Turret damage

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Governing Equation

Gosh. Assuming we're not all working this equation in our heads, what can we usefully learn from it?

To paraphrase Oli Geist, this can be abstracted to:

Chance to hit = 0.5 ^ (tracking term + range term).

General

Remember that anything to the 0th power = 1, so you'll always hit if (tracking+range) = 0. (1 is 100%.) Also remember that for any number 'x' < 1, the value of x^y approaches zero as y increases. Since 0.5 is less than one, we'd like the value of (tracking + range) to be as low as possible for better hits.

Range

So what can we do to maximize hits? Well, the range term becomes zero if we're at or under our turret's optimal range. It goes to 1 at (optimal + falloff), to 4 at (optimal + 2* falloff), and to 9 at (optimal + 3* falloff). 0.5^4 is 0.0625, or a 6.25% chance of hitting a large stationary target at that range. 0.5^9 is 0.002, or a 2/1000 chance of hitting. Good luck with that. So we can say that any range over (optimal + falloff) is very sketchy, and staying at or near optimal is good. No surprises here.

Tracking

What about tracking? Well, if traversal speed = 0, the tracking term evaluates to zero. So getting your target to come straight at you is super if you can do it. If he won't do that, the best way to minimize this term is some combination of: keep the target at longer range, lower the traversal speed, increase your turret's tracking speed, and/or increase the target's signature radius. That's range, webs, tracking computers, and target painters, in concrete terms. You can also choose 'keep at range' on a target to minimize the traversal -- though bear in mind that your target will be able to hit you more easily, too. Note that as range gets smaller, approaching 0, the tracking term inflates toward infinity if there's any traversal speed at all -- so your chance to hit plummets toward zero.

Turret damage values

At the heart of a turrets damage output is a single randomly generated value between 0 and 1 that is several digits long, something like 0.317226. This random number is used both to determine if the turret hits the target and also to determine how much damage the hit did. Should the randomly generated number be less than 0.01 (1% chance), it will be a wrecking hit which always deal exactly three times the normal average damage. So in those cases where the chance to hit is 1% or less, all hits on the target will be perfect and do tripple damage.

The raw damage dealt is calculated by taking the randomly generated number that resulted in a hit, adding 0.49, and multiplying this sum with the turrets base damage. A turrets base damage is a fixed number that is calculated by multiplying the turrets damage multiplier and the sum of the damage types from the ammo (the targets resistances is ignored, its dealt with later). Since the first 0.01% of the random value is used for perfect hits, the random values that hit normally are those between 0.01 and up to 1 at most (1 if chance to hit is 100%). So if the chance to hit was 100%, this means that the normal damage will be between 50% (0.01+0.49) and 149% (1+0.49) of the base damage, or in the case of a perfect hit always exactly 300% of the base damage. This number will then be reduced accordingly by the targets damage resistances in order to obtain the final damage number.

• Damage generation
  • Calculating variables
    • Turret Base Damage = Turret Damage Multiplier * Sum of Ammo Damages
    • Hit Chance = ((calculated by the big equation at the top of this page))
    • X = Random (0 to 1)
  • Calculating raw damage
    • If (X < 0.01) Then RAW DAMAGE = 3 * Turret Base Damage (these are called wrecking or perfect hits)
    • Else If (X < Hit Chance) Then RAW DAMAGE = (X + 0.49) * Turret Base Damage (these are normal hits)
    • Else RAW DAMAGE = 0 (this is a miss)
  • Calculating damage after resistance
    • Applied EM Damage = Ammo EM damage * (100% - Target EM Resistance)
    • Applied Thermal Damage = Ammo Thermal damage * (100% - Target Thermal Resistance)
    • Applied Kinetic Damage = Ammo Kinetic damage * (100% - Target Kinetic Resistance)
    • Applied Explosive Damage = Ammo Explosive damage * (100% - Target Explosive Resistance)
    • APPLIED DAMAGE = RAW DAMAGE * (Sum of Applied Damages) / (Sum of Ammo Damages)

The quality of the hit will be described by the value of the random number + 0.49, ranging from barely scratching (least damage) to excellent (highest damage) for regular hits and there may also perfect hits and misses. On the normal hits this number is multiplied with the turrets average damage. By looking carefully at the damage generation above, it becomes clear that the Hit Chance not only means that a turret can miss but also places a cap on the maximum damage number on the non-perfect hits, the next section looks into how this effects the turrets DPS.

