Pittsburgh Pirates First-Place Clinch Scenario

Pittsburgh's traditional magic number (relative to first-place Milwaukee) is 34 + 107 - 31 + 1 = 111.
Pittsburgh's first-place clinch number is 102.
Pittsburgh must win 102 more games (133 total) to clinch first place.

If Pittsburgh wins 102 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 Pittsburgh wins 102 of their remaining 103 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 Pittsburgh' column gives the
minimum number of games that each team will lose to Pittsburgh if Pittsburgh wins 102 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
Milwaukee        34	21	107	      10 - 1 = 9	132
St. Louis        30	26	106	       6 - 1 = 5	131
Chicago          32	27	103	       6 - 1 = 5	130
Cincinnati       29	28	105	       7 - 1 = 6	128

The table above shows that if Pittsburgh wins 102 more games (133 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 102, consider the following scenario in which Pittsburgh wins 101 more games (132 total) but does not finish in first place:

Team             W	L	PCT	GB
St. Louis        132	30	0.815	0.00
Pittsburgh       132	30	0.815	0.00
Milwaukee        70	92	0.432	62.00
Cincinnati       67	95	0.414	65.00
Chicago          66	96	0.407	66.00

Tie breakers
St. Louis wins the season series with Pittsburgh 7 games to 6.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Milwaukee        34	21	107	0.618	0.0
Chicago          32	27	103	0.542	4.0
St. Louis        30	26	106	0.536	4.5
Pittsburgh       31	28	103	0.525	5.0
Cincinnati       29	28	105	0.509	6.0

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


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

Milwaukee currently has 3 wins against Chicago and 0 losses.
  Milwaukee wins 10 additional games against Chicago and loses 0.
  Milwaukee wins the series 13 games to 0

Milwaukee currently has 0 wins against Cincinnati and 0 losses.
  Milwaukee wins 7 additional games against Cincinnati and loses 6.
  Milwaukee wins the series 7 games to 6

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

Pittsburgh currently has 5 wins against Cincinnati and 1 losses.
  Pittsburgh wins 7 additional games against Cincinnati and loses 0.
  Pittsburgh wins the series 12 games to 1

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

St. Louis currently has 1 wins against Chicago and 1 losses.
  St. Louis wins 11 additional games against Chicago and loses 0.
  St. Louis wins the series 12 games to 1

St. Louis currently has 1 wins against Cincinnati and 1 losses.
  St. Louis wins 11 additional games against Cincinnati and loses 0.
  St. Louis wins the series 12 games to 1

St. Louis currently has 1 wins against Milwaukee and 4 losses.
  St. Louis wins 8 additional games against Milwaukee and loses 0.
  St. Louis wins the series 9 games to 4

St. Louis currently has 5 wins against Pittsburgh and 2 losses.
  St. Louis wins 2 additional games against Pittsburgh and loses 4.
  St. Louis wins the series 7 games to 6

Chicago wins 28 games agains teams outside the division and loses 39.
Cincinnati wins 29 games agains teams outside the division and loses 36.
Milwaukee wins 19 games agains teams outside the division and loses 47.
Pittsburgh wins 74 games agains teams outside the division and loses 0.
St. Louis wins 70 games agains teams outside the division and loses 0.

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