Boston Red Sox First-Place Clinch Scenario

Boston's traditional magic number (relative to first-place New York) is 15 + 137 - 14 + 1 = 139.
Boston's first-place clinch number is 132.
Boston must win 132 more games (146 total) to clinch first place.

If Boston wins 132 more games, their final win total will be at least 146.
The table below shows the best case scenario for each of the other teams if Boston wins 132 of their remaining 136 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 Boston' column gives the
minimum number of games that each team will lose to Boston if Boston wins 132 more games. Assuming that a team wins all of its remaining games except for
the games it loses to Boston, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Boston	Maximum W
Toronto          12	13	137	       9 - 4 = 5	144
New York         15	10	137	      13 - 4 = 9	143
Baltimore        9	14	139	      10 - 4 = 6	142
Tampa Bay        10	14	138	      10 - 4 = 6	142

The table above shows that if Boston wins 132 more games (146 total), then they will finish the season in first place in the division.

To see that Boston's first-place clinch number cannot be less than 132, consider the following scenario in which Boston wins 131 more games (145 total) but does not finish in first place:

Team             W	L	PCT	GB
Toronto          145	17	0.895	0.00
Boston           145	17	0.895	0.00
Baltimore        61	101	0.377	84.00
Tampa Bay        57	105	0.352	88.00
New York         56	106	0.346	89.00

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

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
New York         15	10	137	0.600	0.0
Boston           14	12	136	0.538	1.5
Toronto          12	13	137	0.480	3.0
Tampa Bay        10	14	138	0.417	4.5
Baltimore        9	14	139	0.391	5.0

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


Boston currently has 2 wins against Baltimore and 1 losses.
  Boston wins 10 additional games against Baltimore and loses 0.
  Boston wins the series 12 games to 1

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

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

New York currently has 0 wins against Baltimore and 0 losses.
  New York wins 11 additional games against Baltimore and loses 2.
  New York wins the series 11 games to 2

New York currently has 3 wins against Tampa Bay and 1 losses.
  New York wins 9 additional games against Tampa Bay and loses 0.
  New York wins the series 12 games to 1

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

Toronto currently has 3 wins against Baltimore and 3 losses.
  Toronto wins 7 additional games against Baltimore and loses 0.
  Toronto wins the series 10 games to 3

Toronto currently has 3 wins against Boston and 1 losses.
  Toronto wins 5 additional games against Boston and loses 4.
  Toronto wins the series 8 games to 5

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

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

Baltimore wins 44 games agains teams outside the division and loses 52.
Boston wins 94 games agains teams outside the division and loses 0.
New York wins 21 games agains teams outside the division and loses 68.
Tampa Bay wins 40 games agains teams outside the division and loses 53.
Toronto wins 95 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.
# Boston Red Sox' magic number
# Boston's magic number
# Red Sox' magic number
# MLB Playoff Race