It has been a year or so since we took a Southwest flight and I don't remember if there is a way to check to see if they overbooked the flight. We want to have a back up plan in case we have an option to get bumped.
An airline's advance bookings are usually a closely-guarded secret. There are ways to make guesses from the outside - i.e., based on how many seats have been assigned - but that method doesn't work with Southwest since there are no assigned seats.
Southwest does overbook. The only major U.S. airline that doesn't is JetBlue.
According to U.S. Department of Transportation data, in 2009 out of every 10,000 passengers on Southwest, 1.29 were
involuntarily denied boarding due to overbooking. That is a middle-of-the-pack figure - the overall average for major U.S. airlines in 2009 was a bit lower, 1.19.
But the figure above doesn't account for the number of
voluntary denied boardings on Southwest - i.e., when Southwest solicits volunteers to take a later flight in return for a voucher/etc. in order to avoid involuntarily bumping a passenger. That happens to about 11.23 out of every 10,000 passengers.
In other words, based on math alone and not knowing the particular circumstances of your travel, the odds are low but it does happen.
