Atlanta Braves First-Place Clinch Scenario

Atlanta's traditional magic number (relative to second-place Philadelphia) is 16 + 136 - 17 + 1 = 136.
Atlanta's first-place clinch number is 133.
Atlanta must win 133 more games (150 total) to clinch first place.

If Atlanta wins 133 more games, their final win total will be at least 150.
The table below shows the best case scenario for each of the other teams if Atlanta wins 133 of their remaining 139 games and loses the other 6.
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 Atlanta' column gives the
minimum number of games that each team will lose to Atlanta if Atlanta wins 133 more games. Assuming that a team wins all of its remaining games except for
the games it loses to Atlanta, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Atlanta	Maximum W
Philadelphia     16	10	136	      10 - 6 = 4	148
New York         13	11	138	      10 - 6 = 4	147
Miami            6	20	136	       7 - 6 = 1	141
Washington       10	14	138	      13 - 6 = 7	141

The table above shows that if Atlanta wins 133 more games (150 total), then they will finish the season in first place in the division.

To see that Atlanta's first-place clinch number cannot be less than 133, consider the following scenario in which Atlanta wins 132 more games (149 total) but does not finish in first place:

Team             W	L	PCT	GB
Philadelphia     149	13	0.920	0.00
Atlanta          149	13	0.920	0.00
New York         57	105	0.352	92.00
Washington       55	107	0.340	94.00
Miami            54	108	0.333	95.00

Tie breakers
Philadelphia wins the season series with Atlanta 8 games to 5.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Atlanta          17	6	139	0.739	0.0
Philadelphia     16	10	136	0.615	2.5
New York         13	11	138	0.542	4.5
Washington       10	14	138	0.417	7.5
Miami            6	20	136	0.231	12.5

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

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

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

Philadelphia currently has 1 wins against Atlanta and 2 losses.
  Philadelphia wins 7 additional games against Atlanta and loses 3.
  Philadelphia 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

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

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

Atlanta wins 99 games agains teams outside the division and loses 0.
Miami wins 35 games agains teams outside the division and loses 55.
New York wins 31 games agains teams outside the division and loses 58.
Philadelphia wins 90 games agains teams outside the division and loses 0.
Washington wins 32 games agains teams outside the division and loses 57.

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