What do you think of this ability
Whenever the Pokémon with is ability misses its target, if its Attack (or spAtk) can still be increased AND its Accuracy can still be reduced, its Attack (or spAtk) will increase 2 stages (or should it be only 1 stage? hmm...) and its accuracy will decrease 1 stage.
Pokes with such ability should probably not be able to learn moves such as Aerial Ace and Shock Wave, or have access only to 1 or 2 of 'em?!
My 2nd speculation
When a Pokémon receives an indirect damage (Stealth Rock & Co., Poison, Burn, Rough Skin & Co., Confusion, Rocky Helmet & Co., ...) increase its Speed 1 stage.