Chicago White Sox First-Place Clinch Scenario

Chicago's traditional magic number (relative to first-place Cleveland) is 18 + 127 - 16 + 1 = 130.
Chicago's first-place clinch number is 124.
Chicago must win 124 more games (140 total) to clinch first place.

If Chicago wins 124 more games, their final win total will be at least 140.
The table below shows the best case scenario for each of the other teams if Chicago wins 124 of their remaining 128 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 Chicago' column gives the
minimum number of games that each team will lose to Chicago if Chicago wins 124 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
Kansas City      15	19	128	       9 - 4 = 5	138
Cleveland        18	17	127	      13 - 4 = 9	136
Detroit          18	17	127	      13 - 4 = 9	136
Minnesota        15	20	127	      13 - 4 = 9	133

The table above shows that if Chicago wins 124 more games (140 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 124, consider the following scenario in which Chicago wins 123 more games (139 total) but does not finish in first place:

Team             W	L	PCT	GB
Kansas City      139	23	0.858	0.00
Chicago          139	23	0.858	0.00
Detroit          63	99	0.389	76.00
Cleveland        63	99	0.389	76.00
Minnesota        62	100	0.383	77.00

Tie breakers
Kansas City wins the season series with Chicago 7 games to 6.

Detroit wins the season series with Cleveland 13 games to 0.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Cleveland        18	17	127	0.514	0.0
Detroit          18	17	127	0.514	0.0
Chicago          16	18	128	0.471	1.5
Kansas City      15	19	128	0.441	2.5
Minnesota        15	20	127	0.429	3.0

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 0 losses.
  Chicago wins 13 additional games against Cleveland and loses 0.
  Chicago wins the series 13 games to 0

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

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

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

Kansas City currently has 2 wins against Chicago and 2 losses.
  Kansas City wins 5 additional games against Chicago and loses 4.
  Kansas City wins the series 7 games to 6

Kansas City currently has 1 wins against Cleveland and 2 losses.
  Kansas City wins 10 additional games against Cleveland and loses 0.
  Kansas City wins the series 11 games to 2

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

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

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

Minnesota currently has 4 wins against Detroit and 0 losses.
  Minnesota wins 8 additional games against Detroit and loses 1.
  Minnesota wins the series 12 games to 1

Chicago wins 80 games agains teams outside the division and loses 0.
Cleveland wins 45 games agains teams outside the division and loses 33.
Detroit wins 31 games agains teams outside the division and loses 51.
Kansas City wins 89 games agains teams outside the division and loses 0.
Minnesota wins 26 games agains teams outside the division and loses 56.

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