Washington Nationals First-Place Clinch Scenario

Washington's traditional magic number (relative to first-place New York) is 18 + 137 - 11 + 1 = 145.
Washington's first-place clinch number is 135.
Washington must win 135 more games (146 total) to clinch first place.

If Washington wins 135 more games, their final win total will be at least 146.
The table below shows the best case scenario for each of the other teams if Washington wins 135 of their remaining 138 games and loses the other 3.
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 135 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
New York         18	7	137	     13 - 3 = 10	145
Philadelphia     13	12	137	      10 - 3 = 7	143
Miami            11	13	138	      10 - 3 = 7	142
Atlanta          10	14	138	     13 - 3 = 10	138

The table above shows that if Washington wins 135 more games (146 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 135, consider the following scenario in which Washington wins 134 more games (145 total) but does not finish in first place:

Team             W	L	PCT	GB
New York         146	16	0.901	0.00
Washington       145	17	0.895	1.00
Philadelphia     99	63	0.611	47.00
Atlanta          76	86	0.469	70.00
Miami            74	88	0.457	72.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
New York         18	7	137	0.720	0.0
Philadelphia     13	12	137	0.520	5.0
Miami            11	13	138	0.458	6.5
Washington       11	13	138	0.458	6.5
Atlanta          10	14	138	0.417	7.5

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


Miami currently has 1 wins against Atlanta and 1 losses.
  Miami wins 6 additional games against Atlanta and loses 5.
  Miami wins the series 7 games to 6

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

New York currently has 4 wins against Miami and 2 losses.
  New York wins 7 additional games against Miami and loses 0.
  New York wins the series 11 games to 2

New York currently has 3 wins against Philadelphia and 0 losses.
  New York wins 10 additional games against Philadelphia and loses 0.
  New York wins the series 13 games to 0

Philadelphia currently has 1 wins against Atlanta and 2 losses.
  Philadelphia wins 8 additional games against Atlanta and loses 2.
  Philadelphia wins the series 9 games to 4

Philadelphia currently has 2 wins against Miami and 1 losses.
  Philadelphia wins 5 additional games against Miami and loses 5.
  Philadelphia wins the series 7 games to 6

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

Washington currently has 1 wins against Miami and 2 losses.
  Washington wins 10 additional games against Miami and loses 0.
  Washington wins the series 11 games to 2

Washington currently has 0 wins against New York and 0 losses.
  Washington wins 9 additional games against New York and loses 4.
  Washington wins the series 9 games to 4

Washington currently has 1 wins against Philadelphia and 2 losses.
  Washington wins 10 additional games against Philadelphia and loses 0.
  Washington wins the series 11 games to 2

Atlanta wins 59 games agains teams outside the division and loses 32.
Miami wins 52 games agains teams outside the division and loses 48.
New York wins 94 games agains teams outside the division and loses 0.
Philadelphia wins 73 games agains teams outside the division and loses 24.
Washington wins 92 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