Tampa Bay Rays First-Place Eliminiation Scenario
Tampa Bay must win 6 more games (71 total) to avoid elimination from first place.
Here is a scenario in which Tampa Bay can finish in first place with 71 wins.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Tampa Bay        65	44	53	0.596	0.0
Boston           64	45	53	0.587	1.0
New York         58	49	55	0.542	6.0
Toronto          56	49	57	0.533	7.0
Baltimore        38	69	55	0.355	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 1 games against New York and loses 5.
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 5 games against Baltimore and loses 1.
New York wins 6 games against Boston and loses 0.
New York wins 0 games against Tampa Bay and loses 3.
New York wins 2 games against Toronto and loses 5.
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 5 games against New York and loses 2.
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
Tampa Bay        71	91	0.438	0.0
Boston           71	91	0.438	0.0
New York         71	91	0.438	0.0
Toronto          71	91	0.438	0.0
Baltimore        68	94	0.420	3.0


Next, we explain why Tampa Bay cannot win the division with fewer than 71 wins.

There are a total of 71 games left in the following series of games between teams in the American League East:
Baltimore        vs. Boston           9 games
Baltimore        vs. New York         6 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
TampaBay finishes in first place with a total of 70 wins.

Team             W	Max Additional Wins
Baltimore        38	70 - 38 = 32
Boston           64	70 - 64 = 6
New York         58	70 - 58 = 12
Tampa Bay        65	70 - 65 = 5
Toronto          56	70 - 56 = 14
Total            281	69

Since the total of the Max Additional Wins column is less than 71, it is not possible for TampaBay to win the division with 70 (or fewer) total wins.