Cincinnati Reds First-Place Clinch Scenario

Cincinnati's traditional magic number (relative to first-place Chicago) is 1 + 161 - 0 + 1 = 163.
Cincinnati's first-place clinch number is 156.
Cincinnati must win 156 more games (156 total) to clinch first place.

If Cincinnati wins 156 more games, their final win total will be at least 156.
The table below shows the best case scenario for each of the other teams if Cincinnati wins 156 of their remaining 161 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 Cincinnati' column gives the
minimum number of games that each team will lose to Cincinnati if Cincinnati wins 156 more games. Assuming that a team wins all of its remaining games except for
the games it loses to Cincinnati, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Cincinnati	Maximum W
Pittsburgh       1	0	161	      12 - 5 = 7	155
Chicago          1	0	161	      13 - 5 = 8	154
Milwaukee        0	1	161	      13 - 5 = 8	153
St. Louis        0	1	161	      13 - 5 = 8	153

The table above shows that if Cincinnati wins 156 more games (156 total), then they will finish the season in first place in the division.

To see that Cincinnati's first-place clinch number cannot be less than 156, consider the following scenario in which Cincinnati wins 155 more games (155 total) but does not finish in first place:

Team             W	L	PCT	GB
Pittsburgh       156	6	0.963	0.00
Cincinnati       155	7	0.957	0.00
St. Louis        84	78	0.519	71.00
Chicago          83	79	0.512	72.00
Milwaukee        43	119	0.265	112.00

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:


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

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

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

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 1 wins against Cincinnati and 0 losses.
  Pittsburgh wins 6 additional games against Cincinnati and loses 6.
  Pittsburgh wins the series 7 games to 6

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

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

Chicago wins 82 games agains teams outside the division and loses 28.
Cincinnati wins 110 games agains teams outside the division and loses 0.
Milwaukee wins 31 games agains teams outside the division and loses 79.
Pittsburgh wins 110 games agains teams outside the division and loses 0.
St. Louis wins 58 games agains teams outside the division and loses 51.

Combining the current standings with the wins and losses from the scenario results in the final standings listed above.
# Cincinnati Reds' magic number
# Cincinnati's magic number
# Reds' magic number
# MLB Playoff Race