Pittsburgh Pirates First-Place Clinch Scenario

Pittsburgh's traditional magic number (relative to second-place Chicago) is 0 + 162 - 0 + 1 = 163.
Pittsburgh's first-place clinch number is 156.
Pittsburgh must win 156 more games (156 total) to clinch first place.

If Pittsburgh wins 156 more games, their final win total will be at least 156.
The table below shows the best case scenario for each of the other teams if Pittsburgh wins 156 of their remaining 162 games and loses the other 6.
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 Pittsburgh' column gives the
minimum number of games that each team will lose to Pittsburgh if Pittsburgh wins 156 more games. Assuming that a team wins all of its remaining games except for
the games it loses to Pittsburgh, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Pittsburgh	Maximum W
Chicago          0	0	162	      13 - 6 = 7	155
Cincinnati       0	0	162	      13 - 6 = 7	155
Milwaukee        0	0	162	      13 - 6 = 7	155
St. Louis        0	0	162	      13 - 6 = 7	155

The table above shows that if Pittsburgh wins 156 more games (156 total), then they will finish the season in first place in the division.

To see that Pittsburgh's first-place clinch number cannot be less than 156, consider the following scenario in which Pittsburgh wins 155 more games (155 total) but does not finish in first place:

Team             W	L	PCT	GB
Chicago          156	6	0.963	0.00
Pittsburgh       155	7	0.957	0.00
Milwaukee        74	88	0.457	81.00
St. Louis        59	103	0.364	96.00
Cincinnati       43	119	0.265	112.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          0	0	162	0.000	0.0
Cincinnati       0	0	162	0.000	0.0
Milwaukee        0	0	162	0.000	0.0
Pittsburgh       0	0	162	0.000	0.0
St. Louis        0	0	162	0.000	0.0

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


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

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 0 wins against Pittsburgh and 0 losses.
  Chicago wins 7 additional games against Pittsburgh and loses 6.
  Chicago wins the series 7 games to 6

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 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 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

Pittsburgh currently has 0 wins against Cincinnati and 0 losses.
  Pittsburgh wins 13 additional games against Cincinnati and loses 0.
  Pittsburgh wins the series 13 games to 0

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

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

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

Chicago wins 110 games agains teams outside the division and loses 0.
Cincinnati wins 17 games agains teams outside the division and loses 93.
Milwaukee wins 74 games agains teams outside the division and loses 36.
Pittsburgh wins 110 games agains teams outside the division and loses 0.
St. Louis wins 46 games agains teams outside the division and loses 64.

Combining the current standings with the wins and losses from the scenario results in the final standings listed above.
# Pittsburgh Pirates' magic number
# Pittsburgh's magic number
# Pirates' magic number
# MLB Playoff Race