Rifleman Archive
Thread: An in-depth weapon comparison (WARNING: Long post, filled with Math Geekery)
Page 1 of 1
VolstedGridban
Thu Oct 16, 2003 7:31 am
#1
Preliminaries
This post is, as mentioned in the subject line, long and filled with 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 section labelled "And now, the punch line..." 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.
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.
Now, on to the substance of the post...
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 a damage rating of 100-200, 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 damage per shot. Specifically:
[(Weapon Min + Weapon Max)/2] * 1.5
So for our hypothetical weapon with damage 100-200, the average damage per shot is:
[(100 + 200)/2] * 1.5 = 225
This is already known by a few folks, since I've seen people using this calculation to determine DPS ratings for various weapons. Take the Average Damage Per Shot and divide it by how fast the gun fires, and you've got an average Damage Per Second rating.
The tricky bit is that as you go up through the Advanced weapon professions (Pistoleer, Carbine Specialist, Rifleman), you get faster with weapons of the same Speed. That is, a Novice Marksman with a 3.6 CDEF Rifle will fire once every 3.6 seconds, but a Master Rifleman would fire much faster. So dividing Average Damage Per Shot by Speed doesn't really give you Damage Per Second. Fortunately, the Actual Firing Rate can be easily calculated thusly:
(Base Weapon Speed) * [1 - (Weapon Speed Skill/100)]
where "Weapon Speed Skill" is the weapon specific speed bonus you get for going up the specific weapon trees in the Marksman profession, and then going up the "Special Abilities" tree in the Rifleman/Pistoleer/Carbineer professions.
Due to the way the Actual Firing Rate is calculated, if Weapon A has a higher DPS than Weapon B when you divide the Average Damage Per Shot by the Base Weapon Speed, then Weapon A will always have a higher DPS than Weapon B for the same Weapon Skill SPeed.
To illustrate this point, and to fulfill my promise of there being lots of boring math stuff in this post, let's say that our hypothetical weapon with the 100-200 damage rating is speed 3.5 and has no Armor Piercing. We'll call this Blaster A. And let's compare it to another hypothetical weapon, with a damage rating of 200-300, with a speed of 5.0, and also with no Armor Piercing. We'll call this Blaster B.
Blaster A:
[(100+200)/2] * 1.5 = 225
225/3.5 = 64.3
Blaster B:
[(200+300)/2] * 1.5 = 375
375/5.0 = 75.0
So, based on these numbers, Blaster B is better than Blaster A. The slower fire rate (5.0 vs. 3.5) is compensated for by the higher Average Damage Per Shot (375 vs. 225).
Now, let's say that you've gotten a few boxes of "Weapon Speed Bonuses" under your belt. And you're firing all your weapons faster than what the weapon Speed would indicate. Will Blaster B still be better than Blaster A?
Let's say that your Weapon Speed Skill is +20. That would give you an Actual Fire Rate for Blaster A of:
(3.5) * [1 - (20/100)] = (3.5) * (0.80) = 2.8
The Actual Fire Rate of Blaster B would be:
(5.0) * [1 - (20/100)] = (5.0) * (0.80) = 4.0
Comparing the two weapons again, this time with the faster fire rate:
Blaster A:
[(100+200)/2] * 1.5 = 225
225/2.8 = 80.4
Blaster B:
[(200+300)/2] * 1.5 = 375
375/4.0 = 93.8
Again, Blaster B is the clear winner over Blaster A.
This trend continues regardless of the Weapon Speed Skill, and we can make the following assertion:
Given two weapons with the same Armor Piercing rating, the one with the highest value for (Average Damage Per Shot)/(Base Weapon Speed) will always outperform the other weapon at the same level of Weapon Speed Skill.
With this in mind, we don't have to calculate the Actual Firing Rate for our level of skill if all we want to know is "Which one of these weapons will outperform the others?" If all we want to know is which weapon is the most effective, simply make the foregoing calculations with the Base Weapon Speed. This will give us a Basic Effectiveness Rating.
