User blog:Airborne17th/Proving Call of Duty Balance with Mathematics

Proving Call of Duty Balance with Mathematics

https://docs.google.com/leaf?id=0BwZ3TXdj5ZyHYTc0Mzc4NTgtMDc4Zi00N2ExLTllZTgtMzc3ZjNmMGRmZjFj&hl=en

https://spreadsheets.google.com/ccc?key=0AgZ3TXdj5ZyHdGF3ZEloVzNOMC1qWm83T2pqM1hxWGc&hl=en

http://denkirson.xanga.com/735016527/black-ops/

It’s hard to balance out 40 guns and 2 specials and 4 launchers. However, it is undeniable that there is a wide spread from the most powerful guns and the weakest. However, guns are not all about power. For a gun to be popular they must handle well; in switch time, run speed, and most importantly reload. A gun must be able to take out multiple enemies within one standard magazine without a need for a reload. Power, Capacity, Handling these are the three categories applied to these statistics. Using a bit of numbers we should be able to confirm gun ranking against each other.

For power we use this formula

For Close Range (0-25m)

RPM*MaxDmg*(1-ADS)+(CS-Recoil (Adding up all of the recoil numbers and assuming the highest numbers))

/RPM*MaxDmg*(1-ADS)+(CS-Recoil)

Mid Range (25-50m)

Rate of Accurate Fire (The need to burst fire at range, faster RPM guns slightly suffer here) or ROAF*MedDmg (Halfway between Max and Min if damage drops off here)*(1-ADS)+(CS-Recoil)

/ROAF*MedDmg *(1-ADS)+(CS-Recoil)

Long Range (+50m)

/ROAF*Min Dmg*(1-ADS)+(CS-Recoil)

Why ADS is calculated to firepower ratings

The ADS is in the firepower formula because the ADS time is very important to how accurate damage is put down range. ADS is the need to be accurate and subtly can also represent hipfire since generally faster ADS, the better hipfire.

<p style="margin: 0in 0in 10pt">There are rules to this formula that applies to certain situations.

<p style="margin: 0in 0in 10pt">Skorpion and the pistols

<p style="margin: 0in 0in 10pt">Because of their rapid damage drop off, Skorpion Close Range Dmg is 35 (50+20)/2) and the non-revolvers is 30 (40+20/2)

<p style="margin: 0in 0in 10pt">Rule of 6000

<p style="margin: 0in 0in 10pt">Because of the unique nature of sniper rifles, 6000 firepower rating points were taken out of close range combat stat due to the clumsiness of the SRs in that field and 6000 FPR were added to long range for oblivious reasoning.

<p style="margin: 0in 0in 10pt">One Hit Kill Rule

<p style="margin: 0in 0in 10pt">Here we determine the damage by adding hit the modifiers by limbs and dividing to get the mean.

<p style="margin: 0in 0in 10pt">i.e WA2000 (140 Head)+(140 Neck)+(105 Chest)+(70 Gut)+(70 Arms)+(70 Legs)/6=99.17 (rounded)

<p style="margin: 0in 0in 10pt">To apply this to the Firepower Formula we multiple the damage part of the formula by the number of modifiers the Sniper Rifle has.

<p style="margin: 0in 0in 10pt">So the final form should look like this

<p style="margin: 0in 0in 10pt">i.e. PSG 1 =(C36*D36*I36*3(Neck, Chest, Gut)+(E36-F36)+6000 (Rule of 6000(

<p style="margin: 0in 0in 10pt">Burst Fire *3 Rule

<p style="margin: 0in 0in 10pt">When calculating the burst fire firepower rating, an addition *3 was added representing the three burst fire of the M16 and G11

<p style="margin: 0in 0in 10pt">i.e. =(B12*D12*G12+(E12-F12)*3)

<p style="margin: 0in 0in 10pt">“Average” Trigger Finger Rule

<p style="margin: 0in 0in 10pt">While the firerate for the FAL and M14 is 625, they have been nerfed down to 535 to factor in recoil effects in semi-automatic fire in close range combat. The Rate Of Accurate Fire is mostly based on previously used firecaps in CoD.

<p style="margin: 0in 0in 10pt">Shotguns Fizzle Out Rule

<p style="margin: 0in 0in 10pt">Because shotgun pellets do not go infinitely like other guns and disappear. Shotguns have 0 FRP in Mid range and long range.

