While I'm looking at AA's Customer Service Plan ...
"Just because a flight is overbooked, it does not necessarily mean that customers with reservations will not be accommodated on their flight. The overwhelming majority of overbooked flights depart with all customers who have reservations and are present for departure.
If at departure time more customers with confirmed reservations are present than there are seats available, gate agents will first ask for volunteers who are willing to give up their seats in exchange for compensation and a confirmed seat on a later flight. On extremely rare occasions, a customer may be denied boarding on an involuntary basis, if a sufficient number of volunteers are not obtained. In such events, we will usually deny boarding based upon check-in time, but we may also consider factors such as severe hardships, fare paid, and status within the AAdvantage program. With few exceptions, persons denied boarding involuntarily are entitled to compensation under federal law.
Additional information concerning our overbooking policies can be found in our conditions of carriage. Upon request, reservations representatives or airport agents will advise you if your flight is overbooked at the time your reservation is made or during airport check-in. Bear in mind that, as stated above, most overbooked flights do in fact have sufficient seats to accommodate all customers who are present for departure."
http://www.aa.com/i18n/customerServi...cePlan.jsp#fwo
So ... if you're not an O&D pax, there is minimal chance of being IDB. I suppose if you think the flight is overbooked, you could wait until the last possible minute to check in.
Note that not having a seat assigment is not a factor.
As for rates, this was in the Dallas Morning News from last year ranking AA as no. 7 in bumps. Note that there were 7.02 VOLUNTARY bumps per 10,000 pax and only .56 IDB per 10,000 pax which makes sense because there will usually be sufficient volunteers.
7 American Airlines 7.02 0.56 7.58
http://aviationblog.dallasnews.com/tag/denied-boarding/