Armor Piercing is easy to factor in, with a few caveats. Simply take the Base Effectiveness Rating 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 can lead to some interesting situations, since it is possible for a weapon with less AP to be more effective under some circumstances than a weapon with higher AP. To illustrate, let's look at Blaster A and Blaster B above. Let's say that Blaster A is Heavy AP and Blaster B is Medium AP. That would give us an Adjusted Effectiveness Rating of:
Blaster A:
Basic Effectiveness Rating: [(100+200)/2] * 1.5 = 225
Adjusted Effectiveness Rating: 225 * (1.25)^3 = 439.4
Blaster B:
Basic Effectiveness Rating: [(200+300)/2] * 1.5 = 375
Adjusted Effectiveness Rating: 375* (1.25)^2 = 585.9
Note that Blaster B is still superior to Blaster A, even though Blaster B has a lower AP rating. This will remain true right up until the point where Blaster B is shooting something with AR3. Vs. AR3 critters, Blaster A will be the superior weapon. This leads us to our next assertion:
Given two weapons, the weapon with the highest Adjusted Effectiveness Rating will outperform the other weapon, providing that (A) the AP of the less effective weapon is equal to or lower than the AP of the more effective weapon; and (B) the AR of the target MOB is equal to or lower than the AP of the more effective weapon.
This post is, as mentioned in the subject line, long and filled with 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 section labelled "And now, the punch line..." 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.
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.
Now, on to the substance of the post...
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 a damage rating of 100-200, 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 damage per shot. Specifically:
[(Weapon Min + Weapon Max)/2] * 1.5
So for our hypothetical weapon with damage 100-200, the average damage per shot is:
[(100 + 200)/2] * 1.5 = 225
This is already known by a few folks, since I've seen people using this calculation to determine DPS ratings for various weapons. Take the Average Damage Per Shot and divide it by how fast the gun fires, and you've got an average Damage Per Second rating.
The tricky bit is that as you go up through the Advanced weapon professions (Pistoleer, Carbine Specialist, Rifleman), you get faster with weapons of the same Speed. That is, a Novice Marksman with a 3.6 CDEF Rifle will fire once every 3.6 seconds, but a Master Rifleman would fire much faster. So dividing Average Damage Per Shot by Speed doesn't really give you Damage Per Second. Fortunately, the Actual Firing Rate can be easily calculated thusly:
(Base Weapon Speed) * [1 - (Weapon Speed Skill/100)]
where "Weapon Speed Skill" is the weapon specific speed bonus you get for going up the specific weapon trees in the Marksman profession, and then going up the "Special Abilities" tree in the Rifleman/Pistoleer/Carbineer professions.
Due to the way the Actual Firing Rate is calculated, if Weapon A has a higher DPS than Weapon B when you divide the Average Damage Per Shot by the Base Weapon Speed, then Weapon A will always have a higher DPS than Weapon B for the same Weapon Skill SPeed.
To illustrate this point, and to fulfill my promise of there being lots of boring math stuff in this post, let's say that our hypothetical weapon with the 100-200 damage rating is speed 3.5 and has no Armor Piercing. We'll call this Blaster A. And let's compare it to another hypothetical weapon, with a damage rating of 200-300, with a speed of 5.0, and also with no Armor Piercing. We'll call this Blaster B.
Blaster A:
[(100+200)/2] * 1.5 = 225
225/3.5 = 64.3
Blaster B:
[(200+300)/2] * 1.5 = 375
375/5.0 = 75.0
So, based on these numbers, Blaster B is better than Blaster A. The slower fire rate (5.0 vs. 3.5) is compensated for by the higher Average Damage Per Shot (375 vs. 225).
Now, let's say that you've gotten a few boxes of "Weapon Speed Bonuses" under your belt. And you're firing all your weapons faster than what the weapon Speed would indicate. Will Blaster B still be better than Blaster A?
