Cincinnati Reds First-Place Clinch Scenario

Cincinnati's traditional magic number (relative to first-place Chicago) is 16 + 136 - 12 + 1 = 141.
Cincinnati's first-place clinch number is 134.
Cincinnati must win 134 more games (146 total) to clinch first place.

If Cincinnati wins 134 more games, their final win total will be at least 146.
The table below shows the best case scenario for each of the other teams if Cincinnati wins 134 of their remaining 137 games and loses the other 3.
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 134 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
Milwaukee        13	12	137	       9 - 3 = 6	144
Chicago          16	10	136	     13 - 3 = 10	142
Pittsburgh       10	15	137	      10 - 3 = 7	140
St. Louis        10	15	137	     13 - 3 = 10	137

The table above shows that if Cincinnati wins 134 more games (146 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 134, consider the following scenario in which Cincinnati wins 133 more games (145 total) but does not finish in first place:

Team             W	L	PCT	GB
Milwaukee        145	17	0.895	0.00
Cincinnati       145	17	0.895	0.00
Chicago          83	79	0.512	62.00
St. Louis        80	82	0.494	65.00
Pittsburgh       77	85	0.475	68.00

Tie breakers
Milwaukee wins the season series with Cincinnati 7 games to 6.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          16	10	136	0.615	0.0
Milwaukee        13	12	137	0.520	2.5
Cincinnati       12	13	137	0.480	3.5
Pittsburgh       10	15	137	0.400	5.5
St. Louis        10	15	137	0.400	5.5

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 3 wins against Pittsburgh and 0 losses.
  Cincinnati wins 10 additional games against Pittsburgh 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 0 losses.
  Milwaukee wins 13 additional games against Chicago and loses 0.
  Milwaukee wins the series 13 games to 0

Milwaukee currently has 3 wins against Cincinnati and 1 losses.
  Milwaukee wins 4 additional games against Cincinnati and loses 5.
  Milwaukee wins the series 7 games to 6

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 13 additional games against St. Louis and loses 0.
  Milwaukee wins the series 13 games to 0

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 1 wins against Pittsburgh and 2 losses.
  St. Louis wins 10 additional games against Pittsburgh and loses 0.
  St. Louis wins the series 11 games to 2

Chicago wins 67 games agains teams outside the division and loses 17.
Cincinnati wins 92 games agains teams outside the division and loses 0.
Milwaukee wins 89 games agains teams outside the division and loses 0.
Pittsburgh wins 54 games agains teams outside the division and loses 37.
St. Louis wins 47 games agains teams outside the division and loses 41.

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