This will hopefully become a more general guide, but for now I'm starting with what I think is a critical question. I guess you've all have seen the canonical tactic of hitting a planet with capital ship and then to run back to repairs. Assuming proper timing of the retreat for repairs, the critical question is: how much fleet do you need to kill the capital ship while under repairs. The answer depends of course on a good number of factors. Below I explain how to find out what I think is the most important piece of this answer, namely the break-even DPS under repairs but also under self-repairs for completeness.

But before we get into that, you surely may ask: why is this break-even figure important? It's important because (once converted to an equivalent fleet) any extra damage applied on top of this break-even DPS can converted by a straightforward calculation to an estimated time to death for the capital ship. For example, assuming the break-even DPS is the equivalent of 3 LFs (which [as we shall see] is fairly typical for a capital ship when not under external repairs, i.e. only relying on passive self-regen of hull & shield), then if one brings [say] 20 LFs to a fight and each is capable of [say] 10 raw DPS, after subtracting the break-even DPS, 17 of these LFs will dish out 170 * 0.5 * 0.35 = 29.75 actual DPS to a level 1 cap ship's shields and hull. (The last factor is 1 - mitigation, and a capital ship's mitigation goes up slightly every level, while the middle factor is the LF's attack "bonus" vs. capital ships. In general, 1.75 actual DPS of an LF vs capital ship is a good rule of thumb.) Now, also assuming [as fictitious but easy to follow example] that the target capital ship has 5000 points of effective health, meaning shield points + hull points * (1 + 0.5 * armor), for example 1000 shields and 3200 hull at an armor of 5, then our approx. 30 DPS fleet will take 5000/30 = 166.66 seconds to kill the capital ship, assuming we can maintain their number against losses (by replacements and/or repairs). Why is this kind of estimate important? Well, to start with planets don't regenerate health under bombardment, so it's important to know how much fleet is needed to chase off an enemy capital ship. A typical 1000 health asteroid will take at least 3-4 minutes to kill, unless the attacking capital ship has some special anti-planet abilities. But then, should you press the attack when the enemy runs with its capital ship for repairs? How much [extra] fleet would you need for that?

Now we get to the slightly more difficult math part. I'm actually not going to give the equations here because using them in your head is pretty hard even while not playing the game, and I suspect nigh impossible in real time. What I'm going to provide here are pretty graphs of the break even DPS for a common capital ship, the Mazra, followed by (mathematically deduced) simple rules of thumb for obtaining quickly a good estimate of the break-even DPS. The math-inclined can check out my R code and by changing a few constants generate similar graphs [and rules of thumb] for other capital ships, which will be valid as long as no special self-repair buffs are used (e.g. the Kortul will need extra calculations, more on this at the end of the post.) So, here is the eye candy:

And "zoomed in" by splitting each repair zone to a different Y scale:

There are of course a good number of factors than can affect the effective repair figure. I'm not going to give proof of that here (you can use the Excel spread sheet attached to convince yourself of this), but the variables that really matter are (in order of importance): the external repair level (hull/s), the experience level of the capital ship, and the armor researched. You can see from the graphs attached that while not under external repairs, the armors matters little (for the break-even DPS), but that once external repairs are applied (which vastly outclass the hull self-regen) then armor research starts to matter. The capital ship's experience level also has a bigger effect under repairs (mostly because it provides extra armor and extra shield mitigation) but it has non-linear effect due the shield mitigation (which appears in denominator of the break-even DPS formula). Remembering or even looking up all those graphs is of course impractical, so I've fitted a linear [regression] model through that family of curves. It's an interaction model, meaning that it uses no only the independent variables, but also their products. But this is still relatively easy to translate into rules of thumb. In the case of Mazra we get the following raw coefficients from the linear regression [lm() call in R]:

- (Intercept) 21.675871: this is the base DPS value to which the following are added
- hull_exr 6.091844 [direct effect of every unit of external hull repair, this means about 6 LFs per every 10 units of hull repair, i.e. 12 for the un-upgraded TEC repair platform (which does 20 hp/s).
- xplevel 4.484303 (how much extra DPS each XP level provides, when no external repairs are applied, in this case about half an LF per level.
- armo_res 0.701282: the effect of extra armor (on the break-even DPS) is negligible without external repairs
- hull_exr:xplevel 0.482204: this is the first interaction factor; what it says is that for every unit of external hull repair, you get an additional effect of the ships experience; in game terms this is a half LF for every 10 hp/s repairs, so 20 hp/s repairs get the Mazra an extra LF for every experience level, meaning that every experience level is worth 1.5 LFs when under 20hp/s repairs, 2 LFs when under 30hp/s repairs and so forth.
- hull_exr:armo_res 0.337177: this is the 2nd interaction factor. Translated in game terms, it means that every lab-worth of TEC armor research (which gives +1.5 armor) is worth about half an LF for each 10 hp/s repairs. So at the start-up 20 hp/s repairs that the repairs platform gets, all the armor that first lab allows you to research results in about one LF worth of extra damage that can be sustained continuously (at this level of repairs). At +3 armor (3 labs) and full platform + Hoshiko repairs (60 hp/s), the research armor a bit more valuable buying 6 LFs worth of damage vs. no armor research at this high level of repairs.

So to summarize the rules of thumb for the Mazra insofar, again assuming 1 LF = 10 (raw/infocard) DPS:

- at no external repairs start with 2 LFs, ignore armor researched, and add half an LF per every experience level (including the first one)
- at 20/30/40/... repairs: start with 14/20/26/... LFs and add 1.5/2/2.5/... LFs for every experience level (including the first one), then add 1/1.5/2/... LFs for every lab-worth of armor research (+1.5)

Now this is just a linear approximation of some non-linear characteristics. You can look at the residuals reported by lm() to see how much we err by. It's never more than 3 LFs, and more than half the time it's only by half an LF or less. If you look at the final graph, plotting the fitted lines versus the real characteristics, you'll notice that the lines are underestimating at the ends and overestimating in the middle of the experience interval, so if you want to be more perfectionist you could add 1-2 LFs at the ends (for XP=1,2 or 9,10) and subtract on in the middle (for XP=5,6). This correction for non-linearity is just a heuristic though, not something rigorously deduced.

I've put the package of R code, [SVG] figures and an excel in an archive at http://www50.zippyshare.com/v/66705202/file.html. The Excel spreadsheet has 3 tabs, one is the R-generated data and a pivot table&chart for it (needs Excel 2010 or newer because it uses slicers), while the "formulas" spreadsheet contains some "manual" experimentation and may have some inconsistent portions because I din't bother cleaning it up after I got the R code going. (The R code needs http://www.r-project.org/ to run of course and you need to install the two optional libraries invoked in the code [doBy and ggplot2].)

I've also calculated Kortul's average self-repair rate (including when using Power Surge), but even that sub-topic alone (effect of PS on self-repair rate) needs a table of its own plus fair bit of text to explain and I don't feel like writing it all up tonight. So stay tuned for that. And if you have any questions or comments on the material above, just shoot.