Kansas City Royals First-Place Clinch Scenario

Kansas City's traditional magic number (relative to first-place Cleveland) is 20 + 132 - 19 + 1 = 134.
Kansas City's first-place clinch number is 126.
Kansas City must win 126 more games (145 total) to clinch first place.

If Kansas City wins 126 more games, their final win total will be at least 145.
The table below shows the best case scenario for each of the other teams if Kansas City wins 126 of their remaining 130 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 126 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        20	10	132	      13 - 4 = 9	143
Detroit          18	13	131	      10 - 4 = 6	143
Minnesota        17	13	132	      10 - 4 = 6	143
Chicago          6	25	131	       6 - 4 = 2	135

The table above shows that if Kansas City wins 126 more games (145 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 126, consider the following scenario in which Kansas City wins 125 more games (144 total) but does not finish in first place:

Team             W	L	PCT	GB
Detroit          144	18	0.889	0.00
Kansas City      144	18	0.889	0.00
Cleveland        118	44	0.728	26.00
Minnesota        101	61	0.623	43.00
Chicago          64	98	0.395	80.00

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

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Cleveland        20	10	132	0.667	0.0
Kansas City      19	13	130	0.594	2.0
Detroit          18	13	131	0.581	2.5
Minnesota        17	13	132	0.567	3.0
Chicago          6	25	131	0.194	14.5

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

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

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 2 wins against Kansas City and 1 losses.
  Detroit wins 5 additional games against Kansas City and loses 5.
  Detroit wins the series 7 games to 6

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

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 13 additional games against Cleveland 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 7 wins against Chicago and 0 losses.
  Minnesota wins 6 additional games against Chicago and loses 0.
  Minnesota wins the series 13 games to 0

Minnesota currently has 0 wins against Cleveland and 2 losses.
  Minnesota wins 8 additional games against Cleveland and loses 3.
  Minnesota wins the series 8 games to 5

Chicago wins 58 games agains teams outside the division and loses 41.
Cleveland wins 85 games agains teams outside the division and loses 0.
Detroit wins 92 games agains teams outside the division and loses 0.
Kansas City wins 91 games agains teams outside the division and loses 0.
Minnesota wins 70 games agains teams outside the division and loses 29.

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