Kansas City Royals First-Place Clinch Scenario

Kansas City's traditional magic number (relative to first-place Detroit) is 33 + 110 - 28 + 1 = 116.
Kansas City's first-place clinch number is 108.
Kansas City must win 108 more games (136 total) to clinch first place.

If Kansas City wins 108 more games, their final win total will be at least 136.
The table below shows the best case scenario for each of the other teams if Kansas City wins 108 of their remaining 110 games and loses the other 2.
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 108 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
Detroit          33	19	110	       9 - 2 = 7	136 *See tie-breaking notes below.
Cleveland        28	22	112	       7 - 2 = 5	135
Minnesota        28	22	112	       8 - 2 = 6	134
Chicago          16	35	111	       9 - 2 = 7	120

Tie-breakers:
Kansas City has won 1 game(s) against Detroit and lost 3.
There are 9 games left in the series.
In the scenario above, Kansas City wins 1 + 7 = 8 games against Detroit and loses 3 + 2 = 5.

The table above shows that if Kansas City wins 108 more games (136 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 108, consider the following scenario in which Kansas City wins 107 more games (135 total) but does not finish in first place:

Team             W	L	PCT	GB
Detroit          136	26	0.840	0.00
Kansas City      135	27	0.833	1.00
Cleveland        96	66	0.593	40.00
Minnesota        95	67	0.586	41.00
Chicago          80	82	0.494	56.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Detroit          33	19	110	0.635	0.0
Cleveland        28	22	112	0.560	4.0
Minnesota        28	22	112	0.560	4.0
Kansas City      28	24	110	0.538	5.0
Chicago          16	35	111	0.314	16.5

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

Cleveland currently has 4 wins against Minnesota and 2 losses.
  Cleveland wins 5 additional games against Minnesota and loses 2.
  Cleveland wins the series 9 games to 4

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 2 losses.
  Detroit wins 11 additional games against Cleveland and loses 0.
  Detroit wins the series 11 games to 2

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 4 wins against Chicago and 0 losses.
  Kansas City wins 9 additional games against Chicago and loses 0.
  Kansas City wins the series 13 games to 0

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

Kansas City currently has 1 wins against Detroit and 3 losses.
  Kansas City wins 7 additional games against Detroit and loses 2.
  Kansas City wins the series 8 games to 5

Kansas City currently has 3 wins against Minnesota and 2 losses.
  Kansas City wins 7 additional games against Minnesota and loses 1.
  Kansas City wins the series 10 games to 3

Minnesota currently has 4 wins against Chicago and 2 losses.
  Minnesota wins 7 additional games against Chicago and loses 0.
  Minnesota wins the series 11 games to 2

Chicago wins 54 games agains teams outside the division and loses 21.
Cleveland wins 63 games agains teams outside the division and loses 14.
Detroit wins 70 games agains teams outside the division and loses 0.
Kansas City wins 77 games agains teams outside the division and loses 0.
Minnesota wins 57 games agains teams outside the division and loses 23.

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