- 1 All About Tracking
- 2 Tracking Formula
- 3 Key Points
- 4 Gun Resolution and Signature Radius
- 5 Target Painters do what for tracking?
- 6 But tracking only really helps when trying to hit fast moving targets, right?
- 7 So how do I increase Tracking?
- 8 Show me some graphs
- 9 Conclusion
- 10 Math detail: Part 1
- 11 Math Detail: Part 2
- 12 DPS Calculation and Hit Quality
All About Tracking
Tracking in EVE seems fairly complex, however in reality there is simple math behind the scenes. This little article plans to break-down the tracking equation to help you understand how it works in-game, and how you can best improve your hit quality. Also, EVE-O hasn't been wonderful at explaining tracking, so there may be a few things here that previously you thought worked differently.
Here is the EVE tracking formula:
It looks like a complex piece of math at first, but it's really 3 easy parts combined together:
- Part 1a: (Transversal / (Range * Tracking)): Transversal / Range is Angular Velocity. In other words, part 1 is the comparison of angular velocity (the combination of ship movement) versus the guns ability to rotate and track.
- Part 1b: (Sig_Res/Sid_Rad): The comparison of the ships signature radius versus your gun resolution. Larger guns struggle to hit smaller targets
- Part 2: max(0,Range-Optimal)/Falloff: Entering distance into the equation
So to summarize the formula, it is:
50% ^ [ (Part 1a * Part 1b)^2 + (Part 2)^2 ]
The above math results in the following key points:
- You will only be doing 100% of your damage (EFT related numbers) if you are firing within optimal and have NO transversal.
- Tracking is not binary, i.e. if angular velocity is equal to gun tracking, and gun resolution is equal to ship radius, you will have a 50% hit chance. It is not a binary line where you suddenly can no longer hit.
- At optimal + falloff, you will have a 50% hit chance. At optimal+ (2x falloff), you will hit 6.25% of the time.
- EVE has some random numbers and chances of wrecking hits on the final formula, which means a 50% hit chance will result in 39.5% of EFT DPS. A 100% hit chance is actually equivalent to 102% of EFT DPS (or somewhere around there). More is explained in the math section if you are interested.
- An increase to target signature radius is equal to an increase in your turret tracking, e.g. a 30% sig radius increase (T1 Target Painter) is equivalent to a 30% tracking bonus (e.g. via a T2 tracking computer)
Gun Resolution and Signature Radius
EVE-O explains that Gun Resolution is the area in which the 'bullets' will spray. If Gun Resolution is greater than Signature Radius, then your damage will be reduced accordingly. This is only true if there is transversal. If you are standing still, you will be hit for 100% of the damage.
If you look carefully at the tracking formula, you will notice that Part 1a and Part 1b are multiplied by each other, and Part 1a contains Transversal. As we all know, multiplying a zero will result in a zero, leaving only distance being taken into account for your hit chance.
Note that this is different to missiles, where your sig radius will always result in you taking less damage. It also explains why large artillery can instapop frigates, and why unbonused torps cannot unless the target is kind enough to be stationery with his MWD enabled :)
Target Painters do what for tracking?
For the purposes of turrets, an increase to your tracking speed (e.g. Tracking Computers) is performing exactly the same function as an increase to the targets Sig Radius. Therefore, anything that increases either of those two factors will provide the exact same increase in your ability to lay down the hurt. Therefore, some simple numbers:
- T2 Target Painters: Sig Res +30% (with skills, 37.5%). Available to whole gang and can be further increased to 50% with ship bonuses (Vigil, Bellicose, Hyena, Rapiers, etc.)
- T2 Tracking Computers (tracking speed): Tracking Speed +30% (no skills to increase). Available to your ship only
- T2 Tracking Enhancer: Tracking Speed +9.5% (no skills to increase). Available to your ship only
The most efficient means of increasing your ability to hit a fast moving target with turrets is with a Target Painter, assuming you have the skills, or can place the TP onto a bonused ship. If you combine T2 painters with skills and ship bonuses, it's 66% more effective than a T2 Tracking Computer with speed scripts.
Just pay attention to optimal and falloff with Painters, that's the balancing attribute.
