I'm reminded of the 2nd Law of Thermodynamics, which states something to the effect that energy can't be created or destroyed, just converted from one form into another. I'm thinking that the amount of energy lost to using and exhausting inside air is the same as the amount of energy needed to heat outside air to room temperature, in which case an OAK only serves to supply air that is richer in oxygen and can therefore produce hotter combustion, meaning quicker heating. That would mean that heating the outside air would cause it to expand and thus be less oxygen rich. In winter, air that is very humid is also very cold, and thus very rich in oxygen and that added oxygen would easily help to vaporize moisture in the cold air.
Also, starting with that fact that a perfectly sealed building which has an exhaust fan blowing air outside, that fan will become ineffective at moving air outside at the point at which the vacuum in the building is strong enough to not allow any further air escape. Thus, it would seem that an OAK is far more effective in houses that are very well sealed, while being unnecessary in homes, like mine, that are rife with air leaks. Those who report a significant difference in stove performance after adding an OAK probably have very tightly sealed homes and lack an off-setting air draft to compensate for the exhaust draft. Whether outside air comes in through an OAK or through leaks, it's the same cold air, but with the OAK it doesn't cool the interior, only the interior of the stove's intake pipe.
Also, here's another new thought, the positive pressure from expanded warm air from the convection blower balances the negative pressure from the exhaust fan since the amount of air and heat from both is essentially equal, but the expanded, heated interior air creates a positive interior pressure which resists outside air from so freely being sucked in through leaks. To get good airflow in that situation requires that the amount of house air-leakage has to be great enough to more than match the positive pressure from the stoves heated air. Unfortunately, that describes my house, including the one room I'm using it to heat.
I learned quickly when I first began using my pellet stove, that the amount of heat in the exhaust was about the same as the that from the convection blower. Therefore about half of the price of the pellets was being wasted as exhaust heat. Bad design from an economic stand-point. I dealt with that problem by doing something very unconventional. Instead of using pellet vent pipe, I just used what I had on hand, which was salvaged galvanized gas-water heater pipe and a 4.5' length of heavy 4 inch cast-iron sewer pipe and elbow. I butted the sewer pipe up tight against the 3" stove exhaust pipe insulation and attached the galvanized pipe to it after the 90 degree elbowvia use of an adjustable 90 degree galvanized elbow to angle the pipe at 45 degrees up into an old unused gas water-heater ceiling vent pipe. (about 5 feet of galvanized pipe before the vertical section.) I went 2 steps further in trying to retain exhaust heat. Before connecting the heavy iron sewer pipe, I first cut and inserted 4 4' lengths of heavy old steel plumbing pipe in order to increase the metal mass inside the sewer pipe (to absorb more heat). Since the pipes were pipes, I figured they would let the air pass through fairly unimpeded. Upon finally firing it up, I could see no difference in the strength of the combustion "wind", so it appears that the use of 4 in. pipe inside the house allows adequate air movement, even though the old unused ceiling/roof vent pipe is only 3 inch.
But then I added one last element, I covered much of the inside pipe with wet towels, which dry out in about 1 1/2 hours. When they're baked dry they're barely warm because the heat is being dispersed fairly evenly and no one spot is overly hot. The result of all this seems to match what my curious mind suspected, namely that the amount of heat exiting the exhaust vent above the roof is roughly half what it was when I first tried out my stove using only the galvanized pipe running at a somewhat raised horizontal angle. If that is true, then I'm keeping about half of the lost exhaust heat inside, which would translate to saving about 25% of the cost of a bag of pellets, instead of losing about 50% of the cost to heating the great outdoors.
The whole experimental arrangement is temporary and I'll dismantle it and move the stove outdoors in the Spring since it's not in a convenient location.
It would be wonderful if some one or some company would invent a pellet stove or vent add-on that could retain 95% of the exhaust heat. When that day comes, people will be able to heat their well insulated homes so cheaply that nothing else will be able to compare (unless natural gas becomes as cheap as dirt).
As someone who lives next door to a neighbor who burns wood with half the air his stove needs, and thus badly pollutes the air that I have to breath while outdoors, I am amazed at how the forced-air of pellet stoves results in almost no burn-pot ash residues and clean, almost breathable exhaust air. Now if only they would invent one that's truly high-tech when it comes to heat retention.