The target critter is not vulnerable to the damage type of either weapon. 3) The Weapon Skill Speed is the same for both weapons. 4) The 1.0 second speed cap is not in effect for either weapon.
The weapon with the higher Effectiveness Rating MAY continue to outperform the weapon with the lower Effectiveness Rating even if one or more of these conditions aren't met. But if all four conditions are met, then the weapon with the higher Effectiveness Rating will always be the superior weapon.
This being the case, I will provide the Weapon Speed Skill at which the weapon hits the speed cap when I finally get around to actually comparing various weapons (which, at the rate that I'm going, will probably happen sometime in June 2011).
Finally, if we want to see how weapons compare with respect to firing special attacks (Eye Shot, Torso Shot, Underhand Shot, etc), we can divide the Effectiveness Rating by the HAM costs to get what I call the Volsted Rating. (I call it that because "HAM Effectivness Rating" and "Effectiveness HAM Rating" both sound dorky to me, and because I suck at coming up with names.)
Harking back to our initial hypothetical weapon, the one with the 100-200 damage and the 15/20/25 HAM costs, the Volsted Rating would be:
If you just got here by skipping over all the foregoing algebra, allow me to be among the first to welcome you to the rest of this post. Here's the payoff, where all of those calculations will come into play.
I have taken the stock list of one of the Weaponsmiths on my server (Tempest) and have calculated Effectiveness Ratings and Volsted Ratings for all of his listed weapons. The weapons on your server will almost certainly be different than these (unless you're also on Tempest), but in general they won't be MUCH different. So making a comparison between these weapons as a baseline will give you a rough idea of how your own weapons stack up.
For each listed ranged weapon which has an autofire mode, I will provide the Effectiveness Rating, the Volsted Rating, and the Weapon Speed Skill required to hit the 1.0 second speed cap.
Flamethrower; 422-810 Damage; 4.7 Speed; 75-17-17 HAM; AP: None Effectiveness Rating: 196.6 Volsted Rating: 2.6/11.6/11.6 Hits Speed Cap at: N/A (so far as I'm aware)
Disclaimers
I'm human, so I may have made a math error here or there. I may even (despite the claim of the thread subject) have made some fundamentally flawed assumptions. I don't think I have, but that's why I posted all of the steps and reasons in my methodology. If I've made any errors in math or in reasoning, everything is right there, open to inspection, for someone smarter than me to come along and say "You got this bit wrong here..."
I'm also a little suspicious about the "Hits Speed Cap at:" entries. Nothing I can put my finger on. Just a hunch. But the math is valid, assuming the speed formula I saw was correct.
Finally, keep in mind that these numbers don't tell the whole story. There are several factors that I did not (and cannot) take into account, such as the 2.5x melee damage penalty for Rifles and Heavy Weapons.
Anyhow, hope this message proves to be useful to some non-trivial segment of the playerbase.
I no longer feel that I may be getting too involved with this game? lol
Man, you put alot in to this and for that I thank you. All i know is i get higher up, I get faster, more accurate, and favor certain weapons for many different reasons, mostly situation dependant.
Great post! I was always so excited when I would get a speed slice, now I will be disappointed! I hit the cap long ago, lol.
AtrisloSpecializing in Bounty Hunting. | Specializing in Carbineer. | Specializing in Creature Handling.
Specializing in Rifleman. | Specializing in Architecture | Soon to be Specializing in Teras Kasi Artist.
Atrislo wrote: Great post! I was always so excited when I would get a speed slice, now I will be disappointed! I hit the cap long ago, lol.
Take into account that the cap he's shown only accounts for unstyled shots. When making styled shots you can take advantage of a weapon with much lower speed because of the spd multiplier built into the styled shot.
