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The (Northeast) Playoff Picture

NJKnockouts
Oct 18, 2013, 11:39 AM 0

I already did Baltimore's so I might as well finish the division, since it's really very short. Again, this is all done by hand and as such may contain errors. The historical stats are assumed to hold, as well as all teams being equally matched and the average rating remaining relatively constant through the end of the season.

BOSTON:

Boston requires not only two wins in the final matches, but also for CON to lose both their matches to NE and BAL. Furthermore they have to also catch up in game points. 

a) BOS wins their final two matches with a combined GP score of at least 7.0 (3.5+3.5, 3+4, or 4+3) and CON loses both their matches. [0.091%]

((5.5%*5.5%+11.5%*1.5%+1.5%*11.5%)*37.5%*37.5%)

b) BOS scores a combined 6.5 GP (2.5+4, 3+3.5, 3.5+3, or 4+2.5) while CON manages only at most 2.5 GP (e.g. any combination of two losses besides 1.5+1.5) [0.197%]

[(19.5%*1.5%+11.5%*5.5%+5.5%*11.5%+1.5%*19.5%)*(37.5%*37.5%-18.5%*18.5%)]

c) BOS scores a combined 6 GP (2.5+3.5, 3+3, 3.5+2.5) and CON manages only at most 2 GP (all except 1.5+1.5, 1+1.5, 1.5+1) [0.194%]

[(18.5%*5.5%+11.5%*11.5%+5.5%*18.5%)*(37.5%*37.5%-19.5%*19.5-19.5%*11.5%-11.5%*19.5%)]

d) BOS scores a combined 5.5 GP (2.5+3, 3+2.5) while CON manages only at most 1.5 GP (all except 1.5+1.5, 1.5+1, 1.5+.5, 1+1.5, 1+1, .5+1.5) [0.103%]

[(19.5%*11.5%+11.5%*19.5%)*(37.5%*37.5%-19.5%*19.5%-19.5%*11.5%-19.5%*5.5%-11.5%*19.5%-11.5%*11.5%-5.5%*19.5%)]

e) BOS scores a combined 5 GP (2.5+2.5) while CON manages only at most 1 GP (0+1, .5+.5, 1+0, 0+.5, .5+0, 0+0) [0.032%]

[(19.5%*19.5%)*(1.5%*11.5%+5.5%*5.5%+11.5%*1.5%+1.5%*5.5%+5.5%*1.5%+1.5%*1.5%)]

This sums up to a 0.62% chance of making the playoffs for Boston.

Week 9 elimination scenarios: BOS fails to win over NE OR CON does not lose against BAL 

Week 9 clinching scenarios: None

BALTIMORE:

Baltimore is also looking at the playoffs from the outside in, facing a very difficult road into them. Trailing CON not only by 1.5 MP but 4 GP as well, 2 wins is a near necessity with help along the way. BAL does have two saving graces: the first is that one of their remaining matches is against CON so that's one less result they need to go their way (a win and a CON loss that week is only one match rather than 2 that they need to go their way), and the second is that their average rating is high enough that a MP&GP tie with CON is enough to put them through. 

BAL requires:

a) Win both matches, CON loses both matches (37.5%*37.5%*37.5%) [5.27%]

b) Win both matches while CON draws to NE (and loses to BAL), but BAL wins the tiebreaker [0.86%]

- BAL-CON results in 4-0 or 3.5-0.5 (7%*37.5%*25%)

- BAL-CON results in 3-1 and BAL beats BOS by at least a 3.5-0.5 margin (11.5%*7.5%*25%)

c) Win against CON and draw BOS while CON loses to NE (and BAL), but BAL wins the tiebreaker [0.86%]

-BAL-CON results in 4-0 or 3.5-0.5 (7%*37.5%*25%)

-BAL-CON results in 3-1 and CON loses 0-4 or 0.5-3.5 to NE (11.5%*7.5%*25%)

This sums up to a 6.99% chance of making the playoffs for Baltimore. 

Week 9 elimination scenarios: BAL fails to win against CON.

Week 9 clinching scenarios: None.

NEW ENGLAND:

New England has already clinched a playoff birth by virtue of Boston's loss last week. 

Week 9 elimination scenarios: None

Week 9 clinching scenarios: Anything.

CONNECTICUT:

Connecticut gets the rest, e.g. 200%-100%-6.99%-0.62%=92.39% chance of making the playoffs for Connecticut. 

Week 9 elimination scenarios: None

Week 9 clinching scenarios: Avoids a loss against BAL. 

See the similar calculations done for the Atlantic division at http://www.chess.com/blog/NJKnockouts/the-playoff-picture. If I get time I'll do the West as well.

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