St. Louis Cardinals First-Place Clinch Scenario

St. Louis's traditional magic number (relative to first-place Chicago) is 51 + 76 - 47 + 1 = 81.
St. Louis's first-place clinch number is 73.
St. Louis must win 73 more games (120 total) to clinch first place.

If St. Louis wins 73 more games, their final win total will be at least 120.
The table below shows the best case scenario for each of the other teams if St. Louis wins 73 of their remaining 74 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 73 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          51	35	76	       9 - 1 = 8	119
Milwaukee        48	38	76	       6 - 1 = 5	119
Cincinnati       45	41	76	       6 - 1 = 5	116
Pittsburgh       38	50	74	       4 - 1 = 3	109

The table above shows that if St. Louis wins 73 more games (120 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 73, consider the following scenario in which St. Louis wins 72 more games (119 total) but does not finish in first place:

Team             W	L	PCT	GB
Milwaukee        120	42	0.741	0.00
St. Louis        119	43	0.735	1.00
Chicago          84	78	0.519	36.00
Cincinnati       76	86	0.469	44.00
Pittsburgh       68	94	0.420	52.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          51	35	76	0.593	0.0
Milwaukee        48	38	76	0.558	3.0
St. Louis        47	41	74	0.534	5.0
Cincinnati       45	41	76	0.523	6.0
Pittsburgh       38	50	74	0.432	14.0

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 2 losses.
  Chicago wins 5 additional games against Cincinnati and loses 2.
  Chicago wins the series 9 games to 4

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 2 wins against Chicago and 3 losses.
  Milwaukee wins 8 additional games against Chicago and loses 0.
  Milwaukee wins the series 10 games to 3

Milwaukee currently has 5 wins against Cincinnati and 2 losses.
  Milwaukee wins 6 additional games against Cincinnati and loses 0.
  Milwaukee wins the series 11 games to 2

Milwaukee currently has 4 wins against Pittsburgh and 3 losses.
  Milwaukee wins 6 additional games against Pittsburgh and loses 0.
  Milwaukee wins the series 10 games to 3

Pittsburgh currently has 2 wins against Chicago and 5 losses.
  Pittsburgh wins 5 additional games against Chicago and loses 1.
  Pittsburgh wins the series 7 games to 6

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

St. Louis currently has 4 wins against Cincinnati and 3 losses.
  St. Louis wins 6 additional games against Cincinnati and loses 0.
  St. Louis wins the series 10 games to 3

St. Louis currently has 3 wins against Milwaukee and 4 losses.
  St. Louis wins 4 additional games against Milwaukee and loses 2.
  St. Louis wins the series 7 games to 6

St. Louis currently has 4 wins against Pittsburgh and 5 losses.
  St. Louis wins 4 additional games against Pittsburgh and loses 0.
  St. Louis wins the series 8 games to 5

Chicago wins 27 games agains teams outside the division and loses 19.
Cincinnati wins 22 games agains teams outside the division and loses 28.
Milwaukee wins 50 games agains teams outside the division and loses 0.
Pittsburgh wins 25 games agains teams outside the division and loses 26.
St. Louis wins 49 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