Ships & Modules

So here's the formula for turret chance to hit: https://wiki.eveonline.com/wikiEN/images/thumb/a/aa/ChanceToHitv2.png/800px-ChanceToHitv2.png

ChanceToHit = 0.5 ^ ((((Transversal speed/(Range to target * Turret Tracking))*(Turret Signature Resolution / Target Signature Radius))^2) + ((max(0, Range To Target - Turret Optimal Range))/Turret Falloff)^2)

I tried plugging numbers into this but I got really confused. For example "max(0, Range To Target " what does the comma do after the 0? What does "max" mean? Are the units for this equation in meters? (maybe my math skills aren't developed enough for this)

Anyways, let's simplify the equation a LOT and do this:

ChanceToHit = 0.5 ^ ((((1 / 1)*(1 / 1))^2) + (1 / 1)^2) = 0.25

The underlined part is the target's signature radius. Now let's double the signature radius of our opponent:

ChanceToHit = 0.5 ^ ((((1 / 1)*(1 / 2))^2) + (1 / 1)^2) = 0.42

That's a pretty big increase in chance to hit. If I was better at math, I would put in the exact numbers for an situation where a stabber is kiting an omen and the range is halfway between optimal and falloff, and then compare the difference in damage with/without a target painter.

From what I understand, as you go further into falloff, the damage of your shots goes down only because the chance to hit goes down. You get more glancing blows, completely missed shots, etc. So there's three ways to increase your chance to hit:

1. Get closer to optimal range
2. Decrease the transversal
3. Increase the target's signature radius

Here's what I was thinking: If tracking/transversal is already as good as it can get (kiting), and you want to stay inside falloff, then target painting your opponent should have a pretty noticeable difference on your DPS. But when I recreate kiting scenarios in EFT, I see virtually no difference in DPS with a target painter, unless I set up a situation where traversal is affecting the DPS... this confuses me.

Can someone help me out here? The main reason I'm asking here is because A) I tried messing around with this in EFT and I saw virtually no change in damage when I double or trippled my target's signature radius (I experimented with a variety of different ships classes/sizes, orbits, etc). The only time I saw a big difference with the target painter in EFT is when TRANSVERSAL was the reason the damage was getting lower, NOT fighting in falloff.... O_o

Also, while I'm writing this, I want to point out something that kind of bugs me: when I am orbiting another ship that is stationary, intuitively it makes sense for my angular velocity to be high for my opponent, and his angular velocity to be ZERO for me...but that's not the case in eve. Somehow it's logical for my guns to have a hard time tracking a ship that is stationary in the center of my orbit. Originally I was confused by this, but then I realized that in eve, when it comes to mechanics, all ships are considered as spheres orbiting eachother. And then it dawned on me, in EVE's logic, my sphere never turns at all. It remains in the same orientation the entire time I fly around, only the visual display of my ship indicates that it's turning, spinning etc, but the game engine doesn't see any of that. So that made this last issue of orbiting a stationary target make more sense to me, but it still is illogical for my turrets to have a hard time tracking a stationary target in the center of my orbit.

*EDIT* OHHHHHH!!!! Now I get what you mean by if you are within optimal, then it's set to ZERO! LOL, okay that's to make sure you don't go into the negative or something funky in that top right hand side of the equation.

This still leaves me wondering why the DPS charts in EFT don't show an appreciable difference when applying a target painter to something when shooting it at the edge of falloff while transversal is zero. There should be a DPS increase there (unless I'm conceptualizing this wrong in my head), because the signature radius and the tracking portion of the equation are multiplied together and then that resulting number is squared...so even a small difference in one of the two should result in making a noticeable difference at the end result.

Yup. That's the basic idea.

The reason why painters do nothing when transversal is negligible is that painters only help to mitigate transversal. The second half of the exponent -- the one with the max() function in it -- is only dependent on range. If you've already done all you can to the first half by making transversal 0 there's nothing else for a painter to do.

