New York Yankees First-Place Eliminiation Scenario
New York must win 14 more games (70 total) to avoid elimination from first place.
Here is a scenario in which New York can finish in first place with 70 wins.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Tampa Bay        64	42	56	0.604	0.0
Boston           63	44	55	0.589	1.5
New York         56	48	58	0.538	7.0
Toronto          54	48	60	0.529	8.0
Baltimore        37	67	58	0.356	26.0

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

Baltimore wins 9 games against Boston and loses 0.
Baltimore wins 2 games against New York and loses 7.
Baltimore wins 10 games against Tampa Bay and loses 0.
Baltimore wins 10 games against Toronto and loses 0.
Baltimore wins 0 games agains teams outside the division and loses 0.

Boston wins 0 games against Baltimore and loses 9.
Boston wins 0 games against New York and loses 6.
Boston wins 7 games against Tampa Bay and loses 3.
Boston wins 0 games against Toronto and loses 4.
Boston wins 0 games agains teams outside the division and loses 0.

New York wins 7 games against Baltimore and loses 2.
New York wins 6 games against Boston and loses 0.
New York wins 0 games against Tampa Bay and loses 3.
New York wins 1 games against Toronto and loses 6.
New York wins 0 games agains teams outside the division and loses 0.

Tampa Bay wins 0 games against Baltimore and loses 10.
Tampa Bay wins 3 games against Boston and loses 7.
Tampa Bay wins 3 games against New York and loses 0.
Tampa Bay wins 0 games against Toronto and loses 6.
Tampa Bay wins 0 games agains teams outside the division and loses 0.

Toronto wins 0 games against Baltimore and loses 10.
Toronto wins 4 games against Boston and loses 0.
Toronto wins 6 games against New York and loses 1.
Toronto wins 6 games against Tampa Bay and loses 0.
Toronto wins 0 games agains teams outside the division and loses 0.

Combining the current standings with the wins and losses from the scenario results in the following final standings:
Team             W	L	PCT	GB
New York         70	92	0.432	0.0
Boston           70	92	0.432	0.0
Tampa Bay        70	92	0.432	0.0
Toronto          70	92	0.432	0.0
Baltimore        68	94	0.420	2.0


Next, we explain why New York cannot win the division with fewer than 70 wins.

There are a total of 74 games left in the following series of games between teams in the American League East:
Baltimore        vs. Boston           9 games
Baltimore        vs. New York         9 games
Baltimore        vs. Tampa Bay        10 games
Baltimore        vs. Toronto          10 games
Boston           vs. New York         6 games
Boston           vs. Tampa Bay        10 games
Boston           vs. Toronto          4 games
New York         vs. Tampa Bay        3 games
New York         vs. Toronto          7 games
Tampa Bay        vs. Toronto          6 games

For each team listed above, the table below shows the current number of wins in the (W) column.
The next column shows the maximum number of its remaining games that each team can win assuming that
NYYankees finishes in first place with a total of 69 wins.

Team             W	Max Additional Wins
Baltimore        37	69 - 37 = 32
Boston           63	69 - 63 = 6
New York         56	69 - 56 = 13
Tampa Bay        64	69 - 64 = 5
Toronto          54	69 - 54 = 15
Total            274	71

Since the total of the Max Additional Wins column is less than 74, it is not possible for NYYankees to win the division with 69 (or fewer) total wins.