Let's say that your Weapon Speed Skill is +20. That would give you an Actual Fire Rate for Blaster A of:
(3.5) * [1 - (20/100)] = (3.5) * (0.80) = 2.8
The Actual Fire Rate of Blaster B would be:
(5.0) * [1 - (20/100)] = (5.0) * (0.80) = 4.0
Comparing the two weapons again, this time with the faster fire rate:
Blaster A:
[(100+200)/2] * 1.5 = 225
225/2.8 = 80.4
Blaster B:
[(200+300)/2] * 1.5 = 375
375/4.0 = 93.8
Again, Blaster B is the clear winner over Blaster A.
This trend continues regardless of the Weapon Speed Skill, and we can make the following assertion:
Given two weapons with the same Armor Piercing rating, the one with the highest value for (Average Damage Per Shot)/(Base Weapon Speed) will always outperform the other weapon at the same level of Weapon Speed Skill.
With this in mind, we don't have to calculate the Actual Firing Rate for our level of skill if all we want to know is "Which one of these weapons will outperform the others?" If all we want to know is which weapon is the most effective, simply make the foregoing calculations with the Base Weapon Speed. This will give us a Basic Effectiveness Rating.
Armor Piercing is easy to factor in, with a few caveats. Simply take the Base Effectiveness Rating 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 can lead to some interesting situations, since it is possible for a weapon with less AP to be more effective under some circumstances than a weapon with higher AP. To illustrate, let's look at Blaster A and Blaster B above. Let's say that Blaster A is Heavy AP and Blaster B is Medium AP. That would give us an Adjusted Effectiveness Rating of:
Blaster A:
Basic Effectiveness Rating: [(100+200)/2] * 1.5 = 225
Adjusted Effectiveness Rating: 225 * (1.25)^3 = 439.4
Blaster B:
Basic Effectiveness Rating: [(200+300)/2] * 1.5 = 375
Adjusted Effectiveness Rating: 375* (1.25)^2 = 585.9
Note that Blaster B is still superior to Blaster A, even though Blaster B has a lower AP rating. This will remain true right up until the point where Blaster B is shooting something with AR3. Vs. AR3 critters, Blaster A will be the superior weapon. This leads us to our next assertion:
Given two weapons, the weapon with the highest Adjusted Effectiveness Rating will outperform the other weapon, providing that (A) the AP of the less effective weapon is equal to or lower than the AP of the more effective weapon; and (B) the AR of the target MOB is equal to or lower than the AP of the more effective weapon.
VolstedGridban
Thu Oct 16, 2003 7:32 am
#2
Bah.
Hit "Submit Post" when I meant to hit "Preview Post".
There will be more to follow. Please stand by.
Hit "Submit Post" when I meant to hit "Preview Post".
There will be more to follow. Please stand by.
VDog
Thu Oct 16, 2003 8:30 am
#3
Given two weapons with the same Armor Piercing rating, the one with the highest value for (Average Damage Per Shot)/(Base Weapon Speed) will always outperform the other weapon at the same level of Weapon Speed Skill.
One quick note. Nice write-up, I'm sure this will help some people out however... This sentance is patently false, specifically at Master (or near master) levels. This is due to the 1 second speed cap maximum. Though it applies much more heavily to pistoleers than it does to use Rifleman, it is still true. No weapon can be fired faster than 1 shot per second period. So that nice scout blaster sliced down to 1.1 weapon speed will hit 1.0 with practically any pistol speed mods. So amarksman fires the exact same rate as a master pistoleer with this weapon.
To apply this more to a Rifleman: Take a laser rifle. Say 80-400 dmg with 5.5 speed. At master Rifleman this will hit the 1 second cap. A T21 for example 150-350 dmg 7.5 speed. This will also hit the 1 second cap. By your calculations the laser would be better (assuming target has medium or lower armor) for every skill level. However by master the T21 has a slight advantage since they both fire at 1 second.
VolstedGridban
Thu Oct 16, 2003 8:46 am
#4
Yes. As these things tend to go, I've discovered a couple of flawed assumptions in my post that I did not discover until AFTER hitting the post button accidentally. Had it not been for the accidental hitting of "submit" instead of "preview," I would have uncovered my flawed assumptions before posting, and you would all be in awe of my flawless mathematical prowess. 
