Chicago White Sox First-Place Clinch Scenario

Chicago's traditional magic number (relative to second-place Cleveland) is 51 + 60 - 62 + 1 = 50.
Chicago's first-place clinch number is 50.

If Chicago wins 50 more games, their final win total will be at least 112.
The table below shows the best case scenario for each of the other teams if Chicago wins 50 of their remaining 56 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 ChicagoWhiteSox' column gives the
minimum number of games that each team will lose to ChicagoWhiteSox if ChicagoWhiteSox wins 50 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 and maximum winning percentage are shown in the 'Maximum W' column.

Team             W	L	GL	Losses to ChicagoWhiteSox	Maximum W
Cleveland        51	51	60	               0	111
Detroit          51	57	54	               0	105
Kansas City      45	59	58	               0	103
Minnesota        44	62	56	               0	100

The table above shows that if Chicago wins 50 more games (112 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 50, consider the following scenario in which ChicagoWhiteSox wins 49 more games (111 total) but does not finish in first place.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          62	44	56	0.585	0.0
Cleveland        51	51	60	0.500	9.0
Detroit          51	57	54	0.472	12.0
Kansas City      45	59	58	0.433	16.0
Minnesota        44	62	56	0.415	18.0

Next, we show how the remaining series of games in Chicago's division plays out in the scenario:

Chicago wins 0 games against Cleveland and loses 5.
Chicago wins 6 games against Detroit and loses 0.
Chicago wins 6 games against Kansas City and loses 0.
Chicago wins 3 games against Minnesota and loses 0.
Chicago wins 34 games against teams outside the division and loses 2.

Cleveland wins 5 games against Chicago and loses 0.
Cleveland wins 6 games against Detroit and loses 0.
Cleveland wins 10 games against Kansas City and loses 0.
Cleveland wins 10 games against Minnesota and loses 0.
Cleveland wins 29 games against teams outside the division and loses 0.

Detroit wins 0 games against Chicago and loses 6.
Detroit wins 0 games against Cleveland and loses 6.
Detroit wins 0 games against Kansas City and loses 3.
Detroit wins 0 games against Minnesota and loses 4.
Detroit wins 35 games against teams outside the division and loses 0.

Kansas City wins 0 games against Chicago and loses 6.
Kansas City wins 0 games against Cleveland and loses 10.
Kansas City wins 3 games against Detroit and loses 0.
Kansas City wins 6 games against Minnesota and loses 0.
Kansas City wins 33 games against teams outside the division and loses 0.

Minnesota wins 0 games against Chicago and loses 3.
Minnesota wins 0 games against Cleveland and loses 10.
Minnesota wins 4 games against Detroit and loses 0.
Minnesota wins 0 games against Kansas City and loses 6.
Minnesota wins 33 games against teams outside the division and loses 0.

Combining the current standings with the wins and losses from the scenario results in the following final standings:
TEAM             W	L	GL	PCT
Chicago          111	51	0.685	0.0
Cleveland        111	51	0.685	0.0
Kansas City      87	75	0.537	24.0
Detroit          86	76	0.531	25.0
Minnesota        81	81	0.500	30.0

# Chicago White Sox's magic number
# Chicago's magic number
# White Sox's magic number
# MLB Playoff Race