St. Louis Cardinals First-Place Clinch Scenario

St. Louis's traditional magic number (relative to first-place Chicago) is 30 + 112 - 27 + 1 = 116.
St. Louis's first-place clinch number is 107.
St. Louis must win 107 more games (134 total) to clinch first place.

If St. Louis wins 107 more games, their final win total will be at least 134.
The table below shows the best case scenario for each of the other teams if St. Louis wins 107 of their remaining 112 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 107 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          30	20	112	      13 - 5 = 8	134 *See tie-breaking notes below.
Cincinnati       25	26	111	       9 - 5 = 4	132
Milwaukee        25	26	111	      10 - 5 = 5	131
Pittsburgh       17	34	111	       7 - 5 = 2	126

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 + 8 = 8 games against Chicago and loses 0 + 5 = 5.

The table above shows that if St. Louis wins 107 more games (134 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 107, consider the following scenario in which St. Louis wins 106 more games (133 total) but does not finish in first place:

Team             W	L	PCT	GB
Cincinnati       133	29	0.821	0.00
St. Louis        133	29	0.821	0.00
Chicago          86	76	0.531	47.00
Milwaukee        71	91	0.438	62.00
Pittsburgh       71	91	0.438	62.00

Tie breakers
Cincinnati wins the season series with St. Louis 8 games to 5.

Milwaukee wins the season series with Pittsburgh 13 games to 0.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          30	20	112	0.600	0.0
St. Louis        27	23	112	0.540	3.0
Cincinnati       25	26	111	0.490	5.5
Milwaukee        25	26	111	0.490	5.5
Pittsburgh       17	34	111	0.333	13.5

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


Chicago currently has 2 wins against Milwaukee and 1 losses.
  Chicago wins 9 additional games against Milwaukee and loses 1.
  Chicago wins the series 11 games to 2

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

Cincinnati currently has 0 wins against Chicago and 0 losses.
  Cincinnati wins 13 additional games against Chicago and loses 0.
  Cincinnati 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 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

Cincinnati currently has 2 wins against St. Louis and 2 losses.
  Cincinnati wins 6 additional games against St. Louis and loses 3.
  Cincinnati wins the series 8 games to 5

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

St. Louis currently has 4 wins against Pittsburgh and 2 losses.
  St. Louis wins 7 additional games against Pittsburgh and loses 0.
  St. Louis wins the series 11 games to 2

Chicago wins 42 games agains teams outside the division and loses 24.
Cincinnati wins 73 games agains teams outside the division and loses 0.
Milwaukee wins 33 games agains teams outside the division and loses 37.
Pittsburgh wins 49 games agains teams outside the division and loses 26.
St. Louis wins 73 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