Hit description	Random damage modifier
Perfectly	0.490 to 0.500 (special case, 3x the average damage instead)
Barely scratches	0.500 to 0.625
Hits lightly	0.625 to 0.750
Hits	0.750 to 1.000
Well aimed	1.000 to 1.250
Excellent	1.250 to 1.490

A turret with a 100% hit chance will see a natural and unavoidable damage spread between 50-149% of its base damage for normal hits, and always do exactly 300% of its base damage on perfect hits.

Example: A turret fires on target. The chance to hit is 0.8981, the EVE server rolls a random number between 0 and 1, and gets 0.6573, its less than the chance to hit so the target is struck. At this point 0.49 is added to the random number which then becomes 1.1473. The turret had a damage multiplier of x2.1 and the ammo does 4 EM and 2 Thermal, so the base damage is 2.1 multiplied with 6 (4+2), which is 12.6. After multiplying this with the random number we get the raw damage, which is 1.1473 x 12.6 = 14.456. In this damage the raw EM part is 1.1473 x 2.1 x 4 = 9.6373 and the raw Thermal part is 4.8187. Assuming the targets shield was hit, and that only the normal 20% resistance to Thermal is in effect, the final damage then becomes 9.6373 + (4.8187*0.8) = 13.492 points, in the log the hit will be described as a well aimed one and be rounded off to one decimal place.

Damage reduction due to a decreased hit chance

When a turret has less than 100% chance to hit the turrets damage dealing capabilites are reduced in two different ways. The first and obvious one is that it sometimes misses, the other is that the max damage on normal hits (e.g. not perfect ones) are reduced as well. Both of these effects will decrease the DPS output. If you read the previous section, you may remember that the a random number between 0 and 1 is generated to see if a turret hits. If this value is lower than the chance to hit, the turret hits, this number is then used further by adding 0.49, this sum is then multiplied with the turrets base damage to obtain the raw damage done (damage before resistances). What this all means is that targets that are tricky to hit also take less damage since high and juicy rolls now are discarded as misses. This can be seen in the damage log as well, a hard to hit target never recieves excellent or well aimed hits, sometimes barely scrathing is the highest (perfect hits still happen ofc). The practical effect is that the DPS decreases more than the chance to hit does.

Example: (please note that perfect hits are not considered in this example to make the numbers easier to follow) A turret has 50% chance to hit at optimal+falloff. The highest randomly rolled number that can result in a hit is thus 0.5, higher numbers means a miss. This will shrink the damage interval down to 0.5 to 0.99 for normal hits, which on average is 0.745 ((0.5+0.99)/2). Compare that with a case inside optimal range where the chance to hit is 100%, where the damage interval is 0.5 to 1.49 and the average is 0.995. At optimal+falloff (and ignoring perfect hits) the DPS is hence reduced to 50% x 0.745=37.25% of normal. (If perfect hits are taken into consideration, the DPS value will become 39.5%, see table below)

The table below shows how DPS goes down as a target becomes harder to hit. Do note that the reason for the hit chance reduction doesn't matter, be it because of falloff or just tracking issues, the DPS goes down identically. The table can be used to see both how the damage declines as one goes deeper into falloff, and how the damage declines as a result of a lowered hit chance due to tracking reasons. If you wish to combine the effects of tracking and falloff, you can do this by first picking the hit chance from falloff and then the hit chance from tracking, multiply the values to get the combined hit chance, look in the hit chance column until you find a hit chance that is closest to the product you got, and read your relative DPS from that line.

Comment: The relative DPS above is over 1 at the start, this is not an error. Its because its relative to the base damage of the turret. What puts it above 1 are the perfect hits since they do extra high damage.

