Cincinnati Reds First-Place Clinch Scenario

Cincinnati's traditional magic number (relative to first-place Chicago) is 30 + 112 - 25 + 1 = 118.
Cincinnati's first-place clinch number is 108.
Cincinnati must win 108 more games (133 total) to clinch first place.

If Cincinnati wins 108 more games, their final win total will be at least 133.
The table below shows the best case scenario for each of the other teams if Cincinnati wins 108 of their remaining 111 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 108 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
St. Louis        27	23	112	       9 - 3 = 6	133 *See tie-breaking notes below.
Chicago          30	20	112	     13 - 3 = 10	132
Milwaukee        25	26	111	       9 - 3 = 6	130
Pittsburgh       17	34	111	       7 - 3 = 4	124

Tie-breakers:
Cincinnati has won 2 game(s) against St. Louis and lost 2.
There are 9 games left in the series.
In the scenario above, Cincinnati wins 2 + 6 = 8 games against St. Louis and loses 2 + 3 = 5.

The table above shows that if Cincinnati wins 108 more games (133 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 108, consider the following scenario in which Cincinnati wins 107 more games (132 total) but does not finish in first place:

Team             W	L	PCT	GB
Chicago          133	29	0.821	0.00
Cincinnati       132	30	0.815	1.00
Milwaukee        79	83	0.488	54.00
St. Louis        53	109	0.327	80.00
Pittsburgh       47	115	0.290	86.00

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 10 additional games against Milwaukee and loses 0.
  Chicago wins the series 12 games to 1

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

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 0 losses.
  Cincinnati wins 9 additional games against Chicago and loses 4.
  Cincinnati wins the series 9 games to 4

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 9 additional games against St. Louis and loses 0.
  Cincinnati wins the series 11 games to 2

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

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

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 66 games agains teams outside the division and loses 0.
Cincinnati wins 73 games agains teams outside the division and loses 0.
Milwaukee wins 32 games agains teams outside the division and loses 38.
Pittsburgh wins 30 games agains teams outside the division and loses 45.
St. Louis wins 19 games agains teams outside the division and loses 54.

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