Atlanta Braves First-Place Clinch Scenario

Atlanta's traditional magic number (relative to first-place New York) is 18 + 137 - 10 + 1 = 146.
Atlanta's first-place clinch number is 135.
Atlanta must win 135 more games (145 total) to clinch first place.

If Atlanta wins 135 more games, their final win total will be at least 145.
The table below shows the best case scenario for each of the other teams if Atlanta 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 Atlanta' column gives the
minimum number of games that each team will lose to Atlanta if Atlanta wins 135 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
New York         18	7	137	     13 - 3 = 10	145 *See tie-breaking notes below.
Philadelphia     13	12	137	      10 - 3 = 7	143
Miami            11	13	138	      11 - 3 = 8	141
Washington       11	13	138	     13 - 3 = 10	139

Tie-breakers:
Atlanta has won 0 game(s) against New York and lost 0.
There are 13 games left in the series.
In the scenario above, Atlanta wins 0 + 10 = 10 games against New York and loses 0 + 3 = 3.

The table above shows that if Atlanta wins 135 more games (145 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 135, consider the following scenario in which Atlanta wins 134 more games (144 total) but does not finish in first place:

Team             W	L	PCT	GB
New York         145	17	0.895	0.00
Atlanta          144	18	0.889	1.00
Philadelphia     62	100	0.383	83.00
Miami            62	100	0.383	83.00
Washington       39	123	0.241	106.00

Tie breakers
Philadelphia wins the season series with Miami 7 games to 6.

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:


Atlanta currently has 1 wins against Miami and 1 losses.
  Atlanta wins 11 additional games against Miami and loses 0.
  Atlanta wins the series 12 games to 1

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

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

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

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

New York currently has 0 wins against Washington and 0 losses.
  New York wins 12 additional games against Washington and loses 1.
  New York wins the series 12 games to 1

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 1 wins against Philadelphia and 2 losses.
  Washington wins 6 additional games against Philadelphia and loses 4.
  Washington wins the series 7 games to 6

Atlanta wins 91 games agains teams outside the division and loses 0.
Miami wins 41 games agains teams outside the division and loses 59.
New York wins 94 games agains teams outside the division and loses 0.
Philadelphia wins 40 games agains teams outside the division and loses 57.
Washington wins 16 games agains teams outside the division and loses 76.

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