# Gratuitous Math Battles - Speed

So the other day I ran into Cliff’s explanation of how hit chance is calculated - tracking speed vs. target movement speed, modified by target size.

I wanted to know about what I could expect from setting certain target speeds (or adjusting speed up or down a few tenths of a point), so I made a spreadsheet and had the following observations:

TL;DR version - 2.5 is a good speed for fighters, unless you are up against a lot of defense lasers. Torpedo bombers (or dedicated anti-cruiser fighters) can get away with lower speeds (1.2+) IF we can assume they won’t be up against other fighters, frigates, or defense lasers/pulse lasers (and I almost never see pulse lasers on cruisers). Fast frigates get a large survivability boost (25% increase vs. cruisers, nigh-immunity to cruiser missles/cruiser plasma/MWM) at 0.60 speed, compared to 0.50, and can safely ignore most cruiser weapons at 1.20 speed. Cruisers get about 10% dodge vs. beam weapons for each 0.10 speed, and 16% vs. missiles/plasma/MWM. Against most frigate weapons, they only get 6% or less per .10 movement - in this case, increasing cruiser speed primarily decreases the amount of time they take fire wihtout being able to shoot back (for short range weapons)

Since I tried to post this once and timed out, I’m going to edit in my more long-winded observations.
EDITS:
Size - Basically, the size modifier starts out at 50%, and increases by 10% for every 50m in hull length. A 10m fighter has a 52% size modifier, a 100m frigate has a 70% size modifier, a 150m cruiser would have an 80% size modifier, and a 250m cruiser has a 100% size modifier. The size modifier is multiplied to the base hit chance; a target that is stationary (no engines or stopped moving) has a 100% base chance to be hit, so a fighter with no engines will still only be hit 52% of the time. The size modifier does quite a bit more for fighters and frigates than it does for cruisers, obviously.

Fighters - against other fighters, having a speed of 2.5 will give rockets a 2% chance to hit and lasers/pulse lasers only a 5%-6% chance to hit. For perfectionists, a 2.7 fighter speed will reduce the laser/pulse laser hit chance to 2% as well. A cruiser defence laser (3.7 tracking speed) only has a 5% chance to hit a 3.3 speed fighter, a 10% chance to hit a 2.9 speed fighter, and a 15% chance to hit the 2.5 speed fighter. The Anti-Fighter Missile is obviously better, landing hits 40% of the time vs. a 2.5 speed fighter and 38% of the time vs. a 3.3 speed fighter; even a 4.0 speed fighter will be hit 36% of the time, or more if it gets painted. Slower fighters also appear to be usable; a 1.9 speed fighter can ignore anything slower than a pulse laser (14% hit chance for a cruiser pulse laser, 16% for frigate, 18% fighter) and a 1.2 speed fighter seems ridiculously slow but can still dodge a cruiser’s main weaponry (10% hit chance for 1.5 speed racial weapons, 2% hit chance for beam lasers/etc), but can get torn up by pulse lasers (28% hit chance) and defense lasers (35% hit chance). So, if your oponent has (or you expect there will be) AA fighters/defense lasers/pulse lasers, don’t dip too far below 2.5 speed.

Frigates - Even at low speeds, most frigates will have at least a 30% dodge chance due to their small size. I consider 0.60 to be ‘moderate’ speed for a frigate - it means cruiser missiles/cruiser plasma/MWM will only hit 2% of the time, cruiser lasers/rockets/fast missiles only hit about 23% of the time, beam lasers and frigate plasma only hits 28% of the time, frigate missiles only land 42%, and even fighter rockets and ion cannons only have a 49% chance to hit. Compare that to a frigate moving at 0.50 speed: 12% hit chance for cruiser missiles (500% increase), 30% hit chance for CLs/rockets (30% increase), and a 35% hit chance for beam lasers (25% increase). The difference is smaller vs. frigate missiles and ion cannons/rockets (7% increase for both). A fast frigate at 1.2 speed or higher only has a 2% chance of being hit any cruiser gun with a tracking speed under 1.3, a 10% chance of being hit by a 1.4 speed weapon, and a 14% chance of being hit by a 1.5 speed weapon (frigate missiles, most racial cruiser beams). Against an ion cannon/rockets, the hit chance is 28% - but light enough to move that fast, 1/3 of a rocket fighter salvo can still tear it up. A slow frigate (0.30 speed) is highly vulnerable - 35% chance to be hit by missiles, 45% chance for CL/rockets, 49% chance for beam lasers, and 55%-60% for most other frigate weapons (vs. a 70% hit chance for a non-moving frigate). One thing to note there - ion cannons and fighter rockets only loose half their accuracy on a 1.2 speed frigate vs. a .3 speed one, and fighter lasers go from 63% (vs .3 speed) to 40% (vs 1.2), so a fast frigate would need to be able to take at least half as many hits as a slow, armored one to have equal survivability vs. fighters.

Cruisers - Like frigates, cruisers get a large survivability boost going from .5 speed to .6; even larger, since they don’t have the base 30% miss chance frigates do. However, it’s hard to make a functional cruiser that moves at that pace. As I listed above, each .01 movement translates roughly into 1% miss chance for cruiser beam weapons (CL, cruiser beam, etc) and 1.6% miss for missiles/plasma. a cruiser moving a .1 speed generates a 10% miss chance for cruiser beams, 16% for missiles/MWM, and 25% miss for heavy plasma. Yes, heavy plasma sucks that much vs. anything that isn’t sitting still.
That being said, going from .1 speed to .2 will not only double the miss chance for enemy cruisers, it’ll also cut the amount of time spent closing distance in half (if you have short-range guns). Against frigate weapons and fighters, speed is a laughable defense for cruisers - even at .3 speed, fighters have at least an 85% hit chance (rockets, 90% for lasers) and EMP frigates will still hit 80% of the time.
For cruisers, the time spent closing on targets and moving between parts of the battle is more important than having a lower chance to be hit due to speed.

When dealing with missile hit rate you have to also consider target painters. So while speed is still crucial to close in, frigate with 0.6 speed will be getting hit way more than 2% by MWM.

Well, yea, anything that plays around with the hit chance calculations will change the numbers.

Theoretically the painter laser has a 1.1 tracking speed, so it should only hit (and paint the target) about 32% of the time on a .6 speed frigate, and 2% of the time vs. one moving at 1.1 speed or better; in practice it seems to be a lot more reliable than that, though, to the point where I’d almost consider it equivilent to a tractor beam for missiles when it comes to countering fast targets.

And of course target boosters, tractor beams, and cloaking devices will all change the expected hit rates as well.

Funny you said that since painter doesn’t come with tracking speed on the display screen. I assumed the variable is null, like limpet launchers (which consistently hit fighters despite it’s 0.81 tracking).