*(edit: An apology. I have a couple of blogs. One’s nominally devoted to gaming, the other to stuff in general. Guess who posted in the wrong blog?*

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**Per my personal standards I won’t delete this. I’d rather admit error and go on, however wrong I’ve been. well, there are a few exceptions but this isn’t one. Again, mea culpa.)*

So as I mentioned, I’m trying Eve online again. Way back in the early days of this blog I did a little bit of theory crafting. I decided I’d do it again for this my current interest.

Now before I begin, some old caveats. First, I’m doing this for my learning. So if you’re reading and you see I made a mistake by all means tell me. On the other hand if it’s “you noob” or “drones suck” you’re welcome to go away. Second, again due to me starting on this I’m probably going to do an update later with new lessons learned. Finally, this is almost purely “nominal target”. The enemy, especially a human PVP enemy, will do things to pull out of optimal. But if I’ve got a baseline I can start guessing what I need to deal with the new surprises.

I’m playing with a Tristan. That’s a frigate (smallest player ship for you non-EVE players). Its designed primary weapon system is drones with two turrets for supplemental weapons. Drones are pets. They can be – and in Eve actually are – pretty decent. But because they’re autonomous and driven by the AI they’re dumb. And they’re easier to kill than your ship. And they’re rather restricted in the damage that they can do. But a pack of them can be very worrisome. My goal here is to see how worrisome they are at base, and how much more so I can make them be.

Before I get to that let me point out the benefits the Tristan has for drone combat. First, it’s got enough magazine space for 8 lights or 4 mediums, though the lights are restricted by my ability to control a maximum of 5 drones (after training). I can also squeeze in a heavy or a sentry drone at the cost of 8 lights or 2.5 (well, 3) mediums. Lights are fast, both in base speed and tracking speed, and have the tightest signature resolution. On the other hand they have the smallest damage. Sentries move zero, track like slugs, have large signature resolutions, but have lots and lots of range and damage.

At first pass, then, it’s time for a raw damage comparison. For simplicity I’m ignoring “damage modification” for now. So base damage for a light is 15, for a medium is 25, a heavy has 48, and a sentry has 50. 5 lights base is 75. 4 mediums base is 100. If I toss a heavy or a sentry I can add three lights but even so that’s less than the four heavies. For this (and some other reasons I’m not going into right now) I am dropping the heavies and lights. I think there are situations where they’ll come into play, but not as a relative beginner.

On first pass, then, it’s “obvious” I should use four mediums. But there’s a problem. It’s not just the damage I can do if I hit, it’s hitting to do the damage. That’s where that signature resolution comes into play. Actually, let me take a moment to discuss the whole to-hit formula.

First, it’s derived, not displayed from CCP. That means that so far empirical results match it but it might be slightly wrong, and it might get changed a little bit if CCP deems it necessary. There are also some ‘levelers’ in the program that prevent strings of good (or bad) luck. We’ll ignore those for now.

Base formula simplified is: 0.5 ^ (((signature equation)*(tracking equation))^2 + (range equation)^2).

Signature equation. In simple, smaller ‘bore’ weapons have better accuracy. It’s not right, really, but let’s rephrase that as smaller ‘bore’ weapons have tighter shot groups. The bigger the target the less this matters. And in fact (still keeping this analogy because it’s working) the whole ‘signature resolution’ and ‘signature radius’ discussion can be thought of as ‘shot group size’ and ‘target size.’ If Res is smaller than Rad then obviously it’s going to hit – if everything else cooperates. However we don’t cap this at 1 (100%) because it gets multiplied by the next element, the tracking equation. On the other hand it’s never going to be zero – every target has at least a little radius.

Tracking equation. This gets a little trickier though it’s conceptually simple – it’s ‘how well are you aiming at that moving target’. A target that’s standing still – or is approaching or moving away in a straight line – is essentially stationary. One that’s in a circular orbit is a lot harder. How much harder depends on how many degrees (well, radians really) it moves per second. This is a matter of its range and actual speed.

You can ‘get’ this by simple math without going into trigonometry. Remember that a circumference is pi*diameter, and diameter is 2*radius. Now let’s set a pair of orbits, one 5 units out and one 10 units out. The first orbit is 30.14… units in ‘length’ (circumference), the second is 60.28… units. A ship moving at the same speed takes twice as long to get around the ship when it’s further away.

Now not only does the target move around the ship but the turrets have a limit on how fast they can move. This is their tracking (aka tracking speed). Obviously if the turret can rotate faster than the effective transversal speed then it’s easy to hit, but if the transversal is faster it’s a lot harder.

That’s the tracking equation. Transversal velocity (how fast is it moving from left to right, ignoring speed in or out) divided by the range times the tracking speed. It’s possible for this to be zero, but that’s almost totally under the control of the target.

Finally there’s the range equation. Yes, I know we already used range once but this is something else. Analogy first. Up to a certain range everything flies straight. Once it’s past that range, however, it can start veering a little off target. Here’s the way it works.

All weapons have an optimal and a falloff range. Optimal range is the “up to this range”. Falloff is where things start missing, and the way the formula works the formula winds up with a 50% hit probability at optimal plus falloff. How?

(Actual range – optimal range)/falloff range, limit 0. Limit 0 so no negatives can sneak in. From point blank to optimal range the number is 0, and 0.5 (the base number) to the 0th power is 1 or 100%. At falloff range the number is 1, or 0.5^1 = 0.5 (50%).

The tracking and signature equations are multiplied together and squared, and this is added to the square of the range equation. The squaring among other things cuts out the corner cases that might give a negative number. And since we’re adding two things together, if both sets give us “1″ then we’ve got a 50% chance to hit.

Remember why I went to the gunnery equation? To show why the mediums weren’t an easy preference over the lights. There are two Big Deals. First, there’s the respective signature resolutions. Lights are 25. Mediums are 125. In general, frigates (like the Tristan) have signature radiuses (radii?) of 30-50, with some of the specialized ducks running 60, 65, or even 90.

The signature equation for lights against frigates, then, is less than 1. For mediums it’s 3 or even 4. 0.5^(25/30) is still 56% chance of hitting. 0.5^3, however, is 12.5, or about four and a half times worse. And 25 base medium damage is not four and a half times greater than 15 from a light.

That’s a lot of words but it gives us the base information we need for theory crunching. I’ll stop here and run some more in a bit.

meantime, have fun.