Boston Red Sox First-Place Elimination Scenario
Boston must win 24 more games (48 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Boston finishes in first place with 48 wins:

Team             W	L	PCT	GB
Boston           48	114	0.296	0.00
Toronto          48	114	0.296	0.00
Baltimore        47	115	0.290	1.00
Tampa Bay        47	115	0.290	1.00
New York         47	115	0.290	1.00

Tie breakers
Boston wins the series with Toronto 10 games to 3

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Tampa Bay        35	20	107	0.636	0.0
New York         35	23	104	0.603	1.5
Toronto          29	30	103	0.492	8.0
Baltimore        27	32	103	0.458	10.0
Boston           24	33	105	0.421	12.0

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 4 additional game(s) against Boston and loses 6.
Baltimore loses the series 5 games to 8.
Baltimore wins 0 additional game(s) against teams outside the division and loses 70.

Baltimore currently has 2 win(s) against New York and 5 loss(es).
Baltimore wins 5 additional game(s) against New York and loses 1.
Baltimore wins the series 7 games to 6.
Baltimore wins 0 additional game(s) against teams outside the division and loses 70.

Baltimore currently has 3 win(s) against Tampa Bay and 3 loss(es).
Baltimore wins 7 additional game(s) against Tampa Bay and loses 0.
Baltimore wins the series 10 games to 3.
Baltimore wins 0 additional game(s) against teams outside the division and loses 70.

Baltimore currently has 1 win(s) against Toronto and 2 loss(es).
Baltimore wins 4 additional game(s) against Toronto and loses 6.
Baltimore loses the series 5 games to 8.
Baltimore wins 0 additional game(s) against teams outside the division and loses 70.

Boston currently has 0 win(s) against New York and 3 loss(es).
Boston wins 3 additional game(s) against New York and loses 7.
Boston loses the series 3 games to 10.
Boston wins 0 additional game(s) against teams outside the division and loses 65.

Boston currently has 1 win(s) against Tampa Bay and 2 loss(es).
Boston wins 6 additional game(s) against Tampa Bay and loses 4.
Boston wins the series 7 games to 6.
Boston wins 0 additional game(s) against teams outside the division and loses 65.

Boston currently has 1 win(s) against Toronto and 2 loss(es).
Boston wins 9 additional game(s) against Toronto and loses 1.
Boston wins the series 10 games to 3.
Boston wins 0 additional game(s) against teams outside the division and loses 65.

New York currently has 1 win(s) against Tampa Bay and 4 loss(es).
New York wins 3 additional game(s) against Tampa Bay and loses 5.
New York loses the series 4 games to 9.
New York wins 0 additional game(s) against teams outside the division and loses 71.

New York currently has 2 win(s) against Toronto and 2 loss(es).
New York wins 1 additional game(s) against Toronto and loses 8.
New York loses the series 3 games to 10.
New York wins 0 additional game(s) against teams outside the division and loses 71.

Tampa Bay currently has 5 win(s) against Toronto and 1 loss(es).
Tampa Bay wins 3 additional game(s) against Toronto and loses 4.
Tampa Bay wins the series 8 games to 5.
Tampa Bay wins 0 additional game(s) against teams outside the division and loses 75.

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