Cincinnati Reds First-Place Clinch Scenario

Cincinnati's traditional magic number (relative to first-place Chicago) is 19 + 131 - 16 + 1 = 135.
Cincinnati's first-place clinch number is 128.
Cincinnati must win 128 more games (144 total) to clinch first place.

If Cincinnati wins 128 more games, their final win total will be at least 144.
The table below shows the best case scenario for each of the other teams if Cincinnati wins 128 of their remaining 131 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 128 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        19	11	132	      10 - 3 = 7	144 *See tie-breaking notes below.
Chicago          19	12	131	     13 - 3 = 10	140
St. Louis        14	17	131	     13 - 3 = 10	135
Pittsburgh       14	18	130	     13 - 3 = 10	134

Tie-breakers:
Cincinnati has won 1 game(s) against Milwaukee and lost 2.
There are 10 games left in the series.
In the scenario above, Cincinnati wins 1 + 7 = 8 games against Milwaukee and loses 2 + 3 = 5.

The table above shows that if Cincinnati wins 128 more games (144 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 128, consider the following scenario in which Cincinnati wins 127 more games (143 total) but does not finish in first place:

Team             W	L	PCT	GB
Milwaukee        144	18	0.889	0.00
Cincinnati       143	19	0.883	1.00
St. Louis        87	75	0.537	57.00
Pittsburgh       66	96	0.407	78.00
Chicago          65	97	0.401	79.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Milwaukee        19	11	132	0.633	0.0
Chicago          19	12	131	0.613	0.5
Cincinnati       16	15	131	0.516	3.5
St. Louis        14	17	131	0.452	5.5
Pittsburgh       14	18	130	0.438	6.0

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 1 wins against Milwaukee and 2 losses.
  Cincinnati wins 6 additional games against Milwaukee and loses 4.
  Cincinnati wins the series 7 games to 6

Cincinnati currently has 0 wins against Pittsburgh and 0 losses.
  Cincinnati wins 13 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 2 wins against Pittsburgh and 2 losses.
  Milwaukee wins 8 additional games against Pittsburgh and loses 1.
  Milwaukee wins the series 10 games to 3

Milwaukee currently has 3 wins against St. Louis and 0 losses.
  Milwaukee wins 10 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 0 wins against Pittsburgh and 0 losses.
  St. Louis wins 8 additional games against Pittsburgh and loses 5.
  St. Louis wins the series 8 games to 5

Chicago wins 46 games agains teams outside the division and loses 33.
Cincinnati wins 82 games agains teams outside the division and loses 0.
Milwaukee wins 90 games agains teams outside the division and loses 0.
Pittsburgh wins 33 games agains teams outside the division and loses 49.
St. Louis wins 52 games agains teams outside the division and loses 30.

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