Boston Red Sox First-Place Eliminiation Scenario
Boston must win 24 more games (38 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Boston finishes in first place with 38 wins:

Team             W	L	PCT	GB
Boston           38	124	0.235	0.00
New York         38	124	0.235	0.00
Baltimore        37	125	0.228	1.00
Tampa Bay        37	125	0.228	1.00
Toronto          37	125	0.228	1.00

Tie breakers
Boston wins the series with New York 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         17	8	137	0.680	0.0
Baltimore        16	8	138	0.667	0.5
Boston           14	11	137	0.560	3.0
Toronto          13	12	137	0.520	4.0
Tampa Bay        13	13	136	0.500	4.5

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 4 additional game(s) against Boston and loses 6.
Baltimore wins the series 7 games to 6.
Baltimore wins 0 additional game(s) against teams outside the division and loses 89.

Baltimore currently has 0 win(s) against New York and 0 loss(es).
Baltimore wins 6 additional game(s) against New York and loses 7.
Baltimore loses the series 6 games to 7.
Baltimore wins 0 additional game(s) against teams outside the division and loses 89.

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

Baltimore currently has 0 win(s) against Toronto and 0 loss(es).
Baltimore wins 9 additional game(s) against Toronto and loses 4.
Baltimore wins the series 9 games to 4.
Baltimore wins 0 additional game(s) against teams outside the division and loses 89.

Boston currently has 0 win(s) against New York and 0 loss(es).
Boston wins 7 additional game(s) against New York and loses 6.
Boston wins the series 7 games to 6.
Boston wins 0 additional game(s) against teams outside the division and loses 88.

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 88.

Boston currently has 0 win(s) against Toronto and 0 loss(es).
Boston wins 4 additional game(s) against Toronto and loses 9.
Boston loses the series 4 games to 9.
Boston wins 0 additional game(s) against teams outside the division and loses 88.

New York currently has 2 win(s) against Tampa Bay and 1 loss(es).
New York wins 7 additional game(s) against Tampa Bay and loses 3.
New York wins the series 9 games to 4.
New York wins 0 additional game(s) against teams outside the division and loses 94.

New York currently has 3 win(s) against Toronto and 3 loss(es).
New York wins 1 additional game(s) against Toronto and loses 6.
New York loses the series 4 games to 9.
New York wins 0 additional game(s) against teams outside the division and loses 94.

Tampa Bay currently has 2 win(s) against Toronto and 2 loss(es).
Tampa Bay wins 4 additional game(s) against Toronto and loses 5.
Tampa Bay loses the series 6 games to 7.
Tampa Bay wins 0 additional game(s) against teams outside the division and loses 91.

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