Chicago Cubs First-Place Clinch Scenario

Chicago's traditional magic number (relative to second-place St. Louis) is 28 + 111 - 31 + 1 = 109.
Chicago's first-place clinch number is 104.
Chicago must win 104 more games (135 total) to clinch first place.

If Chicago wins 104 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 104 of their remaining 111 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 104 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
St. Louis        28	23	111	      13 - 7 = 6	133
Milwaukee        25	27	110	      10 - 7 = 3	132
Cincinnati       25	27	110	      12 - 7 = 5	130
Pittsburgh       18	34	110	      10 - 7 = 3	125

The table above shows that if Chicago wins 104 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 104, consider the following scenario in which Chicago wins 103 more games (134 total) but does not finish in first place:

Team             W	L	PCT	GB
St. Louis        134	28	0.827	0.00
Chicago          134	28	0.827	0.00
Milwaukee        87	75	0.537	47.00
Cincinnati       52	110	0.321	82.00
Pittsburgh       43	119	0.265	91.00

Tie breakers
St. Louis wins the season series with Chicago 8 games to 5.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          31	20	111	0.608	0.0
St. Louis        28	23	111	0.549	3.0
Cincinnati       25	27	110	0.481	6.5
Milwaukee        25	27	110	0.481	6.5
Pittsburgh       18	34	110	0.346	13.5

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


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

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

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

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 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 1 losses.
  Milwaukee wins 7 additional games against Pittsburgh and loses 4.
  Milwaukee wins the series 8 games to 5

St. Louis currently has 0 wins against Chicago and 0 losses.
  St. Louis wins 8 additional games against Chicago and loses 5.
  St. Louis wins the series 8 games to 5

St. Louis currently has 2 wins against Cincinnati and 2 losses.
  St. Louis wins 9 additional games against Cincinnati and loses 0.
  St. Louis wins the series 11 games to 2

St. Louis currently has 2 wins against Milwaukee and 1 losses.
  St. Louis wins 10 additional games against Milwaukee and loses 0.
  St. Louis wins the series 12 games to 1

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

Chicago wins 66 games agains teams outside the division and loses 0.
Cincinnati wins 20 games agains teams outside the division and loses 53.
Milwaukee wins 46 games agains teams outside the division and loses 24.
Pittsburgh wins 21 games agains teams outside the division and loses 54.
St. Louis wins 72 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.
# Chicago Cubs' magic number
# Chicago's magic number
# Cubs' magic number
# MLB Playoff Race