What's your ball size?
 

Just got this 700 grizz and I'm adding a hitch ball on the back just for the sake of having a good trailer tie down point. Not sure what I'd be towing with the bike in the future but I suppose I'd like to get whatever ball size would be most common on the things I'd be likely to tow with an ATV.

So which size yall think would be best...1 7/8", 2", or 2 5/16" ?

It all depends on what you want to do with it. I have a 2" ball so I can move my trailer. My friends have 1-7/8" balls for lawn carts and that may be what you'll need. I could probably just use a smaller ball when I move my trailer since I don't have far to go. IMO you'll never need a 2-5/16" ball.

Your trailer tells you what ball you need. Most trail made for the back of a ATV are 1-7/8th.

There are hitch ball systems that allow you to change the ball size without taking off the rest of the hitch ball stem. Like this: http://www.ebay.com/itm/Master-Lock-10000lb-Interchangeable-Mount-Steel-Hitch-Ball-1-7-8-And-2-x-1-/221546871729?hash=item339538fbb1&vxp=mtr I use mostly the 2" but need the 1-7/8" every so often.

That looks like a good setup. Having both the 1 7/8 and 2" pretty much covers almost anything you would ever tow with an atv. Some of the newer quads actually have a receiver hitch like on a truck. That would be much quicker to change out(just pull a pin) but I can guess it costs you a couple inches of ground clearance at the rear axle.

If you have the receiver style hitch on your quad and you want to avoid dragging the hitch just flip it over 180 degrees. A stock height hitch insert flipped over is about a 2" rise. 2" drop is about a 4" rise, etc. I had a 1-1/4" on my Polaris and did it that way. With the stock hitch from Can-Am I put one of the convertible balls on like the link. Has worked great for me.

I have just a small amount of drop on my hitch and I have it going down. I just checked and without me on the quad I have about 12" of clearance to the bottom of the nut. The nut is even with the end of the shank after I cut the shank to length. Now there aren't any exposed threads to get buggered up. I leave the hitch on all the time and never had a problem with ground clearance.

One of my friends has his hitch turned up and he takes the ball off and bolts on a wooden box he made to fit a small gas can. I think it's 2 gallons. It's out of the way and he can still use his cargo boxes on the front and back.

I guess most irs quads have more than sufficient clearance. Unless you have an extreme amount of drop in your receiver hitch, it won't be a problem. If you have zero drop then it basically is the same as just having a ball. Pulling a pin to remove it is much easier than actually having to use a socket or big wrench to take a ball off.

Small trailers and carts usually use 1 7/8. Highway trailers usually use 2"