San Francisco Giants First-Place Clinch Scenario

San Francisco's traditional magic number (relative to first-place Los Angeles) is 31 + 112 - 29 + 1 = 115.
San Francisco's first-place clinch number is 107.
San Francisco must win 107 more games (136 total) to clinch first place.

If San Francisco wins 107 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 San Francisco 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 San Francisco' column gives the
minimum number of games that each team will lose to San Francisco if San Francisco wins 107 more games. Assuming that a team wins all of its remaining games except for
the games it loses to SanFrancisco, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to San Francisco	Maximum W
Los Angeles      31	19	112	      13 - 5 = 8	135
San Diego        27	21	114	      11 - 5 = 6	135
Arizona          26	24	112	      10 - 5 = 5	133
Colorado         8	42	112	       9 - 5 = 4	116

The table above shows that if San Francisco wins 107 more games (136 total), then they will finish the season in first place in the division.

To see that San Francisco's first-place clinch number cannot be less than 107, consider the following scenario in which San Francisco wins 106 more games (135 total) but does not finish in first place:

Team             W	L	PCT	GB
Los Angeles      136	26	0.840	0.00
San Francisco    135	27	0.833	1.00
San Diego        117	45	0.722	19.00
Arizona          85	77	0.525	51.00
Colorado         64	98	0.395	72.00

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

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

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

San Diego currently has 5 wins against Colorado and 1 losses.
  San Diego wins 7 additional games against Colorado and loses 0.
  San Diego wins the series 12 games to 1

San Francisco currently has 1 wins against Arizona and 2 losses.
  San Francisco wins 10 additional games against Arizona and loses 0.
  San Francisco wins the series 11 games to 2

San Francisco currently has 3 wins against Colorado and 1 losses.
  San Francisco wins 9 additional games against Colorado and loses 0.
  San Francisco wins the series 12 games to 1

San Francisco currently has 0 wins against Los Angeles and 0 losses.
  San Francisco wins 7 additional games against Los Angeles and loses 6.
  San Francisco wins the series 7 games to 6

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

Arizona wins 49 games agains teams outside the division and loses 24.
Colorado wins 56 games agains teams outside the division and loses 20.
Los Angeles wins 70 games agains teams outside the division and loses 0.
San Diego wins 70 games agains teams outside the division and loses 0.
San Francisco wins 69 games agains teams outside the division and loses 0.

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