Kansas City Royals First-Place Clinch Scenario

Kansas City's traditional magic number (relative to first-place Cleveland) is 16 + 140 - 13 + 1 = 144.
Kansas City's first-place clinch number is 135.
Kansas City must win 135 more games (148 total) to clinch first place.

If Kansas City wins 135 more games, their final win total will be at least 148.
The table below shows the best case scenario for each of the other teams if Kansas City wins 135 of their remaining 139 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 Kansas City' column gives the
minimum number of games that each team will lose to Kansas City if Kansas City wins 135 more games. Assuming that a team wins all of its remaining games except for
the games it loses to KansasCity, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Kansas City	Maximum W
Cleveland        16	6	140	      13 - 4 = 9	147
Detroit          13	10	139	      13 - 4 = 9	143
Minnesota        8	13	141	      10 - 4 = 6	143
Chicago          3	19	140	       6 - 4 = 2	141

The table above shows that if Kansas City wins 135 more games (148 total), then they will finish the season in first place in the division.

To see that Kansas City's first-place clinch number cannot be less than 135, consider the following scenario in which Kansas City wins 134 more games (147 total) but does not finish in first place:

Team             W	L	PCT	GB
Cleveland        148	14	0.914	0.00
Kansas City      147	15	0.907	1.00
Detroit          90	72	0.556	58.00
Minnesota        61	101	0.377	87.00
Chicago          61	101	0.377	87.00

Tie breakers
Minnesota wins the season series with Chicago 13 games to 0.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Cleveland        16	6	140	0.727	0.0
Detroit          13	10	139	0.565	3.5
Kansas City      13	10	139	0.565	3.5
Minnesota        8	13	141	0.381	7.5
Chicago          3	19	140	0.136	13.0

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


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

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

Cleveland currently has 2 wins against Minnesota and 0 losses.
  Cleveland wins 11 additional games against Minnesota and loses 0.
  Cleveland wins the series 13 games to 0

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

Kansas City currently has 6 wins against Chicago and 1 losses.
  Kansas City wins 6 additional games against Chicago and loses 0.
  Kansas City wins the series 12 games to 1

Kansas City currently has 0 wins against Cleveland and 0 losses.
  Kansas City wins 8 additional games against Cleveland and loses 5.
  Kansas City wins the series 8 games to 5

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

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

Minnesota currently has 1 wins against Chicago and 0 losses.
  Minnesota wins 12 additional games against Chicago and loses 0.
  Minnesota wins the series 13 games to 0

Minnesota currently has 3 wins against Detroit and 4 losses.
  Minnesota wins 6 additional games against Detroit and loses 0.
  Minnesota wins the series 9 games to 4

Chicago wins 58 games agains teams outside the division and loses 44.
Cleveland wins 93 games agains teams outside the division and loses 0.
Detroit wins 67 games agains teams outside the division and loses 30.
Kansas City wins 97 games agains teams outside the division and loses 0.
Minnesota wins 35 games agains teams outside the division and loses 67.

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