good question, I had a friend when I was a kid who was a gearhead and he always said to flip the cover of the air filter on your car upside down to let more air in and get more power. But I'm guessing the Seadoo engineers have already accounted for that in the bulky air box?
Laws of physics dictate that simply making more air available does not help much unless you account for the capacity internally (jetting) and on the posterior end (exhaust). In fact, if you do not address all these areas, you will have decreased performance. All turning the breather over on your car did was make it sound cool.
an engine is an air pump. the less restrictive the air flow, the more power it can make.
however. the stock one is huge because it directs water away from the intake. its design is to prevent water from getting sucked into the engine... so it sacrifices size / some restrictiveness to prevent water intake damage, which is 100 billion times worse than losing 1-2HP...
Ya I thought about the water thing...and looking at the bulky box its easy to see it's designed to bring in air but try to keep wate out at the same time....I have another question that may be silly...is there supposed to be a filter in the stock air box? Mine never had one...and I've never really noticed them listed on parts sites...am I missing it or am I asking a dumb question?