The (Atlantic) Playoff Picture
I'm going to try and do this by hand, don't lynch me :D
Methodology: Using the historical stats, assume the result of a match is 25% 2-2, 39% 2.5-1.5, 23% 3-1, 11% 3.5-0.5, 3% 4-0. Furthermore assume that all teams are exactly evenly matched (e.g. a team has a 19.5% chance of winning 2.5-1.5 and a 19% chance of losing 2.5-1.5) Obviously this is an oversimplification but it'll do.
In the below I assume that the average rating tiebreak will stay as it is as the last two weeks should not make a meaningful difference in average rating of opponents. In other words I assume, for example, that if Manhattan ends up tied with any team on both MP and GP, they will win the average rating tiebreak (2411 vs. 2402, 2401, or 2383)
I believe that I covered all possible cases below and didn't overcount any scenarios, but as anyone who knows me from the math front knows, I'm really really bad at Combinatorics so there's a decent chance I overlooked something. I doubt people are going to be glossing over my numbers here with a fine-toothed comb, but if you really want to the numbers are here.
Philadelphia:
is in a tough spot, requiring:
Win over MAN and Win over NY and either
i) NY-NJ results in a tie and NJ-Manhattan is a decisive match and Philadelphia catches up in GP enough to take over both NY and (loser of NJ-Manhattan).
or
ii) NJ beats NY and NJ beats MAN and Philly catches up in GP to pass Manhattan.
In other words, PHI has a .813% chance of qualifying for the playoffs. To put it more simply, PHI is basically eliminated.
Week 9 elimination scenarios: PHI fails to win over MAN OR NY defeats NJ.
Week 9 clinching scenarios: None.
Every other team controls their destiny.
New Jersey:
a) NJ needs a win and either
a.i) NJ not losing to MAN
a.ii) NJ losing to MAN and NY not defeating PHI
a.iii) NJ losing to MAN, NY defeating PHI, but NJ wins the GP tiebreaker over NY
b) NJ needs a draw and either
b.i) A better result against MAN than NY has against PHI (e.g. win over MAN while NY draws PHI) or
b.ii) The same result against MAN as NY has against PHI but wins the GP tiebreaker over NY
b.iii) NJ defeats MAN and MAN fails to defeat PHI
e.g. NJ has a 58.33% chance of making the playoffs.
Week 9 elimination scenarios: MAN does not lose to PHI AND NY defeats NJ at least 3.5-0.5.
Week 9 clinching scenarios: None.
New York:
(a)
NY needs a win and either
a.i) NY not losing to PHI
a.ii) NY losing to PHI and NJ not defeating MAN
a.iii) NY losing to PHI, NJ defeating MAN, but NY winning the GP tiebreaker over NJ
a.iv) NY losing to PHI, NJ defeating MAN, PHI defeats MAN
a.v) NY loses to PHI, NJ defeats MAN, PHI draws MAN, NY wins GP tiebreaker over MAN and loses to NJ
a.iv) NY losing to PHI, NJ defeating MAN, PHI defeats MAN
a.v) NY loses to PHI, NJ defeats MAN, PHI draws MAN, NY wins GP tiebreaker over MAN
(b)
NY draws against NJ and either
b.i) NY defeats PHI and NJ fails to defeat MAN
b.ii) NY defeats PHI, NJ defeats MAN, NY wins the GP tiebreaker over NJ
b.iii) NY defeats PHI, NJ defeats MAN, PHI defeats or draws MAN
b.iv) NY defeats PHI, NJ defeats MAN, PHI loses to MAN, NY loses the GP tiebreak to NJ but defeats MAN
b.v) NY draws PHI, NJ fails to defeat MAN
b.vi) NY draws PHI, NJ defeats MAN, PHI defeats MAN
b.vii) NY loses to PHI, NJ loses to MAN other than NJ losing 2.5-1.5 and NY losing 4-0.
e.g. NY has a 63.03% chance of making the playoffs.
Week 9 elimination scenarios: None.
Week 9 clinching scenarios: (NY defeats NJ at least 3.5-0.5) OR (NY defeats NJ AND MAN loses to PHI)
Manhattan:
Manhattan has the easiest road to the playoffs with a half-point edge on the division. Easiest way to find their chances is 200%-.813%-58.33%-63.03%=77.8% chance of making the playoffs.
Specific scenarios:
a) Manhattan defeats PHI, plain and simple.
b) Manhattan draws with PHI
b.i) Manhattan does not lose to NJ.
b.ii) Manhattan loses to NJ
b.ii.a) NJ-NY results in an NJ win and NY fails to defeat PHI or NY defeats PHI but loses the GP tiebreak regardless
b.ii.b) NJ-NY results in a draw and NY fails to defeat PHI (because NY would fail to catch MAN of GP)
b.ii.c) NJ-NY results in an NY win (then NJ could not catch MAN on GP)
c) Manhattan loses to PHI
c.i) Manhattan defeats NJ
c.ii) Manhattan draws NJ and either NJ loses to NY or NJ draws NY and Manhattan does not lose 4-0 to PHI.
c.iii) Manhattan loses to NJ and NJ defeats NY and either NY loses to PHI but MAN defeats PHI on GP tiebreak or NY draws with PHI but MAN defeats NY on GP tiebreak.
Week 9 elimination scenarios: None.
Week 9 clinching scenarios: Defeat PHI OR (draw with PHI AND NY defeats NJ) OR (draw with PHI AND NJ defeats NY at least 3.5-0.5).
If you're ever looking to completely waste a morning, the above is a great way to do it :D
-Alexander Katz
