Cincinnati Reds First-Place Clinch Scenario

Cincinnati's traditional magic number (relative to first-place Chicago) is 25 + 125 - 20 + 1 = 131.
Cincinnati's first-place clinch number is 123.
Cincinnati must win 123 more games (143 total) to clinch first place.

If Cincinnati wins 123 more games, their final win total will be at least 143.
The table below shows the best case scenario for each of the other teams if Cincinnati wins 123 of their remaining 125 games and loses the other 2.
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 123 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
Chicago          25	12	125	      10 - 2 = 8	142
Pittsburgh       20	17	125	       7 - 2 = 5	140
St. Louis        21	15	126	     13 - 2 = 11	136
Milwaukee        19	16	127	     13 - 2 = 11	135

The table above shows that if Cincinnati wins 123 more games (143 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 123, consider the following scenario in which Cincinnati wins 122 more games (142 total) but does not finish in first place:

Team             W	L	PCT	GB
Chicago          143	19	0.883	0.00
Cincinnati       142	20	0.877	1.00
Milwaukee        60	102	0.370	83.00
Pittsburgh       47	115	0.290	96.00
St. Louis        35	127	0.216	108.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          25	12	125	0.676	0.0
St. Louis        21	15	126	0.583	3.5
Milwaukee        19	16	127	0.543	5.0
Cincinnati       20	17	125	0.541	5.0
Pittsburgh       20	17	125	0.541	5.0

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


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

Chicago currently has 1 wins against Pittsburgh and 2 losses.
  Chicago wins 10 additional games against Pittsburgh and loses 0.
  Chicago wins the series 11 games to 2

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

Cincinnati currently has 0 wins against Chicago and 3 losses.
  Cincinnati wins 7 additional games against Chicago and loses 3.
  Cincinnati wins the series 7 games to 6

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 1 wins against Pittsburgh and 5 losses.
  Cincinnati wins 7 additional games against Pittsburgh and loses 0.
  Cincinnati wins the series 8 games to 5

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

Milwaukee currently has 1 wins against St. Louis and 1 losses.
  Milwaukee wins 11 additional games against St. Louis and loses 0.
  Milwaukee wins the series 12 games to 1

Pittsburgh currently has 0 wins against St. Louis and 4 losses.
  Pittsburgh wins 9 additional games against St. Louis and loses 0.
  Pittsburgh wins the series 9 games to 4

Chicago wins 79 games agains teams outside the division and loses 0.
Cincinnati wins 82 games agains teams outside the division and loses 0.
Milwaukee wins 20 games agains teams outside the division and loses 60.
Pittsburgh wins 18 games agains teams outside the division and loses 71.
St. Louis wins 14 games agains teams outside the division and loses 66.

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