Parts into falloff	Hit chance	Relative DPS	Reduction in DPS by %
0	1,0000	1,0151	0,0%
0,1	0,9931	1,0048	-1,0%
0,2	0,9727	0,9747	-4,0%
0,3	0,9395	0,9268	-8,7%
0,4	0,8950	0,8641	-14,9%
0,5	0,8409	0,7906	-22,1%
0,6	0,7792	0,7104	-30,0%
0,7	0,7120	0,6274	-38,2%
0,8	0,6417	0,5454	-46,3%
0,9	0,5704	0,4672	-54,0%
1	0,5000	0,3951	-61,1%
1,1	0,4323	0,3303	-67,5%
1,2	0,3686	0,2736	-73,0%
1,3	0,3099	0,2249	-77,8%
1,4	0,2570	0,1840	-81,9%
1,5	0,2102	0,1502	-85,2%
1,6	0,1696	0,1225	-87,9%
1,7	0,1349	0,1003	-90,1%
1,8	0,1058	0,0825	-91,9%
1,9	0,0819	0,0685	-93,2%
2	0,0625	0,0576	-94,3%
2,1	0,0470	0,0492	-95,2%
2,2	0,0349	0,0428	-95,8%
2,3	0,0256	0,0379	-96,3%
2,4	0,0185	0,0343	-96,6%
2,5	0,0131	0,0316	-96,9%
2,6	0,0092	0,0277	-97,3%
2,7	0,0064	0,0192	-98,1%
2,8	0,0044	0,0131	-98,7%

The formulas used to calculate this table were:

• Chance to Hit: 0.5^(0+(Falloff parts / 100%)^2)
• Relative DPS: if(HitChance>0.01 then (HitChance-0.01)*((0.50)+(HitChance+0.49))/2+0.01*3 else HitChance*3)
• Reduction in DPS: (RelativeDPSat100%hit/RelativeDPScurrent)*100%-100%

Answers to some questions

Do small targets take less damage?

Yes and no. They take the full damage whenever they are hit, which means that a BS can pop a small target with one volley. But since they are harder to hit, they get hit much less often, and as such they can be said to take less overall damage.

Can a turret hit a target with a larger angular velocity than its own tracking?

Yes it can. From the chance to hit equation it can be deduced that the tracking part can be broken down into:

Chance to hit (tracking part) = 0.5 ^ (((Angular velocity / Turret tracking) * (Size ratio between gun and target))^2)

From this it can be seen that the angular velocity and the turret tracking is compared as a ratio, its not an upper limit. So turrets with less tracking than a targets angular velocity can still hit, the only thing that happens is that the chance to hit is reduced. If we consider the case where the angular velocity is equal to the turret tracking, and assuming that the size ratio between gun and target is 1 (the guns signal resolution is equal to the targets signature radius), we get Chance to hit = 0.5^((1/1*1)^2) = 0.5^1 = 0.5, or 50%. So roughly speaking a gun will hit 50% of the time when angular velocity and turret tracking are the same on same sized targets. If the angular velocity is twice as high as the tracking (and gun and ship still have identical sizes), the chance to hit becomes 0.5^4 = 6.25%. If the tracking is twice as big as the angular velocity (and again, size ratio is 1) then the chance to hit will be 0.5^((0.5)^2) = 0.5^0.25 = 84.1%. In theory small and fast ships could benefit more from tracking bonuses than they would from raw damage bonuses, at least if nobody tries any clever manual piloting moves.

Are frigates with a smaller signature radius better than larger frigates?

The difference is negligable on most distances. However, when two frigates are really close to eachother, the one with the smallest radius get a small advantage. This is many times mitigated by the fact that the larger signature frigates uses guns that generally has higher tracking values (the trend is: projectiles have the worst tracking, lasers are in between, hybrids have the best; when compared on an equal basis).

(unclear, rewrite or delete)

Are target painters useful for turrets?

Yes, but only if the chance to hit is below 100% due to poor tracking or from using large guns against a smaller target, if the decreased hit chance is because of falloff a target painter will not help at all. A regular target painter I increases the signature radius of a ship by +25%. Since all tracking terms are multiplied with another in the hit chance equation, the number can be moved around inside it to see how it effects the other factors. So another way to look at it is this: the signature radius increase is identical to what would happen if the target instead had reduced its angular velocity to 80% (100%/125%) of its current or as if the turrets had gotten +25% more tracking against the target. Keep in mind that this last part was only a comparison, a target painter doesn't actually reduce anyones speed or improves anyones tracking.

Tracking Examples

coming soon

References:

http://wiki.eveonline.com/wiki/Turret_damage

http://www.eve-ivy.com/forum/viewtopic.php?p=201888#201888

http://www.eve-ivy.com/forums/viewtopic.php?p=216525#p216525

http://www.hostile.dk/files/eve/eve-tracking101.swf