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Offense affects Damage, as you guessed.
Defense affects Hull and Sails (meaning a ship with higher defense will have more hull and sail HP than one with a lower defense stat).
Support affects the Diplomacy stat, which directly affects things such as price discount, and amount of HP recovered by the water barrel.
These can be viewed by mousing over the relevant stats in your inventory screen, where you'll see a percentage value on the stat's description popup. This should be the same as the value listed in the town's ship page. (i.e, a ship with, say, an offense 'stat' of 300 would show 300% on the damage stat card.)
Oh man, that's what those "effectiveness" percentages mean? Suddenly so many things make sense. Thanks a bunch for the explanation. : )
...So, my previous explanation is apparently completely wrong.
Since I don't have any idea on the exact mechanics now, I'm guessing the ship's stat modifier now takes your current stats and applies the multiplier to that.
The effectiveness value looks like it shows the percentage of the base stat that you currently have.
As an example of this, one of my characters, who currently has a corvette, has a damage stat of ~1100ish, and the effectiveness value is 992%.
Support at -10% is better as it decreases cooldown time by 10%. stack with a talent focus in support and you can get some very fast cycle time going on. Trade off is taking a +10% to another set of talents. It gives a strength and weakness obviously. Plus crews and captains can have this trait as well.
Obviously this lets you try and build specialist builds that are devestating when done right. Imagine taking the offense specialization which shaves off cooldown time a good bit. Then getting a specialist who removes another 10% from offensive talents. THEN get a crew who does the same thing. Now a captain who loves cannons and cannon accessories.
Bam, you now have gatling cannons and a firebarrel launcher on steriods.
The only drawback is whatever skills are nerfed in the process of stacking those reductions.