Ships & Modules

tracking computer can be changed to fit the situation, web only works on stuff that gets within 10k of you (14km for fed navy)

Within the range of the web, it will do more for you than a TC. Think about it--since a web reduces their speed by 60% or whatever, it's more than doubling your effective tracking against them, since they're orbiting at less than half their normal speed.

Outside of the web's range, obviously the web does nothing and the TC is better.

When you look at the formula for turret damage then you will see that transversal speed is being divided by tracking speed. Because webs reduce a target's speed (and thereby the transversal speed) by up to 60% and tracking computers increase your tracking speed by up to 30% are webs better than tracking computers.

In practise do webs not instantly slow a target to its new speed, you first need to catch it, and once caught may your ship need to adjust its own speed, and this difference takes time to come into effect. Tracking computers can work over a greater distance (the range of your weapons) than webs and give you an advantage sooner.

I could now tell you to use a tracking computer, but do not neglect the difference. This small difference is multiplied by the ratio of the signatures and the smaller a target is when compared to your guns the more this difference begins to matter. If you were then shooting with large weapons (400m weapon signature) at a frigate (40m signature) will it tenfold! So do not make the mistake of disregarding it as negligible.

Use a tracking computer for when your targets are not very small and you plan on using drones against the smallest ones. Use a web when you believe your survivability depends on it.

Edit:
Corrected the tracking speed gain to 30%. Not sure why I thought they would give a 50% bonus. Sorry.

Don't forget that webs also give you range control or the ability to pin someone down when they might escape. Webs are generally awesome, even on kiting ships that try to stay out of web range you can use a web yourself, keep it on overheat and use it on things that approaching you to slow them down so that you can pull range before they can get on top of you (defensive web), on brawling ships it helps you keep the targets pinned and also increases the effectiveness of your weapons. I feel tracking computers are more for range or big fights where other people are going to tackle for your anyway.

For PvE you generally want TCs as most mission NPCs spawn far away and have an orbit that is outside web range, as for frigs that get under your guns, thats what drones are for.

I have a question about that bold part. Mathematically (yes, I know) it does not matter if you divide first or multiply first. As such, I see people claim, "If the targets transversal is higher/faster than your tracking, you can't hit it". While in 'real life' that makes sense, there is nothing in any of the math formulas I have ever seen to indicate this is the case. The formula is simply an equation which gives a number at the end. You can make up for the lack of tracking by boosting other parts of the formula to overcome it. Does anyone have links to a formula/discussion showing: if your tracking is slower than transversal, you can't hit the target?

On a similar note, people often say painting a target to make it larger than the explosion radius of a missile is a waste. Mathematically there is nothing in the formulas to indicate this is the case. In 'real llife' that would seem to make sense but EVE is just spreadsheet game underneath the pretty ships.

I've tried testing to see but I've not been able to come up with tests which reliably hold all variables constant and only change one.

As far as which to use? I use webs and painters often as they helped everyone in the fleet. TC/TE/etc. only help one person. When you take the effects of multiple players using webs and painters on a target, TC/TE doesn't stack up well.

Some players confuse transversal speed with angular velocity, because both speeds are closely related and behave similar. More accurate is to say that "when your tracking speed is less than a target's angular velocity will you miss it". You can turn on a column in the overview to see the angular velocity of other ships. The value has got the same unit as the tracking speed of turrets (rad per second) and you can directly compare both and thereby know how close you are to missing a target.
It is however not quite this simple, because the formula always accounts for the ratio of weapon signature and target signature. So when you compare your turrets' tracking speed with a target's angular velocity will you see misses occur sooner for small targets, while for bigger targets will it take longer. Still, the overview column is quite useful for flying turret ships and for knowing how close one is to crossing from hits into misses.

The transversal speed itself is the speed of a ship as perceived by you from your view point and is nothing more than its angular velocity multiplied with its distance. If you put this into the formula then the part with "transversal speed / (range * tracking speed)" will turn into a simple "angular velocity / tracking speed".
When both are somewhat equal, meaning you are just about to cross from hits into misses, will their division result in a number close to 1. If you ignore the rest of the formula for a moment and simply take 0.5 to the power of 1 do you get 0.5, meaning, you get a 50:50-chance to hit it in such a situation. Improving your tracking then means the division will yield a smaller number, one less than 1, and taken as the power of 0.5 will result in a better chance for you to hit the ship. The line between hit and miss is not a sharp cut as you might expect it, but a smooth curve and taken to the power of 2, which it does, makes a bit steeper.

