Toronto Blue Jays First-Place Clinch Scenario

Toronto's traditional magic number (relative to second-place New York) is 49 + 72 - 52 + 1 = 70.
Toronto's first-place clinch number is 68.
Toronto must win 68 more games (120 total) to clinch first place.

If Toronto wins 68 more games, their final win total will be at least 120.
The table below shows the best case scenario for each of the other teams if Toronto wins 68 of their remaining 72 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 Toronto' column gives the
minimum number of games that each team will lose to Toronto if Toronto wins 68 more games. Assuming that a team wins all of its remaining games except for
the games it loses to Toronto, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Toronto	Maximum W
New York         49	41	72	       6 - 4 = 2	119
Tampa Bay        49	41	72	       7 - 4 = 3	118
Boston           45	45	72	               0	117
Baltimore        40	49	73	       7 - 4 = 3	110

The table above shows that if Toronto wins 68 more games (120 total), then they will finish the season in first place in the division.

To see that Toronto's first-place clinch number cannot be less than 68, consider the following scenario in which Toronto wins 67 more games (119 total) but does not finish in first place:

Team             W	L	PCT	GB
New York         120	42	0.741	0.00
Toronto          119	43	0.735	1.00
Tampa Bay        108	54	0.667	12.00
Boston           74	88	0.457	46.00
Baltimore        73	89	0.451	47.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Toronto          52	38	72	0.578	0.0
New York         49	41	72	0.544	3.0
Tampa Bay        49	41	72	0.544	3.0
Boston           45	45	72	0.500	7.0
Baltimore        40	49	73	0.449	11.5

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 4 losses.
  Baltimore wins 6 additional games against Boston and loses 0.
  Baltimore wins the series 9 games to 4

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

New York currently has 1 wins against Boston and 5 losses.
  New York wins 7 additional games against Boston and loses 0.
  New York wins the series 8 games to 5

New York currently has 4 wins against Tampa Bay and 3 losses.
  New York wins 6 additional games against Tampa Bay and loses 0.
  New York wins the series 10 games to 3

New York currently has 2 wins against Toronto and 5 losses.
  New York wins 5 additional games against Toronto and loses 1.
  New York wins the series 7 games to 6

Tampa Bay currently has 3 wins against Baltimore and 4 losses.
  Tampa Bay wins 6 additional games against Baltimore and loses 0.
  Tampa Bay wins the series 9 games to 4

Tampa Bay currently has 2 wins against Boston and 4 losses.
  Tampa Bay wins 7 additional games against Boston and loses 0.
  Tampa Bay wins the series 9 games to 4

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

Toronto currently has 1 wins against Tampa Bay and 5 losses.
  Toronto wins 7 additional games against Tampa Bay and loses 0.
  Toronto wins the series 8 games to 5

Baltimore wins 27 games agains teams outside the division and loses 20.
Boston wins 29 games agains teams outside the division and loses 20.
New York wins 46 games agains teams outside the division and loses 0.
Tampa Bay wins 46 games agains teams outside the division and loses 0.
Toronto wins 49 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.
# Toronto Blue Jays' magic number
# Toronto's magic number
# Blue Jays' magic number
# MLB Playoff Race