Sadly, as it stands, I'm now having to re-work and re-write the post to correct the flawed assumptions, and you are all now aware that I'm a moron.
In any event, if you have read the above post, disregard it. It is wrong in a couple of very crucial respects. A shiny new post with revisions and everything will be along later today.
Sadly, as it stands, I'm now having to re-work and re-write the post to correct the flawed assumptions, and you are all now aware that I'm a moron.
In any event, if you have read the above post, disregard it. It is wrong in a couple of very crucial respects. A shiny new post with revisions and everything will be along later today.
Arcanis_Paimae
Thu Oct 16, 2003 8:53 am
#5
Very good information!!!! I can't wait for part 2!
You know what would be really cool? To have some sort of calculator that we can plug in the min/max damage, speed, and ap of a weapon and have it spit out the base effectiveness, adjusted effectiveness, based on what AR they are hitting? How cool would that be 
I might work something out in visual basic. hmmm.
VolstedGridban
Thu Oct 16, 2003 9:00 am
#6
Arcanis_Paimae wrote:
Very good information!!!! I can't wait for part 2!
Part 2?!?
First you hafta see Part 1 without the mistakes!
RebRifle
Thu Oct 16, 2003 2:14 pm
#7
The thing about it though is the random factor of the amount of the hit so if a laser rifle is 50-340, and a t21 120-340 so in theroy the t21 is better take in mind this is a number i made up off the tip of my head
Laipi
Thu Oct 16, 2003 4:52 pm
#8
exactly.. the post about the t21 with its much higher minimum is a huge deal
though even with a powerup my t21 is 175 -616 and my laser rifle is 58- 818..
if i want to ensure i win the fight against a creature i will pull out the t21 everytime as mine only uses 20 more mind than my laser and gets a huge bonus (double damage) against unarmored and i know my shots will never stray below 2k dmg with strafe 2 spammage
CaLVines
Fri Oct 17, 2003 12:43 am
#9
Just some more thoughts:
While getting the DPS is a nice thing to know, there is more to the effectiveness of a weapon than that number can tell. Even with same DPS two weapons may be very different and one of them may be much better suited for a certain job. In swg, this is affected by 2 factors: "over-damage" and HAM-cost, but both basically come down to speed. Note: Due to the strange system of weapon speed calculation, this point is only interesting if not Master, since at Master most things shoot at 1 second anyway.
"Over-damage" (for the lack of a better word) is not SWG specific. The concept is that when you look at 2 weapons with same DPS, the one with the faster fire rate is always the more effective one in killing stuff. For an extreme example, assume you have Weapon A with an average dmg of 1 and a speed of 1, and Weapon B with an average damage of 100 and a speed of 100. Both have DPS of 100. Both take 100 seconds to kill a MOB with 100 health (or mind or action). However, look at a MOB with 101 health points. Weapon A takes 101 seconds to deal out 101 points of damage. Weapon B takes 200 seconds to deal out 200 points of damage, but 99 points of damage are worthless (hence over-damage). So fighting a single opponent is quicker with weapon A, and when fightin multiple MOBs you migth be able to kill 2 in almost the same time as it takes Weapon B. So, speed is very important. Due to this, depending on the MOBs you fight a faster weapon with a lower DPS may still outperform a slow weapon with higher DPS. The exact breakpoint depends on the MOB.
The second, SWG specific concept is HAM usage. Taking the weapons from the previous example and assuming you use a special attack, and assuming the special costs 10 mind. Shooting that 100 HP MOB takes Weapon A 100 shots, using up 1000 mind. For 100 dmg this is 0.1 dmg per HAM. Weapon B only takes one shot, using 10 mind. Which is 10 dmg per HAM. 100 times more effective. For the 101 HP MOB, weapon A is again at 0.1 dmg per HAM, and Weapon B drops to 5 dmg per HAM. Still I'd prefer weapon B.
As you see, those two concepts contradict each other. So the ideal weapon would be the one that shoots as fast as possible while having the dmg per HAM just as high that you can afford it to use. Which means, the more mind you have, the faster your gun should be (still assuming same special costs and DPS for each weapon).
