What's the probability that an NFL team with a given win/loss record makes the playoffs? For example, if I know that a team has a record of 11 wins and 5 losses, but no nothing about the records of any other teams, what is the probability that this team makes the playoffs?
The current (simplified) NFL rules for playoffs are that the team must either have the best record in its division (three other teams), OR have one of the best two records among teams in the conference that did not win the division.
So I suppose what I'm trying to figure out is:


*

*What is the probability that at least one out of three teams has a better win-loss record? This is easy if I assume that the win/loss records of each team in the division are independent (they aren't because each team plays each team in the division twice), but how inaccurate will that make the final answer?

*What is the probability that at least two other teams had a better win/loss record, but did not win their division? I really have no idea where to begin with this. Again, the odds of two teams having a better win/loss record is easy, but I'm not sure how to incorporate them winning their division.


(I mentioned 11-5 as an example record, but really I'm trying to solve this in general for any number of wins/losses, teams in a division, divisions, and teams in a conference)
 A: In any realistic model, it's going to be very difficult to get a closed-form solution.  So you should try a simulation.  Run a million or so simulations of NFL seasons according to your model.  In those million simulations, say there are a total of $N$ cases where a team had an $11-5$ record, and of those the team made the playoffs in $A$ cases.  Then 
$A/N$ should be a good approximation of the probability.
A: This is only a long comment, rather than an answer, mostly to lay out the (current) structure of the NFL schedule, in case anyone wants to run some simulations.
There are two "conferences" in the NFL, each consisting of 16 teams divided into 4 "divisions" of 4 teams each.  Six teams in each conference make the playoffs:  the winner of each division, and two more teams with the best records among the 12 non-winners.  (There are elaborate tie-breaking procedures that frequently come into play, but these are irrelevant for the OP's problem, where it's only the won-loss records that matter, not who holds them.)
For the OP's problem, we need only consider one conference.  Call the divisions N, S, E, and W, and the teams in them N1, N2, N3, N4, etc.  In a typical NFL season, each team plays the other 3 teams in its own division twice (once at home and once away); each team in N plays each team in S while each team in E plays each team in W; Ni and Si play Ei and Wi for i=1 to 4; finally, each team plays the 4 teams in one of the divisions in the other conference.  (The exact match-ups rotate from season to season, but this is irrelevant for the OP's problem.)  The total number of games each team plays is thus 6+4+2+4=16.
The structure of the schedule makes it conceivable for all four teams in a division to finish 3-13 (by all four teams winning their home games against their three division opponents and losing the rest) and hence send a division "winner" to the playoffs with a 3-13 record.  It is not possible to make the playoffs with a 2-14 record:  you simply can't have 11 teams in a single conference with 14 or more losses.  (There are 96 games played within the conference and 64 games played against the other conference, so the total number of losses cannot exceed 150.)
Conversely, it's possible to miss the playoffs with a 13-3 record, but not with a 14-2 record.  In practice, teams that go 11-5 or better rarely miss the playoffs, and teams that go 8-8 or worse rarely make it.  (I think both extremes have occurred, but someone would have to check how often.)  It can and does happen on occasion that a 10-6 team will miss the playoffs while a 9-7 division winner makes it.  Them's the breaks.
It could be worth running simulations with coin flips to determine the outcomes of games, to see how the statistics stack up against the historical statistics.  It might also be of interest to alter the schedule, say by eliminating inter-conference play and having Ni and Si play everyone in E and W except Ei and Wi, for i=1 to 4, to see if this has any effect on the stats.
