Since we now have the type chart, we should be able to calculate a range for Fairy Wind's Base Power. In this video, we can see that Hydreigon, which is doubly weak to Fairy, takes 96 damage from Gardevoir's Fairy Wind:

http://www.youtube.com/watch?feature=player_embedded&v=gmywDbnC5oc#t=82

From this, we can get a range of Base Powers that Fairy Wind must be contained in.

Gardevoir's SpAtk at Lv. 50: 117 - 194 (291 w/Choice Specs)

Hydreigon's SpDef at Lv. 50: 85 - 156

(Part of the damage + 2) x 1.5 x 2 x 2 = 96

Part of the damage = 14 = 22 x BP x SpAtk / 50 / SpDef

*Note that once we calculate the BP's, we should try other values close by in the formula due to the way the game rounds.

Min BP:

22 x BP x 291 / 50 / 117 = 14

BP = 13

Max BP:

22 x BP x 117 / 50 / 156 = 16.824 (This is due to the random damage part in the damage formula. 16 / .85 - 2 = 16.824)

BP = 54

So the BP must be within 13 and 54, assuming neither Pokemon had boosted its stats and Hydreigon didn't have Light Screen up. If we look at the scenario where both Pokemon had neutral natures, 31 IVs, and 0 EVs, we can get the following range.

Min BP:

22 x BP x 145 / 50 / 110 = 14

BP = 25

Max BP:

22 x BP x 145 / 50 / 110 = 16.824

BP = 31

**tl;dr: Fairy Wind's Base Power must be between 13 and 54. If we assume Gardevoir and Hydreigon have neutral Natures, 31 IVs, and 0 EVs, its Base Power must be between 25 and 31.**This is all assuming neither Pokemon had boosted its stats and Hydreigon didn't have Light Screen up (and that Fairy Wind's Special, but I don't see how that wouldn't be the case).

Generation 30: The first time you see this, copy it into your own signature (on any forum) and add one to the generation number. Social experiment.