Washington Nationals First-Place Eliminiation Scenario
Washington must win 23 more games (38 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Washington finishes in first place with 38 wins:

Team             W	L	PCT	GB
Washington       38	124	0.235	0.00
Miami            38	124	0.235	0.00
New York         38	124	0.235	0.00
Atlanta          38	124	0.235	0.00
Philadelphia     38	124	0.235	0.00

Tie breakers
Washington wins the series with Atlanta 7 games to 6
Washington wins the series with Miami 7 games to 6
Washington wins the series with New York 7 games to 6
Washington wins the series with Philadelphia 7 games to 6

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Atlanta          20	9	133	0.690	0.0
Philadelphia     21	11	130	0.656	0.5
New York         15	15	132	0.500	5.5
Washington       15	15	132	0.500	5.5
Miami            8	24	130	0.250	13.5

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

Atlanta currently has 5 win(s) against Miami and 1 loss(es).
Atlanta wins 0 additional game(s) against Miami and loses 7.
Atlanta loses the series 5 games to 8.
Atlanta wins 0 additional game(s) against teams outside the division and loses 93.

Atlanta currently has 1 win(s) against New York and 2 loss(es).
Atlanta wins 10 additional game(s) against New York and loses 0.
Atlanta wins the series 11 games to 2.
Atlanta wins 0 additional game(s) against teams outside the division and loses 93.

Atlanta currently has 2 win(s) against Philadelphia and 1 loss(es).
Atlanta wins 2 additional game(s) against Philadelphia and loses 8.
Atlanta loses the series 4 games to 9.
Atlanta wins 0 additional game(s) against teams outside the division and loses 93.

Atlanta currently has 0 win(s) against Washington and 0 loss(es).
Atlanta wins 6 additional game(s) against Washington and loses 7.
Atlanta loses the series 6 games to 7.
Atlanta wins 0 additional game(s) against teams outside the division and loses 93.

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

Miami currently has 0 win(s) against Philadelphia and 0 loss(es).
Miami wins 13 additional game(s) against Philadelphia and loses 0.
Miami wins the series 13 games to 0.
Miami wins 0 additional game(s) against teams outside the division and loses 88.

Miami currently has 0 win(s) against Washington and 4 loss(es).
Miami wins 6 additional game(s) against Washington and loses 3.
Miami loses the series 6 games to 7.
Miami wins 0 additional game(s) against teams outside the division and loses 88.

New York currently has 0 win(s) against Philadelphia and 0 loss(es).
New York wins 8 additional game(s) against Philadelphia and loses 5.
New York wins the series 8 games to 5.
New York wins 0 additional game(s) against teams outside the division and loses 83.

New York currently has 0 win(s) against Washington and 0 loss(es).
New York wins 6 additional game(s) against Washington and loses 7.
New York loses the series 6 games to 7.
New York wins 0 additional game(s) against teams outside the division and loses 83.

Philadelphia currently has 2 win(s) against Washington and 1 loss(es).
Philadelphia wins 4 additional game(s) against Washington and loses 6.
Philadelphia loses the series 6 games to 7.
Philadelphia wins 0 additional game(s) against teams outside the division and loses 84.

# Washington Nationals' magic number
# Washington's magic number
# Nationals' magic number
# MLB Playoff Race