Just not in the same season.*
The Texans won their last two games of the '06 season against Indy and Cleveland and won their first two games of the '07 season against Kansas City and Carolina.
That's four in a row. So there.
Yeah I know, that kind of four in a row doesn't count because it wasn't all in the same season. And it doesn't count because a team winning four in a row in that fashion could still go 2-14 in each of those seasons, but it's not likely.
It's also possible a team could go 11-5 without a three-game win streak, but that's not likely either. Even in the years when a weak NFC was putting multiple 8-8 teams into the playoffs, those teams usually had at least one three-game win streak in them. And it usually takes at least one three-game win streak to make the playoffs.
Although while looking through one of my favorite football resource websites, I was surprised to find a case where a team (the '05 Redskins) lost 6 of 8 in the middle of the season but still finished 10-6 and made it to the Divisional round of the playoffs. But that's rare.
Just as rare as not winning three in a row and making the playoffs, it seems. In case you were wondering, I haven't had the time to dig back past 2004 to see if it's ever happened.
I guess I'm just getting tired of hearing statistics that associate our team with newness and futility -- although now it's more about futility than newness. And hearing this 'never won three in a row' stuff just brings back really, really bad memories of a former Texans quarterback's 'omg' moment.
Anyway, for the record, the Texans five failed opportunities for three-game win streaks in the same season* go like this:
Let's hope we end it -- the streak and the futility -- some time soon.