Boston Red Sox First-Place Eliminiation Scenario
Boston must win 22 more games (40 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Boston finishes in first place with 40 wins:

Team             W	L	PCT	GB
Boston           40	122	0.247	0.00
Toronto          40	122	0.247	0.00
Baltimore        40	122	0.247	0.00
Tampa Bay        40	122	0.247	0.00
New York         39	123	0.241	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
Baltimore        19	11	132	0.633	0.0
New York         20	12	130	0.625	0.0
Boston           18	13	131	0.581	1.5
Toronto          15	17	130	0.469	5.0
Tampa Bay        14	18	130	0.438	6.0

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

Baltimore currently has 3 win(s) against Boston and 0 loss(es).
Baltimore wins 3 additional game(s) against Boston and loses 7.
Baltimore loses the series 6 games to 7.
Baltimore wins 0 additional game(s) against teams outside the division and loses 86.

Baltimore currently has 2 win(s) against New York and 1 loss(es).
Baltimore wins 10 additional game(s) against New York and loses 0.
Baltimore wins the series 12 games to 1.
Baltimore wins 0 additional game(s) against teams outside the division and loses 86.

Baltimore currently has 0 win(s) against Tampa Bay and 0 loss(es).
Baltimore wins 7 additional game(s) against Tampa Bay and loses 6.
Baltimore wins the series 7 games to 6.
Baltimore wins 0 additional game(s) against teams outside the division and loses 86.

Baltimore currently has 0 win(s) against Toronto and 0 loss(es).
Baltimore wins 1 additional game(s) against Toronto and loses 12.
Baltimore loses the series 1 games to 12.
Baltimore wins 0 additional game(s) against teams outside the division and loses 86.

Boston currently has 0 win(s) against New York and 0 loss(es).
Boston wins 1 additional game(s) against New York and loses 12.
Boston loses the series 1 games to 12.
Boston wins 0 additional game(s) against teams outside the division and loses 82.

Boston currently has 0 win(s) against Tampa Bay and 0 loss(es).
Boston wins 7 additional game(s) against Tampa Bay and loses 6.
Boston wins the series 7 games to 6.
Boston wins 0 additional game(s) against teams outside the division and loses 82.

Boston currently has 0 win(s) against Toronto and 0 loss(es).
Boston wins 7 additional game(s) against Toronto and loses 6.
Boston wins the series 7 games to 6.
Boston wins 0 additional game(s) against teams outside the division and loses 82.

New York currently has 2 win(s) against Tampa Bay and 1 loss(es).
New York wins 0 additional game(s) against Tampa Bay and loses 10.
New York loses the series 2 games to 11.
New York wins 1 additional game(s) against teams outside the division and loses 89.

New York currently has 3 win(s) against Toronto and 3 loss(es).
New York wins 6 additional game(s) against Toronto and loses 1.
New York wins the series 9 games to 4.
New York wins 1 additional game(s) against teams outside the division and loses 89.

Tampa Bay currently has 2 win(s) against Toronto and 2 loss(es).
Tampa Bay wins 3 additional game(s) against Toronto and loses 6.
Tampa Bay loses the series 5 games to 8.
Tampa Bay wins 1 additional game(s) against teams outside the division and loses 84.

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