Ships & Modules

Optimal is the first stat, fall off the second. You will be able to hit out to 40km but that is near the end of your fall off so they won't necessarily be good hits. There is a fancy graph in one of the menus that will show you the drop off in DPS in relation to fall off.

Keep in mind this is all theoretical best case scenario as there is the RNG as well as the movement of your target to consider.

Enjoy playing around with it (2nd page).

The whole tracking thing is pretty well explained too.

Tracking Guide

Two different topics.

First,
the optimal range - or the first value on the fitting screen - is the maximum range were your guns can do 100% damage. The second value is falloff which is added to the optimal range and at the end of falloff your guns can only do 50% damage.

At 2x falloff of your guns, you will do zero damage but that is not documented.


Second,
pulse lasers and beam lasers are different. Pulses do a little more dps on the fitting screen than beams do but do not be fooled by what the dps value is.
What beam lasers may lack in dps they make up in alpha damage, which is the first volley your group of guns can do before they start to cycle.
Pulse lasers are the 'short range dps guns' and beams are the 'long range alpha guns'.

Optimal

Inside this range the gun will suffer no reduction in hit chance due to distance. If the target is sitting still inside the optimal range, every single attack will hit it.

Falloff

Falloff is an extra range that goes beyond your optimal range. This is, however, not a limit value, like the optimal range is. It is best described as a gradual loss of hit chance, where the given number (plus optimal) represents the distance at which you are down to a 50% hit chance. At two times your falloff value your hit chance is down to 6.25%, even though it is unlikely you can still hit your target at that range, and at three times your falloff range the chance to hit is only 0.2%.

Damage loss from Falloff and Tracking

Targets out in falloff, along with targets that must be tracked, are harder to hit. A lower hit chance means less damage done. The real question is, how much less damage? So lets look at that. First of all, one really nice thing with falloff and tracking is that they both behave exactly the same way, so the data table below applies to both of them.
The "Percent of Tracking or Falloff" values means how much of the listed falloff or tracking you are looking at. If your falloff is 12 km then 33.3% means one third of that, so 4 km. If your tracking is 0.4 rad/s then 50% would mean 0.2 rad/s.

Percent of
Tracking or Falloff Hit chance DPS reduction
0% 100% 0.0%
25% 95.8% −6.1%
33.3% 92.6% −10.6%
50% 84.1% −22.1%
84.8% 60.8% −50.0%
100% 50.0% −61.1%
150% 21.0% −85.2%
200% 6.25% −94.3%
300% 0.20% −99.4%


Enjoy reading.

The only bling you need on a paladin are 3 imperial navy heat sink (240 mil) , 2 c-type energized adaptive (200mil), a corpus/centus x-type large armor rep (350mil-450mil) and if you really into mad shopping mode, a faction webifier with 14km base range at least (dark blood / federation, around 50-60 mil).

The paladin cost 950 mil, the above fittings cost other 950 mil, rule of thumb of "your fittings shouldn't cost more than of your ship" fullfilled

At 40km you'll be doing 63% damage with your 27+16 guns and 90% damage with your 28+31 guns. Since 90% of 800 > 63% of 1080, ignoring all other factors you'll want to use the beams.

Spreadsheet for some quick calculations if you care to do them yourself.