Houston Astros First-Place Clinch Scenario

Houston's traditional magic number (relative to first-place Seattle) is 23 + 121 - 21 + 1 = 124.
Houston's first-place clinch number is 117.
Houston must win 117 more games (138 total) to clinch first place.

If Houston wins 117 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 Houston wins 117 of their remaining 121 games and loses the other 4.
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 Houston' column gives the
minimum number of games that each team will lose to Houston if Houston wins 117 more games. Assuming that a team wins all of its remaining games except for
the games it loses to Houston, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Houston	Maximum W
Seattle          23	18	121	      10 - 4 = 6	138 *See tie-breaking notes below.
Oakland          22	20	120	      13 - 4 = 9	133
Los Angeles      17	24	121	      10 - 4 = 6	132
Texas            22	21	119	      13 - 4 = 9	132

Tie-breakers:
Houston has won 1 game(s) against Seattle and lost 2.
There are 10 games left in the series.
In the scenario above, Houston wins 1 + 6 = 7 games against Seattle and loses 2 + 4 = 6.

The table above shows that if Houston wins 117 more games (138 total), then they will finish the season in first place in the division.

To see that Houston's first-place clinch number cannot be less than 117, consider the following scenario in which Houston wins 116 more games (137 total) but does not finish in first place:

Team             W	L	PCT	GB
Seattle          138	24	0.852	0.00
Houston          137	25	0.846	1.00
Texas            86	76	0.531	52.00
Oakland          80	82	0.494	58.00
Los Angeles      63	99	0.389	75.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Seattle          23	18	121	0.561	0.0
Oakland          22	20	120	0.524	1.5
Houston          21	20	121	0.512	2.0
Texas            22	21	119	0.512	2.0
Los Angeles      17	24	121	0.415	6.0

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


Houston currently has 2 wins against Los Angeles and 1 losses.
  Houston wins 10 additional games against Los Angeles and loses 0.
  Houston wins the series 12 games to 1

Houston currently has 0 wins against Oakland and 0 losses.
  Houston wins 13 additional games against Oakland and loses 0.
  Houston wins the series 13 games to 0

Houston currently has 0 wins against Texas and 0 losses.
  Houston wins 13 additional games against Texas and loses 0.
  Houston wins the series 13 games to 0

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

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

Seattle currently has 2 wins against Houston and 1 losses.
  Seattle wins 5 additional games against Houston and loses 5.
  Seattle wins the series 7 games to 6

Seattle currently has 2 wins against Los Angeles and 0 losses.
  Seattle wins 11 additional games against Los Angeles and loses 0.
  Seattle wins the series 13 games to 0

Seattle currently has 4 wins against Oakland and 3 losses.
  Seattle wins 6 additional games against Oakland and loses 0.
  Seattle wins the series 10 games to 3

Seattle currently has 5 wins against Texas and 1 losses.
  Seattle wins 7 additional games against Texas and loses 0.
  Seattle wins the series 12 games to 1

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

Houston wins 75 games agains teams outside the division and loses 0.
Los Angeles wins 40 games agains teams outside the division and loses 37.
Oakland wins 47 games agains teams outside the division and loses 35.
Seattle wins 86 games agains teams outside the division and loses 1.
Texas wins 52 games agains teams outside the division and loses 31.

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