Now, EVE also has this wonderful attribute called 'stacking penalties'. Therefore running two Tracking computers means the second one suffers a penalty. Since an increase to Sig Radius and Tracking Speed are different attributes, these don't stack. So imagine having two Target Painters lighting up a target, and two Tracking Computers. It's a substantial boost to your ability to hit.
But tracking only really helps when trying to hit fast moving targets, right?
Not at all. The issue with tracking is that it is invisible to you, which is also why I believe Tracking Disruptors are so potent, people do not see the impact unless they are paying attention to damage notifications. Obviously when tracking crosses the line of 'can / cannot' hit, it's very apparent, and most of those fine line situations are against fast moving targets. However, let's take another example, in this case we have:
- battlecruisers orbiting each other (guns sizes matching target size)
- at close range (autocannons vs blasters)
- using no propulsion mods
- using close-range, fast tracking weapon systems and ammo
The two test cases are a Hurricane with 220mm Vulcans (Motion Tracking V vs. none), and a Myrm with Electron Blasters (Motion Tracking V vs. none).
The fully skilled Hurricane pilot is doing:
- 102% more damage at 500m
- 19% more at 1,000
- 4% more at 2,000
- 2% more at 3,000.
The fully skilled Myrm pilot is doing:
- 156% more at 500m
- 27% more at 1,000
- 6% more at 2,000
- 3% more at 3,000
Note, these percentages are created by having 25% more tracking (due to skills). However, this numbers are even greater if the tracking difference is greater, e.g. through a Tracking Computer, or Target Painter.
So how do I increase Tracking?
- Train up the Gunnery: Motion Prediction skill (5% per level)
- Fit a Target Painter, Tracking Computer, Tracking Enhancer, or rigs
- Fly a ship with tracking bonuses (thrasher and Megas are a good examples)
Show me some graphs
Comparison of Target Painters vs Tracking Computers (with Tracking Speed scripts)
An increase in Tracking Speed and Signature Resolution result in the same thing for tracking with turrets. Target painters provide a greater increase to turret tracking than tracking computers.
Here is a graph of a Hurricane Artillery setup (650mm T2 guns firing T1 ammo) at a Vaga orbitting at 4,000 m/s
- Green line: Standard setup (100 DPS at 20km)
- Pink line: 2 T2 Tracking Computers on the 'cane (150 DPS at 20km)
- Blue line: 2 T2 Target Painters on the 'cane lighting up the Vaga (160 DPS at 20KM)
- Yellow line: 2 T2 Target Painters (non-bonused ship) lighting up the Vaga, and 2 T2 Tracking Computers (180 DPS at 20 KM)
Comparison of Hurricane with autocannons and tracking skills
- Red line: No gunnery tracking skills
- Green line: Motion Prediction V trained (25% tracking increase)
- Pink line: Motion Predication V and a T2 Target Painter (25% + 37.5% tracking increase)
I hope the above helped you to understand how turret tracking in EVE works. Obviously tracking is important, however like all things in EVE it's a balance of skills and fitting.
Will Motion Predication skills and a Tracking Computer (tracking speed) / Target Painter always provide a turret user a benefit? Yes, in all circumstances except where transversal is 0 (i.e. both ships never have *any* lateral movement for the entire engagement), and very negligible (and probably not noticeable) when fighting at extreme range. However, where you are not fighting up close, or you start shifting beyond the peak of the DPS curve, tracking becomes largely irrelevant and range starts to play a bigger factor. Personally I am not planning on fitting a Target Painter on my Hurricane any time soon, I would rather fit a Tracking Disruptor, however do not assume that the Motion Predication skill is not doing anything for you, it just could be doing a lot.
Math detail: Part 1
So now that we have the parts, let's use an example to try bring it together.
