Boston Red Sox First-Place Clinch Scenario

Boston's traditional magic number (relative to first-place Tampa Bay) is 65 + 53 - 64 + 1 = 55.
Boston's first-place clinch number is 50.

If Boston wins 50 more games, their final win total will be at least 114.
The table below shows the best case scenario for each of the other teams if Boston wins 50 of their remaining 53 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 50 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 and maximum winning percentage are shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Boston	Maximum W
Toronto          56	49	57	       4 - 3 = 1	112
Tampa Bay        65	44	53	      10 - 3 = 7	111
New York         58	49	55	       6 - 3 = 3	110
Baltimore        38	69	55	       9 - 3 = 6	87

The table above shows that if Boston wins 50 more games (114 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 50, consider the following scenario in which Boston wins 49 more games (113 total) but does not finish in first place.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Tampa Bay        65	44	53	0.596	0.0
Boston           64	45	53	0.587	1.0
New York         58	49	55	0.542	6.0
Toronto          56	49	57	0.533	7.0
Baltimore        38	69	55	0.355	26.0

Next, we show how the remaining series of games in Boston's division plays out in the scenario:

Baltimore wins 0 games against Boston and loses 9.
Baltimore wins 0 games against New York and loses 6.
Baltimore wins 0 games against Tampa Bay and loses 10.
Baltimore wins 0 games against Toronto and loses 10.
Baltimore wins 20 games against teams outside the division and loses 0.

Boston wins 9 games against Baltimore and loses 0.
Boston wins 6 games against New York and loses 0.
Boston wins 10 games against Tampa Bay and loses 0.
Boston wins 0 games against Toronto and loses 4.
Boston wins 24 games against teams outside the division and loses 0.

New York wins 6 games against Baltimore and loses 0.
New York wins 0 games against Boston and loses 6.
New York wins 3 games against Tampa Bay and loses 0.
New York wins 0 games against Toronto and loses 7.
New York wins 33 games against teams outside the division and loses 0.

Tampa Bay wins 10 games against Baltimore and loses 0.
Tampa Bay wins 0 games against Boston and loses 10.
Tampa Bay wins 0 games against New York and loses 3.
Tampa Bay wins 0 games against Toronto and loses 6.
Tampa Bay wins 24 games against teams outside the division and loses 0.

Toronto wins 10 games against Baltimore and loses 0.
Toronto wins 4 games against Boston and loses 0.
Toronto wins 7 games against New York and loses 0.
Toronto wins 6 games against Tampa Bay and loses 0.
Toronto wins 30 games against teams outside the division and loses 0.

Combining the current standings with the wins and losses from the scenario results in the following final standings:
TEAM             W	L	GL	PCT
Boston           113	49	0.698	0.0
Toronto          113	49	0.698	0.0
New York         100	62	0.617	13.0
Tampa Bay        99	63	0.611	14.0
Baltimore        58	104	0.358	55.0

# Boston Red Sox's magic number
# Boston's magic number
# Red Sox's magic number
# MLB Playoff Race