St. Louis Cardinals First-Place Clinch Scenario

St. Louis's traditional magic number (relative to first-place Chicago) is 1 + 161 - 0 + 1 = 163.
St. Louis's first-place clinch number is 155.
St. Louis must win 155 more games (155 total) to clinch first place.

If St. Louis wins 155 more games, their final win total will be at least 155.
The table below shows the best case scenario for each of the other teams if St. Louis wins 155 of their remaining 161 games and loses the other 6.
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 155 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          1	0	161	      13 - 6 = 7	155 *See tie-breaking notes below.
Pittsburgh       1	0	161	      13 - 6 = 7	155 *See tie-breaking notes below.
Cincinnati       0	1	161	      13 - 6 = 7	154
Milwaukee        0	1	161	      13 - 6 = 7	154

Tie-breakers:
St. Louis has won 0 game(s) against Chicago and lost 0.
There are 13 games left in the series.
In the scenario above, St. Louis wins 0 + 7 = 7 games against Chicago and loses 0 + 6 = 6.
St. Louis has won 0 game(s) against Pittsburgh and lost 0.
There are 13 games left in the series.
In the scenario above, St. Louis wins 0 + 7 = 7 games against Pittsburgh and loses 0 + 6 = 6.

The table above shows that if St. Louis wins 155 more games (155 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 155, consider the following scenario in which St. Louis wins 154 more games (154 total) but does not finish in first place:

Team             W	L	PCT	GB
Milwaukee        155	7	0.957	0.00
St. Louis        154	8	0.951	0.00
Chicago          87	75	0.537	67.00
Cincinnati       67	95	0.414	87.00
Pittsburgh       53	109	0.327	101.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          1	0	161	1.000	0.0
Pittsburgh       1	0	161	1.000	0.0
Cincinnati       0	1	161	0.000	1.0
Milwaukee        0	1	161	0.000	1.0
St. Louis        0	1	161	0.000	1.0

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

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

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

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

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

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

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 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 73 games agains teams outside the division and loses 37.
Cincinnati wins 55 games agains teams outside the division and loses 55.
Milwaukee wins 110 games agains teams outside the division and loses 0.
Pittsburgh wins 39 games agains teams outside the division and loses 71.
St. Louis wins 109 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