A vagabond is orbiting your poor stationary battlecruiser at 20,000 meters, and this nano pilot makes this vagabond power at 4,000 m/s (darn nano heads). You fire up your Heavy Pulse lazors and (tracking calculation kicks in):
- Transversal = 4,000 m/s
- Range = 20,000 m
- Angular Velocity = 0.2 (transversal / range, or 4,000/20,000)
- Heavy Pulse Tracking = 0.08 (rounded) * 1.25 (skills) = 0.1 (rounded)
So, your guns are moving at half the speed (0.1 rads/sec) that the vaga is orbiting you (0.2 rads / sec). If you were to punch in the data into the hit formula, your damage would be extremely close to 0. However, this is only half of the story, and zero is nowhere close to reality. Let's punch this data in part 1:
= 0.5 ^ (Angular Velocity / Tracking)^2
= 0.5 ^ (0.2 / 0.1) ^2
= 6.25% (Due to hit quality and wrecking hits, this will result in you doing about 3% of your EFT DPS)
Math Detail: Part 2
Tracking is an arbitrary number, guns don't really track the physical target and it's not an on/off switch. For example, if the angular velocity was 0.2, and:
- Your tracking was 0.2, you would do 39% of your DPS (assuming range isn't an issue).
- Your tracking was 0.19, you would do 36%
- Your tracking was 0.18, 32%
To show this via the formula again:
Tracking Adjustment = 0.5 ^ (Angular Velocity / Tracking)^2
= 0.5 ^ (0.1 / 0.1) ^2
= 0.5 ^ 1 (0.5)
Chance to Hit = 50% (Due to hit quality and wrecking hits, you'll be doing 39% of your EFT DPS)
As you can see, tracking isn't binary - it simply impacts the chances to hit, and therefore over time the average DPS you perform.
Now that we understand that tracking is a measure, there is another important component to calculate, i.e. Modified Tracking (the target footprint), and that's to consider the signature radius of the target and the signature resolution of your guns (in other words, to factor in part 2 of the equation). To put it simply, if the Signature Radius of the target is larger than the Signature Resolution of your guns, it's starts tracking faster as a straight factor. If the target sig is double the resolution of your guns, your tracking speed doubles. Conversely, if the target sig is half the resolution of your guns, your tracking speed halves.
Back the above example, since that Vagabond is using MWD to achieve those figures, this makes him a much bigger target (910 sig radius). Back to the calculation:
- Transversal = 4,000 m/s (unchanged)
- Range = 20,000 m (unchanged)
- Angular Velocity = 0.2
- Heavy Pulse Tracking = 0.08 * 1.25 (skills) = 0.1 (unchanged)
- Part 2 (gun resolution) = 910/125 (the signature radius of the well lit Vaga / the signature resolution of your guns)
Adjusted Tracking = 0.1 (part 1 tracking) * 910/125 = 0.73
Now our guns can easily track that vaga, they have gone from being half the speed, to being nearly 4x quicker. If you now punch the data into the hit formula, your damage is closer to 50% DPS, however the reduction in DPS is largely due to the Vaga orbitting outside optimal range of your lazors. If that vaga was closer to optimal (15,000), that DPS percentage climbs to 91%
Tracking Adjustment = (0.5 ^ (Angular Velocity / Modified Tracking)^2)
= 0.5 ^ (0.2 / 0.73) ^2
= 0.5 ^ 0.075
Chance to hit = 95% (Due to hit quality and wrecking hits, you'll be doing 94% of your EFT DPS)
DPS Calculation and Hit Quality
The resulting Hit Chance gets plugged into a second equation where the 'quality' of the hit is determined, including if the shot results in a wrecking shot.
To put it simply, EVE picks a random number between 0 and 1 (constant)
- If it picks 0.01, you get a wrecking shot and 3x damage.
- If it picks a number less than your Hit Chance, you hit for damage (which is equal to the (constant + 0.5) * turret damage)
- If it picks a constant greater than your Hit Chance, you miss
A quick example. I am firing upon a frigate, which is standing still, and it's slightly in falloff giving me a hit chance of 50%. EVE rolls it's random number and:
If it picks:
- 0.01: Wrecking shot, I get the damage per my turret multiplied by 3
- 0.10: 10% is less than 50%, so I hit. The damage done is (10% + 50%), or 60% per turret
- 0.50: 50% is equal to 50%, so I hit. The damage done is (50% + 50%), or 100% per turret
- Anything greater than 0.5 is a miss.
As you can see from the above, when I have a 50% hit chance, that does not mean I will be doing 50% of my DPS, as there will be a spread of random numbers where I do less damage (e.g. the 10% example). In reality, a 50% hit chance will result in doing 39% of your EFT DPS.
--Secluse 00:25, 5 January 2009 (PST)