Washington Nationals First-Place Clinch Scenario

Washington's traditional magic number (relative to first-place Philadelphia) is 21 + 130 - 15 + 1 = 137.
Washington's first-place clinch number is 129.
Washington must win 129 more games (144 total) to clinch first place.

If Washington wins 129 more games, their final win total will be at least 144.
The table below shows the best case scenario for each of the other teams if Washington wins 129 of their remaining 132 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 129 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
Philadelphia     21	11	130	      10 - 3 = 7	144 *See tie-breaking notes below.
Atlanta          20	9	133	     13 - 3 = 10	143
New York         15	15	132	     13 - 3 = 10	137
Miami            8	24	130	       9 - 3 = 6	132

Tie-breakers:
Washington has won 1 game(s) against Philadelphia and lost 2.
There are 10 games left in the series.
In the scenario above, Washington wins 1 + 7 = 8 games against Philadelphia and loses 2 + 3 = 5.

The table above shows that if Washington wins 129 more games (144 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 129, consider the following scenario in which Washington wins 128 more games (143 total) but does not finish in first place:

Team             W	L	PCT	GB
Atlanta          144	18	0.889	0.00
Washington       143	19	0.883	1.00
New York         82	80	0.506	62.00
Philadelphia     81	81	0.500	63.00
Miami            37	125	0.228	107.00

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 in the division play out in the scenario:


Atlanta currently has 5 wins against Miami and 1 losses.
  Atlanta wins 7 additional games against Miami and loses 0.
  Atlanta wins the series 12 games to 1

Atlanta currently has 1 wins against New York and 2 losses.
  Atlanta wins 10 additional games against New York and loses 0.
  Atlanta wins the series 11 games to 2

Atlanta currently has 2 wins against Philadelphia and 1 losses.
  Atlanta wins 10 additional games against Philadelphia and loses 0.
  Atlanta wins the series 12 games to 1

Miami currently has 0 wins against New York and 0 losses.
  Miami wins 7 additional games against New York and loses 6.
  Miami wins the series 7 games to 6

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 10 additional games against New York and loses 3.
  Philadelphia wins the series 10 games to 3

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

Washington currently has 4 wins against Miami and 0 losses.
  Washington wins 9 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 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 93 games agains teams outside the division and loses 0.
Miami wins 22 games agains teams outside the division and loses 66.
New York wins 58 games agains teams outside the division and loses 25.
Philadelphia wins 37 games agains teams outside the division and loses 47.
Washington wins 87 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