Los Angeles Dodgers First-Place Clinch Scenario

Los Angeles's traditional magic number (relative to second-place San Francisco) is 29 + 112 - 31 + 1 = 111.
Los Angeles's first-place clinch number is 107.
Los Angeles must win 107 more games (138 total) to clinch first place.

If Los Angeles wins 107 more games, their final win total will be at least 138.
The table below shows the best case scenario for each of the other teams if Los Angeles wins 107 of their remaining 112 games and loses the other 5.
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 Los Angeles' column gives the
minimum number of games that each team will lose to Los Angeles if Los Angeles wins 107 more games. Assuming that a team wins all of its remaining games except for
the games it loses to LADodgers, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Los Angeles	Maximum W
Arizona          26	24	112	       6 - 5 = 1	137
San Diego        27	21	114	      13 - 5 = 8	133
San Francisco    29	21	112	      13 - 5 = 8	133
Colorado         8	42	112	      10 - 5 = 5	115

The table above shows that if Los Angeles wins 107 more games (138 total), then they will finish the season in first place in the division.

To see that Los Angeles's first-place clinch number cannot be less than 107, consider the following scenario in which Los Angeles wins 106 more games (137 total) but does not finish in first place:

Team             W	L	PCT	GB
Arizona          138	24	0.852	0.00
Los Angeles      137	25	0.846	1.00
Colorado         61	101	0.377	77.00
San Diego        51	111	0.315	87.00
San Francisco    41	121	0.253	97.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Los Angeles      31	19	112	0.620	0.0
San Francisco    29	21	112	0.580	2.0
San Diego        27	21	114	0.562	3.0
Arizona          26	24	112	0.520	5.0
Colorado         8	42	112	0.160	23.0

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


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

Arizona currently has 3 wins against Los Angeles and 4 losses.
  Arizona wins 6 additional games against Los Angeles and loses 0.
  Arizona wins the series 9 games to 4

Arizona currently has 0 wins against San Diego and 0 losses.
  Arizona wins 13 additional games against San Diego and loses 0.
  Arizona wins the series 13 games to 0

Arizona currently has 2 wins against San Francisco and 1 losses.
  Arizona wins 10 additional games against San Francisco and loses 0.
  Arizona wins the series 12 games to 1

Colorado currently has 1 wins against San Diego and 5 losses.
  Colorado wins 7 additional games against San Diego and loses 0.
  Colorado wins the series 8 games to 5

Colorado currently has 1 wins against San Francisco and 3 losses.
  Colorado wins 9 additional games against San Francisco and loses 0.
  Colorado wins the series 10 games to 3

Los Angeles currently has 3 wins against Colorado and 0 losses.
  Los Angeles wins 10 additional games against Colorado and loses 0.
  Los Angeles wins the series 13 games to 0

Los Angeles currently has 0 wins against San Diego and 0 losses.
  Los Angeles wins 13 additional games against San Diego and loses 0.
  Los Angeles wins the series 13 games to 0

Los Angeles currently has 0 wins against San Francisco and 0 losses.
  Los Angeles wins 13 additional games against San Francisco and loses 0.
  Los Angeles wins the series 13 games to 0

San Diego currently has 2 wins against San Francisco and 0 losses.
  San Diego wins 11 additional games against San Francisco and loses 0.
  San Diego wins the series 13 games to 0

Arizona wins 73 games agains teams outside the division and loses 0.
Colorado wins 37 games agains teams outside the division and loses 39.
Los Angeles wins 70 games agains teams outside the division and loses 0.
San Diego wins 13 games agains teams outside the division and loses 57.
San Francisco wins 12 games agains teams outside the division and loses 57.

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