Will not having an advance seat assignment increase my chances of getting bumped if the flight is oversold?

This is a common perception, but a seat assignment is itself not an important factor in involuntary bumping. Each airline has its own algorithm for deciding who will be bumped if enough volunteers are not available. The major factors are a combination of: traveler status in the loyalty program, cost of the ticket, whether the ticket was purchased through a corporate contract, and time of check-in. All of these factor may influence the chances of not having an advance seat assignment which feeds the false misperception that the seat assignment is key.