Cincinnati Reds First-Place Clinch Scenario

Cincinnati's traditional magic number (relative to first-place Chicago) is 49 + 78 - 44 + 1 = 84.
Cincinnati's first-place clinch number is 77.
Cincinnati must win 77 more games (121 total) to clinch first place.

If Cincinnati wins 77 more games, their final win total will be at least 121.
The table below shows the best case scenario for each of the other teams if Cincinnati wins 77 of their remaining 78 games and loses the other 1.
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 77 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          49	35	78	       7 - 1 = 6	121 *See tie-breaking notes below.
Milwaukee        47	37	78	       6 - 1 = 5	120
St. Louis        47	38	77	       6 - 1 = 5	119
Pittsburgh       35	50	77	       7 - 1 = 6	106

Tie-breakers:
Cincinnati has won 2 game(s) against Chicago and lost 4.
There are 7 games left in the series.
In the scenario above, Cincinnati wins 2 + 6 = 8 games against Chicago and loses 4 + 1 = 5.

The table above shows that if Cincinnati wins 77 more games (121 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 77, consider the following scenario in which Cincinnati wins 76 more games (120 total) but does not finish in first place:

Team             W	L	PCT	GB
Milwaukee        120	42	0.741	0.00
Cincinnati       120	42	0.741	0.00
Chicago          113	49	0.698	7.00
St. Louis        71	91	0.438	49.00
Pittsburgh       70	92	0.432	50.00

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          49	35	78	0.583	0.0
Milwaukee        47	37	78	0.560	2.0
St. Louis        47	38	77	0.553	2.5
Cincinnati       44	40	78	0.524	5.0
Pittsburgh       35	50	77	0.412	14.5

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


Chicago currently has 5 wins against Pittsburgh and 2 losses.
  Chicago wins 6 additional games against Pittsburgh and loses 0.
  Chicago wins the series 11 games to 2

Chicago currently has 2 wins against St. Louis and 2 losses.
  Chicago wins 9 additional games against St. Louis and loses 0.
  Chicago wins the series 11 games to 2

Cincinnati currently has 2 wins against Chicago and 4 losses.
  Cincinnati wins 7 additional games against Chicago and loses 0.
  Cincinnati wins the series 9 games to 4

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 3 wins against St. Louis and 4 losses.
  Cincinnati wins 6 additional games against St. Louis and loses 0.
  Cincinnati wins the series 9 games to 4

Milwaukee currently has 2 wins against Chicago and 3 losses.
  Milwaukee wins 7 additional games against Chicago and loses 1.
  Milwaukee wins the series 9 games to 4

Milwaukee currently has 5 wins against Cincinnati and 2 losses.
  Milwaukee wins 2 additional games against Cincinnati and loses 4.
  Milwaukee wins the series 7 games to 6

Milwaukee currently has 4 wins against Pittsburgh and 3 losses.
  Milwaukee wins 6 additional games against Pittsburgh and loses 0.
  Milwaukee wins the series 10 games to 3

Milwaukee currently has 4 wins against St. Louis and 3 losses.
  Milwaukee wins 6 additional games against St. Louis and loses 0.
  Milwaukee wins the series 10 games to 3

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 48 games agains teams outside the division and loses 0.
Cincinnati wins 52 games agains teams outside the division and loses 0.
Milwaukee wins 52 games agains teams outside the division and loses 0.
Pittsburgh wins 35 games agains teams outside the division and loses 16.
St. Louis wins 17 games agains teams outside the division and loses 32.

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