Toronto Blue Jays First-Place Clinch Scenario

Toronto's traditional magic number (relative to second-place New York) is 83 + 13 - 87 + 1 = 10.
Toronto's first-place clinch number is 9.
Toronto must win 9 more games (96 total) to clinch first place.

If Toronto wins 9 more games, their final win total will be at least 96.
The table below shows the best case scenario for each of the other teams if Toronto wins 9 of their remaining 13 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 9 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         83	66	13	               0	96 *See tie-breaking notes below.
Boston           82	68	12	               0	94
Tampa Bay        73	76	13	       7 - 4 = 3	83
Baltimore        69	80	13	               0	82

Tie-breakers:
Toronto has won 8 game(s) against New York and lost 5.
There are no games left in the series.

The table above shows that if Toronto wins 9 more games (96 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 9, consider the following scenario in which Toronto wins 8 more games (95 total) but does not finish in first place:

Team             W	L	PCT	GB
New York         96	66	0.593	0.00
Toronto          95	67	0.586	1.00
Boston           88	74	0.543	8.00
Tampa Bay        82	80	0.506	14.00
Baltimore        74	88	0.457	22.00

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Toronto          87	62	13	0.584	0.0
New York         83	66	13	0.557	4.0
Boston           82	68	12	0.547	5.5
Tampa Bay        73	76	13	0.490	14.0
Baltimore        69	80	13	0.463	18.0

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

Boston has won the season series with Baltimore 8 games to 5.
Boston has won the season series with New York 9 games to 4.
New York has won the season series with Tampa Bay 9 games to 4.
Toronto has won the season series with Baltimore 7 games to 6.
Toronto has won the season series with New York 8 games to 5.

Baltimore currently has 5 wins against Tampa Bay and 5 losses.
  Baltimore wins 2 additional games against Tampa Bay and loses 1.
  Baltimore wins the series 7 games to 6

Boston currently has 8 wins against Tampa Bay and 2 losses.
  Boston wins 0 additional games against Tampa Bay and loses 3.
  Boston wins the series 8 games to 5

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

Tampa Bay currently has 5 wins against Toronto and 1 losses.
  Tampa Bay wins 5 additional games against Toronto and loses 2.
  Tampa Bay 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

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