Made by @Hareeb_alSaq from twitter.  Thanks to various for double-checking my calculations.

This is a demonstration that Football Outsiders is mangling NFL tiebreakers.  To be more specific, it appears that if 2 teams are tied on Strength of Victory, they simply split the equity between the two teams and do *not* bother to calculate Strength of Schedule (for some inexplicable reason).  Because there are infinite ways they could be screwing up, I can't be sure this is the case of course, but it fits their mistake on DET #2 seed odds and also fits the utterly incomprehensible TB 0.4% 6-seed for a team with literally no path to the playoffs in their sims.

I am using the NFC playoff odds at http://imgur.com/a/7sff6 that were calculated *before* DET-DAL Monday Night Football on 12/26.  All tiebreak scenarios were calculated by hand and checked with the ESPN playoff machine at http://www.espn.com/nfl/playoffs/machine (although the result of MNF will make using it to check the 11-5 scenarios impossible).  Calculations ignore FUTURE ties (since FO's simulations do, and the point is to show their simulations are screwing up tiebreaks).

There are 5 games that affect NFC seeding at a level above strength of victory tiebreakers and we can use algebra to determine exactly what game win%s the FO simulator is using, and once we have those, it will become obvious that their tiebreakers are FUBAR.  Since nobody wants to read algebra, I've put the derivation at the end.

The 5 games and the probabilities he's using are:
DET-DAL MNF (week 16) "DAL"  DAL .790 / DET .210
GB-DET 				GB .588/ DET .412
NYG-WAS 			NYG .408/WAS .592
NO-ATL				NO .342/ATL .658
SEA-SF				SEA .595/SF .405

Again, these numbers don't necessarily reflect reality (ok, don't reflect reality), but they're the probabilities he's assigning to each game, +/- like .002 due to rounding.

His numbers for the GB and SEA seeds are consistent with the above because they don't involve Strength of Victory, but his numbers for DET #2 (and ATL #2) are wrong.  The ATL-DET tiebreak is complicated.  At 10-6, Detroit always wins (common games), but at 11-5, ATL *almost always* wins by Strength of Victory (or Schedule).

DET has (had) 3 scenarios to get the 2-seed:  1) Win out, ATL loses.  2) Lose to DAL, beat GB, ATL and SEA both lose.  3) Win out, ATL wins, DET hits the strength of victory miracle (Det always loses strength of schedule here if SoV is a tie)

1) has odds of .210*.412*.342 = .0296
2) has odds of .790*.412*.342*.405 = .0451

3) is trickier.  First, Det winning out * Atl winning = .210*.412*.658 = .0569.  To win SoV, DET has to have 5 other games go right.  I'm going to use the upper bound of his lines for the last three games (gotten from his median wins, so LAR on 4 wins and median 4.4 has a max win% of .45 in week 17) and the number is still going to come out much lower than what he reports.

SEA>SF (.595 via FO), WAS>NYG (.592 via FO), LA>ARI (.45 max via FO median wins), MIN>CHI (.55 max via FO median wins), TB>CAR (.65 max via FO median wins).  The probability of winning SoV is the product of all of these, so .0567.  SO scenario 3 is .0569*.0567 = .0032

The sum of these is .0779, 7.79%.  He has 8.4%, far outside the bounds of rounding error.  He *must* be screwing up the tiebreaks somewhere in the DET-gets-the-2 scenario.  And he was clearly screwing up the tiebreaks in the TB 6-seed scenario before- he was giving them 0.4% equity when they literally had no path to the playoffs without a NYG-WAS tie, which wasn't even part of his simulations.

----------------------------------------

It was interesting trying to figure out what in the actual fuck they were doing to come up with these nonsense numbers, and it appears to fit a very simple (and very, very stupid) explanation- if teams are tied after SoV, FO simply splits the equity 50/50 instead of calculating SoS.  Looking at the Det#2 (3) scenario, Det ties SoV 22.4% of the time.  So if you give them half of that, plus the .0567 they win it, that's .0569*(.0567+.112) = .0096.  That would make the total for DET#2 8.43%  Dead-on match to his 8.4%

Now let's see if that explains the TB 0.4% 6-seed tardoff from earlier (he "fixed" it in response to a tweet before I took the picture).  With no future game ties allowed, TB needed the following to tie for strength of victory with GB for the #6 (they lose SoS in this scenario, but it appears FO didn't know this)

DAL week 16 (.790 exact)
TB (.6 median)
IND (.6 median)
DAL (.5 median)
TEN (.7 median)
DET (.412 exact)
SF (.405 exact)
NYG (.408 exact)

That parlay is .00677, so half would be 0.338%.  A tad low.  Now using the maximums for the 4 median games, the parlay comes out to be .00937, so half would be .468%- actually high lol.  But there's a wide swath where his numbers average out on the high side of the possible range that would round to 0.4%.  And I'll be damned if I have *any* other idea how they were giving equity to a team that had literally none if their sims handled tiebreaks correctly.  Both of their obvious fuckups fit this simple explanation.



**** Algebra
---------------------------

We know he has GB 58.8% to beat Detroit because GB wins the division if and only if they do.  Let's write some equations for other seeds

WAS 6  .519 = WAS * (DAL + (1-DAL)*DET) = WAS * (DAL + 0.412*(1-DAL))
SEA 2  .186 = SEA * (1-ATL) * (DAL + (1-DAL)*GB) = SEA * (1-ATL) * (DAL + 0.588*(1-DAL))
SEA 4  .438 = (1-SEA) + SEA*ATL*(1-DAL)*DET = (1-SEA) + SEA*ATL*(1-DAL)*.412
DET 6  .313 = GB* (DAL*(1-WAS) + (1-DAL)) = .588 *(DAL*(1-WAS) + (1-DAL))

Using DET 6 and WAS 6

.519 = WAS*DAL + .412*WAS - .412*WAS*DAL  -> .519 = .588*WAS*DAL + . 412*WAS
.313= .588*DAL - .588*DAL*WAS +.588 -.588*DAL = - .588*DAL*WAS + .588

The bottom line means DAL*WAS = .4677, and plugging that into the top line gives WAS = .592 and therefore DAL =.790

Now we can plug that DAL value into the SEA 2 and SEA 4 to get his numbers for the other 2 games

SEA 2   .186 = .9135*SEA - .9135 *SEA*ATL -> SEA*ATL=  -.2036 + SEA
SEA 4	.438 = 1 - SEA + .0865*SEA*ATL

Plugging in gives .438 = 1 - SEA + .0865*(-.2122+SEA) -> .9135*SEA = .5436, SEA = .595, ATL = .658