New York Yankees First-Place Clinch Scenario

New York's traditional magic number (relative to second-place Baltimore) is 15 + 140 - 15 + 1 = 141.
New York's first-place clinch number is 135.
New York must win 135 more games (150 total) to clinch first place.

If New York wins 135 more games, their final win total will be at least 150.
The table below shows the best case scenario for each of the other teams if New York wins 135 of their remaining 139 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 New York' column gives the
minimum number of games that each team will lose to New York if New York wins 135 more games. Assuming that a team wins all of its remaining games except for
the games it loses to NYYankees, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to New York	Maximum W
Toronto          13	10	139	       7 - 4 = 3	149
Baltimore        15	7	140	      13 - 4 = 9	146
Tampa Bay        12	12	138	      10 - 4 = 6	144
Boston           13	10	139	      13 - 4 = 9	143

The table above shows that if New York wins 135 more games (150 total), then they will finish the season in first place in the division.

To see that New York's first-place clinch number cannot be less than 135, consider the following scenario in which New York wins 134 more games (149 total) but does not finish in first place:

Team             W	L	PCT	GB
Toronto          149	13	0.920	0.00
New York         149	13	0.920	0.00
Baltimore        96	66	0.593	53.00
Tampa Bay        75	87	0.463	74.00
Boston           75	87	0.463	74.00

Tie breakers
Toronto wins the season series with New York 8 games to 5.

Tampa Bay wins the season series with Boston 7 games to 6.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Baltimore        15	7	140	0.682	0.0
New York         15	8	139	0.652	0.5
Boston           13	10	139	0.565	2.5
Toronto          13	10	139	0.565	2.5
Tampa Bay        12	12	138	0.500	4.0

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


Baltimore currently has 3 wins against Boston and 0 losses.
  Baltimore wins 10 additional games against Boston and loses 0.
  Baltimore wins the series 13 games to 0

Baltimore currently has 0 wins against Tampa Bay and 0 losses.
  Baltimore wins 13 additional games against Tampa Bay and loses 0.
  Baltimore wins the series 13 games to 0

New York currently has 0 wins against Baltimore and 0 losses.
  New York wins 13 additional games against Baltimore and loses 0.
  New York wins the series 13 games to 0

New York currently has 0 wins against Boston and 0 losses.
  New York wins 13 additional games against Boston and loses 0.
  New York wins the series 13 games to 0

New York currently has 2 wins against Tampa Bay and 1 losses.
  New York wins 10 additional games against Tampa Bay and loses 0.
  New York wins the series 12 games to 1

Tampa Bay currently has 0 wins against Boston and 0 losses.
  Tampa Bay wins 7 additional games against Boston and loses 6.
  Tampa Bay wins the series 7 games to 6

Toronto currently has 0 wins against Baltimore and 0 losses.
  Toronto wins 13 additional games against Baltimore and loses 0.
  Toronto wins the series 13 games to 0

Toronto currently has 0 wins against Boston and 0 losses.
  Toronto wins 13 additional games against Boston and loses 0.
  Toronto wins the series 13 games to 0

Toronto currently has 3 wins against New York and 3 losses.
  Toronto wins 5 additional games against New York and loses 2.
  Toronto wins the series 8 games to 5

Toronto currently has 2 wins against Tampa Bay and 2 losses.
  Toronto wins 9 additional games against Tampa Bay and loses 0.
  Toronto wins the series 11 games to 2

Baltimore wins 58 games agains teams outside the division and loses 33.
Boston wins 56 games agains teams outside the division and loses 34.
New York wins 96 games agains teams outside the division and loses 0.
Tampa Bay wins 56 games agains teams outside the division and loses 37.
Toronto wins 96 games agains teams outside the division and loses 1.

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