St. Louis Cardinals First-Place Clinch Scenario

St. Louis's traditional magic number (relative to first-place Chicago) is 13 + 140 - 9 + 1 = 145.
St. Louis's first-place clinch number is 137.
St. Louis must win 137 more games (146 total) to clinch first place.

If St. Louis wins 137 more games, their final win total will be at least 146.
The table below shows the best case scenario for each of the other teams if St. Louis wins 137 of their remaining 142 games and loses the other 5.
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 137 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
Chicago          13	9	140	      13 - 5 = 8	145
Milwaukee        11	9	142	      13 - 5 = 8	145
Cincinnati       10	10	142	      13 - 5 = 8	144
Pittsburgh       8	13	141	      10 - 5 = 5	144

The table above shows that if St. Louis wins 137 more games (146 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 137, consider the following scenario in which St. Louis wins 136 more games (145 total) but does not finish in first place:

Team             W	L	PCT	GB
Chicago          146	16	0.901	0.00
St. Louis        145	17	0.895	1.00
Cincinnati       72	90	0.444	74.00
Pittsburgh       70	92	0.432	76.00
Milwaukee        58	104	0.358	88.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          13	9	140	0.591	0.0
Milwaukee        11	9	142	0.550	1.0
Cincinnati       10	10	142	0.500	2.0
St. Louis        9	11	142	0.450	3.0
Pittsburgh       8	13	141	0.381	4.5

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 0 wins against Milwaukee and 0 losses.
  Chicago wins 13 additional games against Milwaukee and loses 0.
  Chicago wins the series 13 games to 0

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

Cincinnati currently has 1 wins against Milwaukee and 3 losses.
  Cincinnati wins 9 additional games against Milwaukee and loses 0.
  Cincinnati wins the series 10 games to 3

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

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

St. Louis currently has 0 wins against Chicago and 0 losses.
  St. Louis wins 7 additional games against Chicago and loses 6.
  St. Louis wins the series 7 games to 6

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

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

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

Chicago wins 88 games agains teams outside the division and loses 0.
Cincinnati wins 43 games agains teams outside the division and loses 54.
Milwaukee wins 35 games agains teams outside the division and loses 59.
Pittsburgh wins 61 games agains teams outside the division and loses 34.
St. Louis wins 93 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