Boston Red Sox First-Place Clinch Scenario

Boston's traditional magic number (relative to first-place New York) is 20 + 130 - 18 + 1 = 133.
Boston's first-place clinch number is 128.
Boston must win 128 more games (146 total) to clinch first place.

If Boston wins 128 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 128 of their remaining 131 games and loses the other 3.
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 128 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
Baltimore        19	11	132	      10 - 3 = 7	144
New York         20	12	130	     13 - 3 = 10	140
Toronto          15	17	130	     13 - 3 = 10	135
Tampa Bay        14	18	130	     13 - 3 = 10	134

The table above shows that if Boston wins 128 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 128, consider the following scenario in which Boston wins 127 more games (145 total) but does not finish in first place:

Team             W	L	PCT	GB
Baltimore        145	17	0.895	0.00
Boston           145	17	0.895	0.00
Toronto          70	92	0.432	75.00
New York         69	93	0.426	76.00
Tampa Bay        54	108	0.333	91.00

Tie breakers
Baltimore 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        19	11	132	0.633	0.0
New York         20	12	130	0.625	0.0
Boston           18	13	131	0.581	1.5
Toronto          15	17	130	0.469	5.0
Tampa Bay        14	18	130	0.438	6.0

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 4 additional games against Boston and loses 6.
  Baltimore wins the series 7 games to 6

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

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

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

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 0 wins against Tampa Bay and 0 losses.
  Boston wins 13 additional games against Tampa Bay and loses 0.
  Boston wins the series 13 games to 0

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

Toronto currently has 3 wins against New York and 3 losses.
  Toronto wins 4 additional games against New York and loses 3.
  Toronto wins the series 7 games to 6

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 86 games agains teams outside the division and loses 0.
Boston wins 82 games agains teams outside the division and loses 0.
New York wins 36 games agains teams outside the division and loses 54.
Tampa Bay wins 40 games agains teams outside the division and loses 45.
Toronto wins 42 games agains teams outside the division and loses 46.

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