Let's rewrite the equation and give an example. To simplify matters, let's say that ChanceToHit = 0.5^(Transversal + Falloff). If both Transversal and Falloff are 0, then ChanceToHit = .5^0 = 1. Now, because Transversal and Falloff are additive, driving only one of them to 0 doesn't do anything to the other. As a result, inside of optimal range, Falloff = 0 and ChanceToHit only depends on Transversal.

On the flip side, let's say that Falloff = 1 (which effectively means that you're at optimal + falloff). Transversal has a minimum value of 0 and no effective cap. Painters effectively make the Transversal term smaller. However, since 0 is as small as the Transversal term can go, the best you can get for ChanceToHit is ChanceToHit = 0.5^(0+1) = 0.5 when you're at optimal + falloff.

So that's the effect you're seeing. Painters only tweak the first half of the exponent. Once the first half is minimized (say, neither you nor your target are moving) you can't do anything else to it and the only effect comes from the second part of the exponential, which deals exclusively with range beyond optimal. Thus, painters only help mitigate tracking issues, not range issues.

I think you're right but one thing needs to be clarified. Let's say you're a battleship, using 1400mm artillery cannons, and you're shooting at an interceptor from 100km away and the interceptor has his microwarp drive on. If you put a target painter on the interceptor, it will make practically no difference in your overall DPS. That's because the portion of the equation that factors in the difference between your guns signature radius and the interceptors signature radius will already be near it's minimum value (zero), because the angular velocity at 100km is practically zero. The target painter makes the biggest difference when the angular velocity of your target is high.

just wanna say that a stabber cant "kite" an omen. have you seen the optimal range with scorch on medium pulses? just letting you know that youll need a lot of tank for a stabber if you intend on doing that

EDIT: also, if you are orbiting a stationary object, there is still angular velocity because you are moving. your guns still need to be able to track a specific point effectively. just because your TARGET isnt moving, doesnt mean there is no angular velocity.

Ships do not have front of back or sides in eve. They have movement vectors and nothing else. They are not a model that is turning around and keeping same side facing the enemy. That is the same reason why there is no such thing as being PASSIVE aligned. When you are standing still your movement vector is void and you do not have ANY alignment.

You are a point... and your guns need to turn while you orbit. Remember your ship model only exist on the server for collision detection purposes, nothing else.

Would be great is eve had a proper ship orientation and guns turned relative ot it, but it is not like that.

Keep in mind that webs will have a larger impact than target painters when at close range. You can see a stasis web II lowers the target's speed by 60%, whereas a target painter only increases their sig radius by 30%. Since these two terms (speed and sig radius are multiplied directly), the web and target painter have the same effect on the tracking formula, but the web is stronger.

For example, with a web II the first term (transversal speed) is multiplied by 0.4 (decreased by 60%). With a TP II, signature radius is multiplied by 1.3 (Increased by 30%). Since sig radius is in the denominator the new factor can be moved to the numerator as 1 / 1.3 = 0.77. Since we want this term to be as small as possible (0 means perfect tracking) the first case is better, because we are multiplying by 0.4 instead of 0.77, which will always yield a smaller value.

You will sometimes see target painters on kiting fits because they can operate much further than webs. Fortunately, transversal is less of a problem at long ranges because the angular velocity is lower, so the smaller bonus of the TP has a similar effect to a web at close range.

Keep in mind some ships are bonused for either web or target painter effectiveness, or both, which can change your selection choice.

Edit: As others have said, the two terms in the formula (tracking and range) are independent. So the easiest way to think about it is first consider range to find your "base damage" assuming perfect tracking. We see 0.5 ^ (0 + 1) = 50% chance to hit at optimal+falloff, for example. Then any transveral/tracking considerations can only decrease your damage by increasing the first time from 0.

1 .. yes.. But both are stack nerfed. So If you have more than 3 ships in a fleet, it is not bad Idea to have 1 or 2 TP.