Again, all moot points for a master. However, both the Master and the non-Master should take into consideration the HAM cost per weapon. If you have 2 weapons with identical speed and damage, the one with the lower HAM cost wins. Since it's usually not that easy to compare guns, let me just say that a real fast real hard-hitting weapon won't help you if you run out of mind too soon. In other words, think if you really want that weapon stock
And as a last point, think about min damage as well. If you rely on killing the MOB before it reaches you, you might want to to a weapon with high min dmg. Sure, the Laser usually has better DPS than a DTL20. But if using the Laser means you can one-hit kill the MOB 3 out of 4 times, and the 4th time it kills you, consider using the DTL20 and 2-hit kill it every time before it reaches you. Not a real valid example, but I think you get the point.
If you guys want, I can make it even more complicated, but I guess this should give enough new ideas for your comparism post. Which, btw, was a great idea and I do appreciate the effort you are making.
While getting the DPS is a nice thing to know, there is more to the effectiveness of a weapon than that number can tell. Even with same DPS two weapons may be very different and one of them may be much better suited for a certain job. In swg, this is affected by 2 factors: "over-damage" and HAM-cost, but both basically come down to speed. Note: Due to the strange system of weapon speed calculation, this point is only interesting if not Master, since at Master most things shoot at 1 second anyway.
"Over-damage" (for the lack of a better word) is not SWG specific. The concept is that when you look at 2 weapons with same DPS, the one with the faster fire rate is always the more effective one in killing stuff. For an extreme example, assume you have Weapon A with an average dmg of 1 and a speed of 1, and Weapon B with an average damage of 100 and a speed of 100. Both have DPS of 100. Both take 100 seconds to kill a MOB with 100 health (or mind or action). However, look at a MOB with 101 health points. Weapon A takes 101 seconds to deal out 101 points of damage. Weapon B takes 200 seconds to deal out 200 points of damage, but 99 points of damage are worthless (hence over-damage). So fighting a single opponent is quicker with weapon A, and when fightin multiple MOBs you migth be able to kill 2 in almost the same time as it takes Weapon B. So, speed is very important. Due to this, depending on the MOBs you fight a faster weapon with a lower DPS may still outperform a slow weapon with higher DPS. The exact breakpoint depends on the MOB.
The second, SWG specific concept is HAM usage. Taking the weapons from the previous example and assuming you use a special attack, and assuming the special costs 10 mind. Shooting that 100 HP MOB takes Weapon A 100 shots, using up 1000 mind. For 100 dmg this is 0.1 dmg per HAM. Weapon B only takes one shot, using 10 mind. Which is 10 dmg per HAM. 100 times more effective. For the 101 HP MOB, weapon A is again at 0.1 dmg per HAM, and Weapon B drops to 5 dmg per HAM. Still I'd prefer weapon B.
As you see, those two concepts contradict each other. So the ideal weapon would be the one that shoots as fast as possible while having the dmg per HAM just as high that you can afford it to use. Which means, the more mind you have, the faster your gun should be (still assuming same special costs and DPS for each weapon).
Again, all moot points for a master. However, both the Master and the non-Master should take into consideration the HAM cost per weapon. If you have 2 weapons with identical speed and damage, the one with the lower HAM cost wins. Since it's usually not that easy to compare guns, let me just say that a real fast real hard-hitting weapon won't help you if you run out of mind too soon. In other words, think if you really want that weapon stock
And as a last point, think about min damage as well. If you rely on killing the MOB before it reaches you, you might want to to a weapon with high min dmg. Sure, the Laser usually has better DPS than a DTL20. But if using the Laser means you can one-hit kill the MOB 3 out of 4 times, and the 4th time it kills you, consider using the DTL20 and 2-hit kill it every time before it reaches you. Not a real valid example, but I think you get the point.
If you guys want, I can make it even more complicated, but I guess this should give enough new ideas for your comparism post. Which, btw, was a great idea and I do appreciate the effort you are making.
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