Washington Nationals First-Place Clinch Scenario

Washington's traditional magic number (relative to first-place Atlanta) is 1 + 161 - 0 + 1 = 163.
Washington's first-place clinch number is 156.
Washington must win 156 more games (156 total) to clinch first place.

If Washington wins 156 more games, their final win total will be at least 156.
The table below shows the best case scenario for each of the other teams if Washington wins 156 of their remaining 161 games and loses the other 5.
For each team, the table shows the current record (number of wins (W) and losses (L)) and the number of games that team has
left to play (GL) in the regular season. Taking the schedule of games left to play into account, the 'Losses to Washington' column gives the
minimum number of games that each team will lose to Washington if Washington wins 156 more games. Assuming that a team wins all of its remaining games except for
the games it loses to Washington, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Washington	Maximum W
Atlanta          1	0	161	      12 - 5 = 7	155
New York         1	0	161	      13 - 5 = 8	154
Miami            0	1	161	      13 - 5 = 8	153
Philadelphia     0	1	161	      13 - 5 = 8	153

The table above shows that if Washington wins 156 more games (156 total), then they will finish the season in first place in the division.

To see that Washington's first-place clinch number cannot be less than 156, consider the following scenario in which Washington wins 155 more games (155 total) but does not finish in first place:

Team             W	L	PCT	GB
Atlanta          156	6	0.963	0.00
Washington       155	7	0.957	0.00
Philadelphia     135	27	0.833	20.00
New York         111	51	0.685	44.00
Miami            109	53	0.673	46.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Atlanta          1	0	161	1.000	0.0
New York         1	0	161	1.000	0.0
Miami            0	1	161	0.000	1.0
Philadelphia     0	1	161	0.000	1.0
Washington       0	1	161	0.000	1.0

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


Atlanta currently has 0 wins against Miami and 0 losses.
  Atlanta wins 13 additional games against Miami and loses 0.
  Atlanta wins the series 13 games to 0

Atlanta currently has 0 wins against New York and 0 losses.
  Atlanta wins 13 additional games against New York and loses 0.
  Atlanta wins the series 13 games to 0

Atlanta currently has 0 wins against Philadelphia and 0 losses.
  Atlanta wins 13 additional games against Philadelphia and loses 0.
  Atlanta wins the series 13 games to 0

Atlanta currently has 1 wins against Washington and 0 losses.
  Atlanta wins 6 additional games against Washington and loses 6.
  Atlanta wins the series 7 games to 6

New York currently has 1 wins against Miami and 0 losses.
  New York wins 7 additional games against Miami and loses 5.
  New York wins the series 8 games to 5

Philadelphia currently has 0 wins against Miami and 0 losses.
  Philadelphia wins 13 additional games against Miami and loses 0.
  Philadelphia wins the series 13 games to 0

Philadelphia currently has 0 wins against New York and 0 losses.
  Philadelphia wins 13 additional games against New York and loses 0.
  Philadelphia wins the series 13 games to 0

Washington currently has 0 wins against Miami and 0 losses.
  Washington wins 13 additional games against Miami and loses 0.
  Washington wins the series 13 games to 0

Washington currently has 0 wins against New York and 0 losses.
  Washington wins 13 additional games against New York and loses 0.
  Washington wins the series 13 games to 0

Washington currently has 0 wins against Philadelphia and 0 losses.
  Washington wins 13 additional games against Philadelphia and loses 0.
  Washington wins the series 13 games to 0

Atlanta wins 110 games agains teams outside the division and loses 0.
Miami wins 104 games agains teams outside the division and loses 6.
New York wins 103 games agains teams outside the division and loses 7.
Philadelphia wins 109 games agains teams outside the division and loses 0.
Washington wins 110 games agains teams outside the division and loses 0.

Combining the current standings with the wins and losses from the scenario results in the final standings listed above.
# Washington Nationals' magic number
# Washington's magic number
# Nationals' magic number
# MLB Playoff Race