Arizona Diamondbacks First-Place Clinch Scenario

Arizona's traditional magic number (relative to first-place Los Angeles) is 32 + 111 - 26 + 1 = 118.
Arizona's first-place clinch number is 111.
Arizona must win 111 more games (137 total) to clinch first place.

If Arizona wins 111 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 Arizona wins all 111 of their remaining games.
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 Arizona' column gives the
minimum number of games that each team will lose to Arizona if Arizona wins 111 more games. Assuming that a team wins all of its remaining games except for
the games it loses to Arizona, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Arizona	Maximum W
Los Angeles      32	19	111	       6 - 0 = 6	137 *See tie-breaking notes below.
San Francisco    30	21	111	     10 - 0 = 10	131
San Diego        28	21	113	     13 - 0 = 13	128
Colorado         9	42	111	     10 - 0 = 10	110

Tie-breakers:
Arizona has won 3 game(s) against Los Angeles and lost 4.
There are 6 games left in the series.
In the scenario above, Arizona wins 3 + 6 = 9 games against Los Angeles and loses 4 + 0 = 4.

The table above shows that if Arizona wins 111 more games (137 total), then they will finish the season in first place in the division.

To see that Arizona's first-place clinch number cannot be less than 111, consider the following scenario in which Arizona wins 110 more games (136 total) but does not finish in first place:

Team             W	L	PCT	GB
Los Angeles      137	25	0.846	0.00
Arizona          136	26	0.840	1.00
San Francisco    77	85	0.475	60.00
Colorado         71	91	0.438	66.00
San Diego        65	97	0.401	72.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Los Angeles      32	19	111	0.627	0.0
San Francisco    30	21	111	0.588	2.0
San Diego        28	21	113	0.571	3.0
Arizona          26	25	111	0.510	6.0
Colorado         9	42	111	0.176	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 5 additional games against Los Angeles and loses 1.
  Arizona wins the series 8 games to 5

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

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 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 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

San Francisco currently has 3 wins against Colorado and 1 losses.
  San Francisco wins 5 additional games against Colorado and loses 4.
  San Francisco wins the series 8 games to 5

Arizona wins 72 games agains teams outside the division and loses 0.
Colorado wins 58 games agains teams outside the division and loses 17.
Los Angeles wins 68 games agains teams outside the division and loses 1.
San Diego wins 19 games agains teams outside the division and loses 50.
San Francisco wins 42 games agains teams outside the division and loses 26.

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