12 teams make the playoffs every year (obviously). Here is how many of them lose in Week 1 and the competition they lose to:
2014: 5 lost in Week 1 - 4 lost to either a playoff team or in a road divisional game (1)
2013: 4 lost in Week 1 - 2 lost to a playoff team
2012: 4 lost in Week 1 - 3 lost to either a playoff team or in a road divisional game (1) (Hawks and Colts had rookie QBs at the time FWIW)
2011: 5 lost in Week 1 - 3 lost to either a playoff team or in a road divisional game (1) (Broncos lost in a divisional game, but it was at home and that team was such a miracle)
2010: 3 lost in Week 1 - 3 lost to either a playoff team or in a road divisional game (1)
2009: 2 lost in Week 1 - 0 lost to either a playoff team or in a road divisional game (Cardinals lost a divisional game, but it was at home and Bengals lost on the ridiculous Stokley play that Gus Johnson called)
2008: 3 lost in Week 1 - 1 lost to a playoff team (Dolphins lost a divisional game to Favre-led Jets before Favre got hurt, but it was at home)
So on average, about 3 or 4 teams each year lose in Week 1 and make the playoffs. However, almost all of them will lose at least divisional game (typically on the road) or to another playoff team. The only teams I counted that didn't lose to a playoff game or a division opponent in Week 1 that still made the postseason were the 2008 Indianapolis Colts (Manning had early injury issues IIRC - Colts started off real slow that year I think which is the main reason he won MVP), 2009 Cincinnati Bengals (against lost on a really flukey play), 2011 Atlanta Falcons, 2012 Indianapolis Colts (lost to Bears, who finished the year 10-6), 2013 San Diego Chargers, 2013 Cincinnati Bengals, and 2014 Dallas Cowboys. Of those 7 teams, only the Chargers and Cowboys made it out of the first round and neither of those two teams made it to the Championship game.
tl;dr - If your team lost in Week 1, there chances of making the playoffs have went down considerably. If your team lost in Week 1 to a team that you don't see either making the playoffs or that wasn't a road divisional game (or a divisional game in general), then it hurts your chances even more. So with this now in mind, of the teams that won and lost in Week 1, which ones do you see missing and making the playoffs?
Going with my "formula" I'll separate it like this...
Winners:
AFC -
New York Jets
New England Patriots
Buffalo Bills
Miami Dolphins
Cincinnati Bengals
Tennessee Titans
San Diego Chargers
Denver Broncos
Kansas City Chiefs
NFC -
Dallas Cowboys
Green Bay Packers
Carolina Panthers
Atlanta Falcons
San Francisco 49ers
St. Louis Rams
Arizona Cardinals
Losers to probable playoff teams (I'll go with a mix of last years playoff teams and who I think have a really good chance, so sorry Browns fans) and/or divisional opponent (bonus points if on road or fit both of criteria):
I won't list teams with below average at best quarterbacks
AFC -
Pittsburgh Steelers
Indianapolis Colts
Baltimore Ravens
NFC -
Chicago Bears*
Seattle Seahawks**
New Orleans Saints
Detroit Lions
New York Giants
Philadelphia Eagles
Minnesota Vikings (I'm being really generous listing them)
9 winners in the AFC compared to 7 in the NFC. Obviously there won't be 4 teams in the AFC East to make the playoffs, so I'm going to say the Jets and Dolphins don't make it. Jets QB is Ryan Fitzpatrick and Dolphins head coach is Joe Philbin. It was a road game against a Washington team that isn't that bad, but they still looked very underwhelming and were lucky to get the win. I think it is safe to say Mariota isn't 4 TDs in one half good and the Titans are still severely lacking in talent elsewhere, so I'll rule out the Titans with confidence.
That shortens the AFC pool to 6. Someone from the AFC South has to make the playoffs and I say it will be the team with Andrew Luck at QB. The only uncertainties I have now are that last Wildcard spot and AFC North. Ravens and Steelers lost to playoff teams QB'd by Brady and Manning, Bengals are always tough in the regular season, and Bills are going to be a tough outing for any team. Will have more of an idea after they play the Patriots next week. If I had to guess, Steelers defense is going to be too bad for them to win the division. So Bengals/Ravens fight it out over the division crown with the loser of that fighting the Bills, Chargers, and MAYBE Chiefs for the last wildcard spot.
AFC: Patriots, Broncos, Colts, Ravens/Bengals, Chiefs, Chargers/Bills/Ravens or Bengals
In that you could have 2 new playoff teams and 2 teams that lost in Week 1.
NFC is a bit more tricky because there are more teams with legit QBs. There is almost no way the Seahawks miss the playoffs. I'll throw out the Rams and 49ers. I still don't trust Nick Foles and even if I did, I don't think they have enough offense/playmakers to win that tough division and 49ers, while I like them more than most, still have some deficiencies that will hold them back. I don't trust the Cardinals either but Arians is a badass coach and I'm done doubting him. Atlanta looked better than Carolina did vs better competition, so I'll go with Atlanta to win the division (or at least lean more towards them at making the playoffs).
That's 5 teams so far. I could see an argument for Detroit, New York, Philadelphia, Carolina, and New Orleans. 4 of those teams were on the road against teams I have making the playoffs and Carolina won in Week 1. Hold a gun to my head, I'll say Detroit. They looked dominant for most of the game against a quality, possible playoff team while being on the road without maybe their best defensive player (DeAndre Levy).
Actually, I forgot that at least 4 new playoff teams have made it since 1990. So Lions out, I'll go with Philadelphia in.
NFC: Dallas Cowboys, Green Bay Packers, Seattle Seahawks, Atlanta Falcons, Arizona Cardinals, Philadelphia Eagles
2 new playoff teams and 2 teams that lost in Week 1