St. Louis Cardinals First-Place Clinch Scenario

St. Louis's traditional magic number (relative to first-place Milwaukee) is 34 + 107 - 30 + 1 = 112.
St. Louis's first-place clinch number is 105.
St. Louis must win 105 more games (135 total) to clinch first place.

If St. Louis 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 St. Louis wins 105 of their remaining 106 games and loses the other 1.
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 St. Louis' column gives the
minimum number of games that each team will lose to St. Louis if St. Louis wins 105 more games. Assuming that a team wins all of its remaining games except for
the games it loses to StLouis, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to St. Louis	Maximum W
Milwaukee        34	21	107	       8 - 1 = 7	134
Pittsburgh       31	28	103	       6 - 1 = 5	129
Chicago          32	27	103	     11 - 1 = 10	125
Cincinnati       29	28	105	     11 - 1 = 10	124

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

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

Team             W	L	PCT	GB
Milwaukee        135	27	0.833	0.00
St. Louis        134	28	0.827	1.00
Chicago          104	58	0.642	31.00
Pittsburgh       96	66	0.593	39.00
Cincinnati       60	102	0.370	75.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Milwaukee        34	21	107	0.618	0.0
Chicago          32	27	103	0.542	4.0
St. Louis        30	26	106	0.536	4.5
Pittsburgh       31	28	103	0.525	5.0
Cincinnati       29	28	105	0.509	6.0

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


Chicago currently has 4 wins against Cincinnati and 0 losses.
  Chicago wins 9 additional games against Cincinnati and loses 0.
  Chicago wins the series 13 games to 0

Chicago currently has 3 wins against Pittsburgh and 4 losses.
  Chicago wins 6 additional games against Pittsburgh and loses 0.
  Chicago wins the series 9 games to 4

Milwaukee currently has 3 wins against Chicago and 0 losses.
  Milwaukee wins 10 additional games against Chicago and loses 0.
  Milwaukee wins the series 13 games to 0

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

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

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

St. Louis currently has 1 wins against Chicago and 1 losses.
  St. Louis wins 11 additional games against Chicago and loses 0.
  St. Louis wins the series 12 games to 1

St. Louis currently has 1 wins against Cincinnati and 1 losses.
  St. Louis wins 11 additional games against Cincinnati and loses 0.
  St. Louis wins the series 12 games to 1

St. Louis currently has 1 wins against Milwaukee and 4 losses.
  St. Louis wins 6 additional games against Milwaukee and loses 2.
  St. Louis wins the series 7 games to 6

St. Louis currently has 5 wins against Pittsburgh and 2 losses.
  St. Louis wins 6 additional games against Pittsburgh and loses 0.
  St. Louis wins the series 11 games to 2

Chicago wins 57 games agains teams outside the division and loses 10.
Cincinnati wins 31 games agains teams outside the division and loses 34.
Milwaukee wins 66 games agains teams outside the division and loses 0.
Pittsburgh wins 58 games agains teams outside the division and loses 16.
St. Louis wins 70 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.
# St. Louis Cardinals' magic number
# St. Louis's magic number
# Cardinals' magic number
# MLB Playoff Race