Boston Red Sox First-Place Clinch Scenario

Boston's traditional magic number (relative to first-place New York) is 30 + 113 - 25 + 1 = 119.
Boston's first-place clinch number is 110.
Boston must win 110 more games (135 total) to clinch first place.

If Boston wins 110 more games, their final win total will be at least 135.
The table below shows the best case scenario for each of the other teams if Boston wins 110 of their remaining 111 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 Boston' column gives the
minimum number of games that each team will lose to Boston if Boston wins 110 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          25	24	113	       6 - 1 = 5	133
New York         30	19	113	     13 - 1 = 12	131
Tampa Bay        23	26	113	      10 - 1 = 9	127
Baltimore        16	32	114	      10 - 1 = 9	121

The table above shows that if Boston wins 110 more games (135 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 110, consider the following scenario in which Boston wins 109 more games (134 total) but does not finish in first place:

Team             W	L	PCT	GB
Toronto          134	28	0.827	0.00
Boston           134	28	0.827	0.00
New York         108	54	0.667	26.00
Baltimore        61	101	0.377	73.00
Tampa Bay        59	103	0.364	75.00

Tie breakers
Toronto 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
New York         30	19	113	0.612	0.0
Toronto          25	24	113	0.510	5.0
Boston           25	26	111	0.490	6.0
Tampa Bay        23	26	113	0.469	7.0
Baltimore        16	32	114	0.333	13.5

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


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

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 4 wins against Tampa Bay and 3 losses.
  New York wins 4 additional games against Tampa Bay and loses 2.
  New York wins the series 8 games to 5

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

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 5 wins against Boston and 2 losses.
  Toronto wins 2 additional games against Boston and loses 4.
  Toronto wins the series 7 games to 6

Toronto currently has 1 wins against New York and 2 losses.
  Toronto wins 10 additional games against New York and loses 0.
  Toronto wins the series 11 games to 2

Toronto currently has 1 wins against Tampa Bay and 2 losses.
  Toronto wins 10 additional games against Tampa Bay and loses 0.
  Toronto wins the series 11 games to 2

Baltimore wins 32 games agains teams outside the division and loses 42.
Boston wins 72 games agains teams outside the division and loses 0.
New York wins 74 games agains teams outside the division and loses 0.
Tampa Bay wins 24 games agains teams outside the division and loses 50.
Toronto wins 80 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