Boston Red Sox First-Place Eliminiation Scenario
Boston must win 18 more games (43 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Boston finishes in first place with 43 wins:

Team             W	L	PCT	GB
Boston           43	119	0.265	0.00
Baltimore        43	119	0.265	0.00
Tampa Bay        43	119	0.265	0.00
Toronto          43	119	0.265	0.00
New York         42	120	0.259	1.00

Tie breakers
Boston wins the series with Baltimore 7 games to 6
Boston wins the series with Tampa Bay 7 games to 6
Boston wins the series with Toronto 7 games to 6

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
New York         30	19	113	0.612	0.0
Toronto          25	24	113	0.510	5.0
Boston           25	26	111	0.490	6.0
Tampa Bay        23	26	113	0.469	7.0
Baltimore        16	32	114	0.333	13.5

Next, we show how the remaining series of games plays out in the scenario:

Baltimore currently has 1 win(s) against Boston and 2 loss(es).
Baltimore wins 5 additional game(s) against Boston and loses 5.
Baltimore loses the series 6 games to 7.
Baltimore wins 0 additional game(s) against teams outside the division and loses 74.

Baltimore currently has 2 win(s) against New York and 1 loss(es).
Baltimore wins 9 additional game(s) against New York and loses 1.
Baltimore wins the series 11 games to 2.
Baltimore wins 0 additional game(s) against teams outside the division and loses 74.

Baltimore currently has 0 win(s) against Tampa Bay and 0 loss(es).
Baltimore wins 13 additional game(s) against Tampa Bay and loses 0.
Baltimore wins the series 13 games to 0.
Baltimore wins 0 additional game(s) against teams outside the division and loses 74.

Baltimore currently has 3 win(s) against Toronto and 3 loss(es).
Baltimore wins 0 additional game(s) against Toronto and loses 7.
Baltimore loses the series 3 games to 10.
Baltimore wins 0 additional game(s) against teams outside the division and loses 74.

Boston currently has 0 win(s) against New York and 0 loss(es).
Boston wins 3 additional game(s) against New York and loses 10.
Boston loses the series 3 games to 10.
Boston wins 0 additional game(s) against teams outside the division and loses 72.

Boston currently has 2 win(s) against Tampa Bay and 1 loss(es).
Boston wins 5 additional game(s) against Tampa Bay and loses 5.
Boston wins the series 7 games to 6.
Boston wins 0 additional game(s) against teams outside the division and loses 72.

Boston currently has 2 win(s) against Toronto and 5 loss(es).
Boston wins 5 additional game(s) against Toronto and loses 1.
Boston wins the series 7 games to 6.
Boston wins 0 additional game(s) against teams outside the division and loses 72.

New York currently has 4 win(s) against Tampa Bay and 3 loss(es).
New York wins 1 additional game(s) against Tampa Bay and loses 5.
New York loses the series 5 games to 8.
New York wins 0 additional game(s) against teams outside the division and loses 74.

New York currently has 2 win(s) against Toronto and 1 loss(es).
New York wins 0 additional game(s) against Toronto and loses 10.
New York loses the series 2 games to 11.
New York wins 0 additional game(s) against teams outside the division and loses 74.

Tampa Bay currently has 2 win(s) against Toronto and 1 loss(es).
Tampa Bay wins 10 additional game(s) against Toronto and loses 0.
Tampa Bay wins the series 12 games to 1.
Tampa Bay wins 0 additional game(s) against teams outside the division and loses 74.

# Boston Red Sox' magic number
# Boston's magic number
# Red Sox' magic number
# MLB Playoff Race