Houston Astros First-Place Clinch Scenario

Houston's traditional magic number (relative to second-place Seattle) is 82 + 12 - 82 + 1 = 13.
Houston's first-place clinch number is 10.
Houston must win 10 more games (92 total) to clinch first place.

If Houston wins 10 more games, their final win total will be at least 92.
The table below shows the best case scenario for each of the other teams if Houston wins 10 of their remaining 11 games and loses the other 1.
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 10 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          82	68	12	       3 - 1 = 2	92 *See tie-breaking notes below.
Texas            79	72	11	       2 - 1 = 1	89
Oakland          70	80	12	       3 - 1 = 2	80
Los Angeles      69	81	12	       3 - 1 = 2	79

Tie-breakers:
Houston has won 5 game(s) against Seattle and lost 5.
There are 3 games left in the series.
In the scenario above, Houston wins 5 + 2 = 7 games against Seattle and loses 5 + 1 = 6.

The table above shows that if Houston wins 10 more games (92 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 10, consider the following scenario in which Houston wins 9 more games (91 total) but does not finish in first place:

Team             W	L	PCT	GB
Seattle          93	69	0.574	0.00
Houston          91	71	0.562	2.00
Texas            82	80	0.506	11.00
Los Angeles      78	84	0.481	15.00
Oakland          72	90	0.444	21.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Seattle          82	68	12	0.547	0.0
Houston          82	69	11	0.543	0.5
Texas            79	72	11	0.523	3.5
Oakland          70	80	12	0.467	12.0
Los Angeles      69	81	12	0.460	13.0

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

Los Angeles has won the season series with Oakland 9 games to 4.
Seattle has won the season series with Los Angeles 9 games to 4.
Seattle has won the season series with Oakland 7 games to 6.
Seattle has won the season series with Texas 10 games to 3.
Texas has won the season series with Los Angeles 8 games to 5.
Texas has won the season series with Oakland 8 games to 5.

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

Houston currently has 4 wins against Oakland and 6 losses.
  Houston wins 3 additional games against Oakland and loses 0.
  Houston wins the series 7 games to 6

Houston currently has 5 wins against Texas and 6 losses.
  Houston wins 2 additional games against Texas and loses 0.
  Houston wins the series 7 games to 6

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

Houston wins 0 games agains teams outside the division and loses 0.
Los Angeles wins 9 games agains teams outside the division and loses 0.
Oakland wins 2 games agains teams outside the division and loses 7.
Seattle wins 9 games agains teams outside the division and loses 0.
Texas wins 3 games agains teams outside the division and loses 6.

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