Chicago White Sox First-Place Clinch Scenario

Chicago's traditional magic number (relative to first-place Detroit) is 15 + 137 - 5 + 1 = 148.
Chicago's first-place clinch number is 138.
Chicago must win 138 more games (143 total) to clinch first place.

If Chicago wins 138 more games, their final win total will be at least 143.
The table below shows the best case scenario for each of the other teams if Chicago wins all 138 of their remaining games.
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 Chicago' column gives the
minimum number of games that each team will lose to Chicago if Chicago wins 138 more games. Assuming that a team wins all of its remaining games except for
the games it loses to ChicagoWhiteSox, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Chicago	Maximum W
Cleveland        14	10	138	     10 - 0 = 10	142
Detroit          15	10	137	     10 - 0 = 10	142
Minnesota        9	15	138	       8 - 0 = 8	139
Kansas City      10	14	138	     13 - 0 = 13	135

The table above shows that if Chicago wins 138 more games (143 total), then they will finish the season in first place in the division.

To see that Chicago's first-place clinch number cannot be less than 138, consider the following scenario in which Chicago wins 137 more games (142 total) but does not finish in first place:

Team             W	L	PCT	GB
Detroit          143	19	0.883	0.00
Chicago          142	20	0.877	1.00
Minnesota        90	72	0.556	53.00
Cleveland        68	94	0.420	75.00
Kansas City      65	97	0.401	78.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Detroit          15	10	137	0.600	0.0
Cleveland        14	10	138	0.583	0.5
Kansas City      10	14	138	0.417	4.5
Minnesota        9	15	138	0.375	5.5
Chicago          5	19	138	0.208	9.5

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


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

Chicago currently has 0 wins against Detroit and 3 losses.
  Chicago wins 9 additional games against Detroit and loses 1.
  Chicago wins the series 9 games to 4

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

Chicago currently has 1 wins against Minnesota and 4 losses.
  Chicago wins 8 additional games against Minnesota and loses 0.
  Chicago wins the series 9 games to 4

Cleveland currently has 0 wins against Minnesota and 0 losses.
  Cleveland wins 12 additional games against Minnesota and loses 1.
  Cleveland wins the series 12 games to 1

Detroit currently has 0 wins against Cleveland and 0 losses.
  Detroit wins 13 additional games against Cleveland and loses 0.
  Detroit wins the series 13 games to 0

Detroit currently has 3 wins against Kansas City and 1 losses.
  Detroit wins 9 additional games against Kansas City and loses 0.
  Detroit wins the series 12 games to 1

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

Kansas City currently has 2 wins against Cleveland and 4 losses.
  Kansas City wins 7 additional games against Cleveland and loses 0.
  Kansas City wins the series 9 games to 4

Minnesota currently has 1 wins against Kansas City and 3 losses.
  Minnesota wins 9 additional games against Kansas City and loses 0.
  Minnesota wins the series 10 games to 3

Chicago wins 97 games agains teams outside the division and loses 0.
Cleveland wins 42 games agains teams outside the division and loses 53.
Detroit wins 95 games agains teams outside the division and loses 0.
Kansas City wins 48 games agains teams outside the division and loses 52.
Minnesota wins 71 games agains teams outside the division and loses 27.

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