Chicago Cubs First-Place Clinch Scenario

Chicago's traditional magic number (relative to second-place St. Louis) is 27 + 112 - 30 + 1 = 110.
Chicago's first-place clinch number is 105.
Chicago must win 105 more games (135 total) to clinch first place.

If Chicago wins 105 more games, their final win total will be at least 135.
The table below shows the best case scenario for each of the other teams if Chicago wins 105 of their remaining 112 games and loses the other 7.
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 Chicago' column gives the
minimum number of games that each team will lose to Chicago if Chicago wins 105 more games. Assuming that a team wins all of its remaining games except for
the games it loses to ChicagoCubs, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Chicago	Maximum W
Milwaukee        25	26	111	      10 - 7 = 3	133
St. Louis        27	23	112	      13 - 7 = 6	133
Cincinnati       25	26	111	      13 - 7 = 6	130
Pittsburgh       17	34	111	      10 - 7 = 3	125

The table above shows that if Chicago wins 105 more games (135 total), then they will finish the season in first place in the division.

To see that Chicago's first-place clinch number cannot be less than 105, consider the following scenario in which Chicago wins 104 more games (134 total) but does not finish in first place:

Team             W	L	PCT	GB
Milwaukee        134	28	0.827	0.00
Chicago          134	28	0.827	0.00
St. Louis        90	72	0.556	44.00
Cincinnati       86	76	0.531	48.00
Pittsburgh       70	92	0.432	64.00

Tie breakers
Milwaukee wins the season series with Chicago 9 games to 4.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          30	20	112	0.600	0.0
St. Louis        27	23	112	0.540	3.0
Cincinnati       25	26	111	0.490	5.5
Milwaukee        25	26	111	0.490	5.5
Pittsburgh       17	34	111	0.333	13.5

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


Chicago currently has 0 wins against Cincinnati and 0 losses.
  Chicago wins 13 additional games against Cincinnati and loses 0.
  Chicago wins the series 13 games to 0

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

Chicago currently has 0 wins against St. Louis and 0 losses.
  Chicago wins 13 additional games against St. Louis and loses 0.
  Chicago wins the series 13 games to 0

Cincinnati currently has 4 wins against Pittsburgh and 2 losses.
  Cincinnati wins 7 additional games against Pittsburgh and loses 0.
  Cincinnati wins the series 11 games to 2

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

Milwaukee currently has 3 wins against Cincinnati and 1 losses.
  Milwaukee wins 9 additional games against Cincinnati and loses 0.
  Milwaukee wins the series 12 games to 1

Milwaukee currently has 1 wins against Pittsburgh and 0 losses.
  Milwaukee wins 12 additional games against Pittsburgh and loses 0.
  Milwaukee wins the series 13 games to 0

Milwaukee currently has 1 wins against St. Louis and 2 losses.
  Milwaukee wins 10 additional games against St. Louis and loses 0.
  Milwaukee wins the series 11 games to 2

St. Louis currently has 2 wins against Cincinnati and 2 losses.
  St. Louis wins 5 additional games against Cincinnati and loses 4.
  St. Louis wins the series 7 games to 6

St. Louis currently has 4 wins against Pittsburgh and 2 losses.
  St. Louis wins 6 additional games against Pittsburgh and loses 1.
  St. Louis wins the series 10 games to 3

Chicago wins 66 games agains teams outside the division and loses 0.
Cincinnati wins 50 games agains teams outside the division and loses 23.
Milwaukee wins 70 games agains teams outside the division and loses 0.
Pittsburgh wins 52 games agains teams outside the division and loses 23.
St. Louis wins 52 games agains teams outside the division and loses 21.

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