Honestly, while not surprising, this definitely hurts the Dolphins. Teams typically get a bump when a coach is fired--even if his replacement is worse. The players know their butts are on the line and there will be a wholesale house-cleaning in the offseason, regardless of who is the next coach. So, the motivation problems and in-fighting stops for a few weeks and they start doing exactly what the coaches have been preaching to do. It usually results in a couple of wins over the next 5 weeks, removing that team from contention for the top pick.
Usually interim-coaches are neither good enough to right the ship, nor backed with enough resources to succeed ... so the season becomes a lame duck. Chances are that Houston's win total is lower now than it would have been with O'Brien for a full season. But, over the next few weeks, we'll see a spike in productivity most likely. Also, there's a real chance to turn things around because they're in a weak division. So, if their players start doing what they should have been doing all along ... they could bounce back to a .500 or better team, despite being 4 games in the hole.
From the Dolphins perspective, I would have liked the O'Brien rot to continue for at least a couple more weeks. They could conceivably be 0-6 before they got any new coach bump (AKA wake up call for lazy players who are blaming everything on the coach). Then their win total probably caps out at 4, and they'd be gifting us a top 10 draft pick. But doing it earlier ... they might get back on track with more than 6 wins and the pick's value drops dramatically.
Oh well, as it has been each week this season, my favorite team is the Dolphins and my 2nd favorite team is whomever is playing the Texans. :D Obviously, it is only because we own their 1st that my 2nd favorite team isn't whomever is playing the Patriots.