.22 bullet drop at 200 yards? Like a fricken rock. I cant give you an actuall measurement but I know with my .22 mag when sighted in at 80 yards its about 26"-28" low at 240 yards. That was when I used to shoot Winchester 40 gr hollow points. There was a woodchuck hole 240 yards from by backdoor across a hay field and I sighted it in just for that reason. With the federal 32 gr loads Im shooting now, sighted in at 80 yards, only drop about 4" at 150, after that they just run out of steam. Someone on here may have a ballistics chart for a .22 and could give you a better answer than I can but I would say a .22LR sighted in at 100 yards will be 6"-8" low at 150 and better than 20" low at 200. All bullets shoot fairly flat out to a certain point then its like they hit a brick wall and start falling drastically. Finding that point is what you need to do to figure out your effective range. With a compound bow its usually at about 50 yards +/-. With a centerfire rifle it could be anywhere from 200 yards with a .22 hornet to 2 miles with a .50 BMG. A .22 LR I would guess would be just past 150 yards. Some loads shoot flatter than others, The best way to answer your question is just spend some time at the bench. Sight it in dead on at 100 then shoot it at 125 and measure how low it is, make a note of it then move to 150 and do the same. Untill you have enough data to compile a ballistics chart of your own. You can probably get a look at some ballistics readings on CCIs website. They make several different LR shells from sub sonics to hyper velocity stingers they should have some info on there.
treat every situation like a dog. If you cant eat it or hump it just piss on it and walk away