I do not want to discuss the formula any further, because it seems to be based on a statistical approach and may possibly originate from dice rolls. CCP can tell you more. If I am not mistake did EVE start as a board game?! ... Anyhow, it mimics physics sufficiently enough for us to have fun with it. The result of the formula is used in combination with a random number generator and in a certain random event is the formula being ignored - the wrecking hit - and you will do a hit despite all physics.
Just remind yourself of math being a tool, one used to describe nature but one that can be used to describe something imaginary, too. Discussing the formula would be like discussing the beauty of one of the ship models.

I have not had a look at the missile formulas for a while, so I cannot say much about it, but they too are approximations. When players talk in absolutes then do not measure too much accuracy to it. All they are saying is that a 3.089% chance of doing damage just is simply not enough for them, or that doing 97.9% of a theoretical maximum is as good as the 100%. Do not discard such statements instantly as false. They can contain experience and wisdom.

Edit:
I have found a good 3D plotter on the Internet and used it to create three images to describe the hit'n'miss chance as a 3D function. On one axis is the angular velocity of the ship you are shooting at, the second axis describes the tracking speed of your guns and the z-axis shows the percentage of the hit'n'miss chance. The colours symbolize 0% (red), 50% (yellow) and 100% (green).

What one can see in the pictures is that for a battleship shooting at a battleship does the tracking need to match the angular velocity. The yellow area (50%-chance) is exactly there where both values equal each other:

Battleship shooting at a battleship

For a battleship shooting at a cruiser (400m weapons shooting at a 150m signature) does the tracking speed of the BS need to be about 2.7 times better than the angular velocity of the cruiser (400 / 150 = 2.666):

Battleship shooting at a cruiser

And for a battleship shooting at a frigate (400m versus 40m) does its tracking speed need to be 10 times better than the angular velocity:

Battleship shooting at a frigate

TLDR: To hit small things with big guns or dictate range with close range weapons against all targets, use webs. To stretch your applied damage curve where you are using long range weapons and can't or don't need to dictate range, use TCs.

If you want to shoot elite frigates with large guns, then dual webs will let you hit them; TCs will not.

You can load up dual faction webs and an AB, and Dual 425mm AC IIs, get into web range of the frigs (assuming they are ones that will get that close to you), then hit the webs, keep at range 13km, and pop them in one or two shots. TCs alone, without webs, will not let you pull this trick in any setup with large guns.

Basically webs let you dictate range, assuming that you can catch the target and your normal speed is greater than that of any webbed or dual webbed thing you plan to shoot. Because they let you dictate range, they also let you dictate angular velocity, since NPCs will continue blindly trying to orbit at their optimal, even when they are webbed down to the point where that is impossible. So if you are faster and you set your own orbit or keep at range <= 14km, you can force their angular to 0 at will.

Dual TCs with tracking speed scripts in an arty setup might let you snipe some otherwise unsnipeable small targets at range, where they already have low transversal, but that's about it.

If you are shooting BCs and battleships, then webs and (speed scripted) TCs both will add little, because you're already hitting close to full damage, and the speed and tracking just aren't an issue. In that case, webs can help you keep large targets that like to orbit at 50km+ in your optimal instead, assuming that you have a prop mod to catch them and close range weapons with an optimal that is inside web range. TCs, on the other hand, also can buff your optimal range, and in cases where you can't dictate range, this lets you increase your applied DPS, assuming you are using long range weapons with an optimal long enough to matter.

I could not stop playing around with the 3D plotter. Let me know when it is too much.

DPS projection

To illustrate how tracking, optimal range and falloff combined make up for the DPS did I create an animated GIF (3s per frame). It shows the DPS projection around a ship for 2 dimensions (DPS is the third dimension) and for different types of turrets / ammos. The values for optimal and falloff should explain themselves. The value for misses is the distance at which misses occur and changes with each frame (1km, 2km and 5km distance).

Again, no wrecking hits included, because these only add a small, fixed amount to the DPS amount. Also the difference in DPS for the actual variations of turret and ammo types are not shown here. Usually, the longer the range of a weapon is the less damage it produces and some ammo types can change the tracking of a turret.