Kansas City Royals First-Place Clinch Scenario

Kansas City's traditional magic number (relative to first-place Detroit) is 33 + 111 - 28 + 1 = 117.
Kansas City's first-place clinch number is 109.
Kansas City must win 109 more games (137 total) to clinch first place.

If Kansas City wins 109 more games, their final win total will be at least 137.
The table below shows the best case scenario for each of the other teams if Kansas City wins 109 of their remaining 111 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 109 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	18	111	       9 - 2 = 7	137 *See tie-breaking notes below.
Cleveland        27	22	113	       7 - 2 = 5	135
Minnesota        27	22	113	       9 - 2 = 7	133
Chicago          15	35	112	       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 109 more games (137 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 109, consider the following scenario in which Kansas City wins 108 more games (136 total) but does not finish in first place:

Team             W	L	PCT	GB
Detroit          137	25	0.846	0.00
Kansas City      136	26	0.840	1.00
Cleveland        107	55	0.660	30.00
Minnesota        67	95	0.414	70.00
Chicago          60	102	0.370	77.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Detroit          33	18	111	0.647	0.0
Cleveland        27	22	113	0.551	5.0
Minnesota        27	22	113	0.551	5.0
Kansas City      28	23	111	0.549	5.0
Chicago          15	35	112	0.300	17.5

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


Cleveland currently has 3 wins against Chicago and 0 losses.
  Cleveland wins 7 additional games against Chicago and loses 3.
  Cleveland wins the series 10 games to 3

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

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 1 losses.
  Detroit wins 12 additional games against Cleveland and loses 0.
  Detroit wins the series 12 games to 1

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 1 losses.
  Kansas City wins 9 additional games against Minnesota and loses 0.
  Kansas City wins the series 12 games to 1

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 42 games agains teams outside the division and loses 34.
Cleveland wins 66 games agains teams outside the division and loses 11.
Detroit wins 70 games agains teams outside the division and loses 0.
Kansas City wins 76 games agains teams outside the division and loses 1.
Minnesota wins 33 games agains teams outside the division and loses 47.

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