Cincinnati Reds First-Place Clinch Scenario

Cincinnati's traditional magic number (relative to first-place Chicago) is 15 + 138 - 14 + 1 = 140.
Cincinnati's first-place clinch number is 134.
Cincinnati must win 134 more games (148 total) to clinch first place.

If Cincinnati wins 134 more games, their final win total will be at least 148.
The table below shows the best case scenario for each of the other teams if Cincinnati wins 134 of their remaining 138 games and loses the other 4.
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        15	8	139	      10 - 4 = 6	148 *See tie-breaking notes below.
Chicago          15	9	138	      13 - 4 = 9	144
Pittsburgh       13	12	137	      13 - 4 = 9	141
St. Louis        11	14	137	      13 - 4 = 9	139

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 + 6 = 7 games against Milwaukee and loses 2 + 4 = 6.

The table above shows that if Cincinnati wins 134 more games (148 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 (147 total) but does not finish in first place:

Team             W	L	PCT	GB
Milwaukee        148	14	0.914	0.00
Cincinnati       147	15	0.907	1.00
St. Louis        85	77	0.525	63.00
Chicago          64	98	0.395	84.00
Pittsburgh       50	112	0.309	98.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Milwaukee        15	8	139	0.652	0.0
Chicago          15	9	138	0.625	0.5
Cincinnati       14	10	138	0.583	1.5
Pittsburgh       13	12	137	0.520	3.0
St. Louis        11	14	137	0.440	5.0

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 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 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

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

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

Chicago wins 43 games agains teams outside the division and loses 43.
Cincinnati wins 88 games agains teams outside the division and loses 1.
Milwaukee wins 96 games agains teams outside the division and loses 0.
Pittsburgh wins 13 games agains teams outside the division and loses 75.
St. Louis wins 65 games agains teams outside the division and loses 23.

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