St. Louis Cardinals First-Place Clinch Scenario

St. Louis's traditional magic number (relative to first-place Chicago) is 19 + 131 - 14 + 1 = 137.
St. Louis's first-place clinch number is 129.
St. Louis must win 129 more games (143 total) to clinch first place.

If St. Louis wins 129 more games, their final win total will be at least 143.
The table below shows the best case scenario for each of the other teams if St. Louis wins 129 of their remaining 131 games and loses the other 2.
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 129 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        19	11	132	      10 - 2 = 8	143 *See tie-breaking notes below.
Chicago          19	12	131	     13 - 2 = 11	139
Cincinnati       16	15	131	     13 - 2 = 11	136
Pittsburgh       14	18	130	     13 - 2 = 11	133

Tie-breakers:
St. Louis has won 0 game(s) against Milwaukee and lost 3.
There are 10 games left in the series.
In the scenario above, St. Louis wins 0 + 8 = 8 games against Milwaukee and loses 3 + 2 = 5.

The table above shows that if St. Louis wins 129 more games (143 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 129, consider the following scenario in which St. Louis wins 128 more games (142 total) but does not finish in first place:

Team             W	L	PCT	GB
Milwaukee        143	19	0.883	0.00
St. Louis        142	20	0.877	1.00
Pittsburgh       86	76	0.531	57.00
Cincinnati       86	76	0.531	57.00
Chicago          84	78	0.519	59.00

Tie breakers
Pittsburgh wins the season series with Cincinnati 11 games to 2.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Milwaukee        19	11	132	0.633	0.0
Chicago          19	12	131	0.613	0.5
Cincinnati       16	15	131	0.516	3.5
St. Louis        14	17	131	0.452	5.5
Pittsburgh       14	18	130	0.438	6.0

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


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

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

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

Milwaukee currently has 2 wins against Pittsburgh and 2 losses.
  Milwaukee wins 9 additional games against Pittsburgh and loses 0.
  Milwaukee wins the series 11 games to 2

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

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

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

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 3 losses.
  St. Louis wins 7 additional games against Milwaukee and loses 3.
  St. Louis wins the series 7 games to 6

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

Chicago wins 61 games agains teams outside the division and loses 18.
Cincinnati wins 59 games agains teams outside the division and loses 23.
Milwaukee wins 89 games agains teams outside the division and loses 1.
Pittsburgh wins 48 games agains teams outside the division and loses 34.
St. Louis wins 82 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