<p style="margin: 0in 0in 10pt">'''Firepower '''

<p style="margin: 0in 0in 10pt">Ok, now that we did all of that let’s look at the stats…the guns have the points they should.

<p style="margin: 0in 0in 10pt">A general rule of thumb.

<p style="margin: 0in 0in 10pt">0 Pellets can’t reach that far 1-9999 this gun can cause damage at this range but, is not recommended 10000-14999 Passable 15000-19999 Player should feel comfortable engaging enemies with this rating 19999-24999 This weapon excels this range +25000 You should win most of the time

<p style="text-indent: 0.5in; margin: 0in 0in 10pt">SMGs while having great close range FPR, suffer at longer ranges due to their weak minimum damage. No SMG is fully suited for mid range or long range combat however, the Skorpion and AK-74u are your best candidates for shooting at longer ranges. Curiously, the Spectre, PM63, and MAC-11 tie in firepower.

<p style="text-indent: 0.5in; margin: 0in 0in 10pt">ARs are of course all-around useful and overall very strong FPR. FAMAS and AUG are the most powerful in close range engagements but, the Commando, AK-47, Galil, and G11 are overall more useful at all ranges.

<p style="text-indent: 0.5in; margin: 0in 0in 10pt">LMGs have the highest FPR. The ''Stoner 63 is the most powerful gun ingame. ''The Stoner 63 has the fast firerate of 937.5 and 40 damage with no dropoff if you want firepower, use the Stoner.

<p style="text-indent: 0.5in; margin: 0in 0in 10pt">Shotguns are shotguns.

<p style="text-indent: 0.5in; margin: 0in 0in 10pt">Sniper Rifles don’t go over 25000 quite rightly because other non-sniper rifles can perform well at long range and pick off an unfortunate sniper. Sniper Rifles are still effective niche guns.

<p style="text-indent: 0.5in; margin: 0in 0in 10pt">Pistols are not powerhouses except for the Python. With a 50-30 a Python ranks 10th overall, impressive for its size.

<p style="text-indent: 0.5in; margin: 0in 0in 10pt">In terms of firepower the guns rank

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l1 level1 lfo1">1. Stoner 63

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l1 level1 lfo1">2. Galil

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l1 level1 lfo1">3. M60

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l1 level1 lfo1">4. Commando (tie)

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l1 level1 lfo1">5. AK-47 (tie)

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l1 level1 lfo1">6. HK21

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l1 level1 lfo1">7. RPK

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l1 level1 lfo1">8. G11

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l1 level1 lfo1">9. FAMAS

<p style="text-indent: -0.25in; margin: 0in 0in 10pt 0.75in; mso-add-space: auto; mso-list: l1 level1 lfo1">10. Python

<p style="margin: 0in 0in 10pt 0.5in">'''Capacity '''

<p style="margin: 0in 0in 10pt 0.5in">This is really simple. How many bullets are in the gun and how many players you can kill with max and min damage. There are a lot of ties so we will avoid ranking the guns right now, just note the difference of M60 able to kill 50 players to the Olympia 2.

<p style="margin: 0in 0in 10pt 0.5in">'''Handling '''

<p style="margin: 0in 0in 10pt 0.5in">Having the best switch times, reload, and run speed is important. A gun that has superior firepower but, poor handling is seen less often than guns that has less firepower but better handling. In general pistols, SMGs, and Shotguns handle the best

<p style="margin: 0in 0in 10pt 0.5in">'''Overall '''

<p style="margin: 0in 0in 10pt 0.5in">After ranking all the guns and adding up their rankings from all three categories we can determine what are the “best” and “worse” guns. By far the best weapon in game is the Colt Commando, while not in the top 3 in any category the Commando has excellent FPR (50745), and reasonable capacity and handling. Luckily, the Commando is unlocked at such a high level, most players will not realize the potential of the weapon and will use more familiar weapons. The Olympia is the worse weapon in game, without a shadow of doubt. So we shall list the Best and Worse Guns here.

