I'm like you, JT. Huge sports fan and a lover of inefficiencies.
x2 on war room. Speaking of DePodesta, Scott Pioli is another guy that came in with a high reputation that was pretty much a failure. Really does a great job on TV now...
I've always wanted to read 2%, I really enjoy Keri's work with espn.com and grantland, but the reviews were always spotty. I guess people were expecting moneyball 2 and it failed to deliver? Also, I've always wanted to read 'Basketball on Paper' by Dean Oliver that goes into the 'four factors of basketball'.
Another sports book I think is excellent is Swing your Sword by Mike Leach and Bruce Feldman. It's not really an advanced stat type of book but Mike Leach is a fascinating character and his path to being a D1 head coach is incredible.
Rather than books, I've had lots of success with sports blog when trying to spot advance stat inefficiencies. footballoutsiders.com, profootballfocus.com, whoscored.com, fangraphs.com, kenpom.com, hoopsdata.com, hockeyprospectus.com, behindthenet.ca, nhlnumbers.com (Hockey is the last of the major sports to really commit to advanced data). Many of these places don't really spoon-feed you the info, you really have to do your own work in trying to understand the data but it's really worth it.