Edit: Looks like a good amount of this information has been obsoleted by the Official Strategy guide that came out. I'd recommend using that over this guide here, but I'm gonna leave this here in case you want some more detailed numbers.
Yo. I did a bunch of testing in the firing range yesterday and compiled a list of my findings on equipment skills. These effects are for one single primary skill only (non-stacked). I haven't thoroughly tested stacking yet, but the diminishing returns are very un-forgiving. Stacking is pretty worthless. Sub-skills have a lessened effect, and I haven't done the math on those yet. All numbers are approximate, but are fairly accurate.
Damage Up - Increases damage given by your main, sub and special weapon by 9%.
Note that weapons have a damage cap on them to prevent them from killing in a lower amount of shots.
Defense Up - Decreases damage taken from all sources by 9%.
Unlike Damage Up, using Defense Up can sometimes increase the number of shots it takes to splat you with certain weapons.
Movement Speed Up - Increases Inkling Run speed by 25%.
Swim Speed Up - Increases Squid Swim speed by 7.5%.
Ninja Squid - Makes you invisible while swimming through ink in squid form (except on walls). Decreases swim speed by 7.5%..
Ink Saver Main - Decreases the amount of ink your main weapon uses by 13.5%.
Ink Saver Sub - Decreases the amount of ink your sub weapon uses by 7.5%.
Special Saver - Decreases the amount of special gauge charge you lose upon being splatted from 50% to 33.3%.
Special Duration Up - Increases the duration of your special ability by 12.5%.
Bubbler goes from 5 seconds to 5.625 seconds.
Kraken, Inkzooka and Bomb Volley go from 6 seconds to 6.75 seconds.
Echolocator goes from 12.5 seconds to 14.062 seconds.
Inkstrike and Killer Wail setup time goes from 10 seconds to 12.5 seconds. The length of the actual 'attack' is not affected.
Cold Blooded - Decreases the effect duration of tracking applied to you by 75%. Found by Outplaytion
Point sensor goes from 10 seconds to 2.5 seconds.
Echolocator goes from 12.5 seconds to 3 seconds.
Boosted Echolocator goes from 14.062 seconds to 3.515 seconds. (Un-tested)
The following are un-tested: Quick Super Jump, Stealth Jump, Quick Respawn.
All other abilities currently remain un-tested since I have no easy means of testing them at this time. I'll be able to test them once custom lobbies come out in August.
If you have any questions, leave them here and I'll do my best to answer them.
Also, you can check out my twitch stream where, at the time of posting this, I have streamed 41 hours of Splatoon in the 3 days it has been out in North America.
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Equipment Skill Numbers
A list showing the exact numbers that equipment skills boost your stats by,