<p style="margin: 0in 0in 10pt 0.5in">Top 10 Best Weapons

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2">1. Commando

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2">2. AK-47

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2">3. G11

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2">4. Galil

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2">5. Stoner 63

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2">6. M16

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2">7. M60

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2">8. AUG

<p style="text-indent: -0.25in; margin: 0in 0in 0pt 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2">9. FAMAS

<p style="text-indent: -0.25in; margin: 0in 0in 10pt 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2">10. HK21

<p style="margin: 0in 0in 10pt 0.5in">Tiebreaker was the better ranking in the guns worse category ranking.

<p style="margin: 0in 0in 10pt 0.5in">Top 10 Worse Weapons

<p style="margin: 0in 0in 0pt 0.75in; mso-add-space: auto">1. Olympia

<p style="margin: 0in 0in 0pt 0.75in; mso-add-space: auto">2. SPAS-12

<p style="margin: 0in 0in 0pt 0.75in; mso-add-space: auto">3. WA2000

<p style="margin: 0in 0in 0pt 0.75in; mso-add-space: auto">4. L96A1

<p style="margin: 0in 0in 0pt 0.75in; mso-add-space: auto">5. HS 10

<p style="margin: 0in 0in 0pt 0.75in; mso-add-space: auto">6. Makarov

<p style="margin: 0in 0in 0pt 0.75in; mso-add-space: auto">7. M1911

<p style="margin: 0in 0in 0pt 0.75in; mso-add-space: auto">8. PSG1

<p style="margin: 0in 0in 0pt 0.75in; mso-add-space: auto">9. CZ75

<p style="margin: 0in 0in 10pt 0.75in; mso-add-space: auto">10. ASP

<p style="margin: 0in 0in 10pt">''But airborne17th according to your stats, players should be using the AK-74u and FAMAS less! ''

<p style="margin: 0in 0in 10pt">This is true. There are a few weapons, in theory, should overall perform better than the AK-74u and FAMAS. But, those two weapons have two things making them extremely popular. First reason has nothing to do with number. The FAMAS and AK-74u have built up a powerful reputation as “overpowered” since the first time anyone got killed by one and this was a “snowball effect” ever since release. Second, is a bit more complex. The FAMAS (26059.4) and AK-74u (25485) both have powerful close range numbers. IN fact they are #1 in their classes. This is the fundamental reason why these weapons are so common. The 0-25m zone is where majority of the fighting is. Having the highest close range number is important but not ''all important. ''However, most players will only care for having the close range advantage and will avoid long range engagements where these guns would do poorly. The FAMAS and AK-74u are dominated in close range combat the most common guns in-game while retaining robust capabilities and are thusly popular.

<p style="margin: 0in 0in 10pt">''Why are shotguns and sniper rifles are on the bottom of the ranking? ''

<p style="margin: 0in 0in 10pt; tab-stops: 166.5pt">Because they are not flexible; they are niche weapons and thus suffer when facing other more robust weapons. Shotguns, while having the dominate close range ratings, they fizzle out and thusly ranked accordingly. Sniper Rifles for all of their power and long range ratings, are very clumsy, have high recoils and unattractive handling characteristics. You are much off using an AR, LMG or SMG which can perform (sometimes not ideally) at all ranges.

<p style="margin: 0in 0in 10pt">''Shotgun Paradoxes ''

<p style="margin: 0in 0in 10pt">According to math, the SPAS-12 is an inferior shotgun that should be used less often and single HS10 should be slightly more common. However, the numbers can’t factor in why the SPAS-12 is one of the more popular shotguns; silencer. The SPAS-12 has no change with a silencer. Thus the SPAS-12 is a powerful silenced close range weapon with a close range rating of 30945 and can be justified in its popularity.

<p style="margin: 0in 0in 10pt">Conclusion

<p style="text-indent: 0.5in; margin: 0in 0in 10pt">I’m not arrogant enough to say that I’m 100% correct but, I’m fairly confident that the stats are roughly correct. For the purpose of ranking the overall best weapon I feel the numbers are pretty close. Still math can’t factor in everything and the individual ranking of guns might be off since some guns have special properties (Kiparis and Assault Rifle Penetration), better iron sights or more attachments it’s clear that a 100% accurate ranking will never happen. Still we can confirm a few opinions on guns and confidently state the rank of a gun with mathematics. Balance is iffy, the Olympia is a terrible gun far under every other gun and the Commando is clearly superior to any other. The spread I feel is too far apart but, what can you do?