Toronto Blue Jays First-Place Clinch Scenario

Toronto's traditional magic number (relative to first-place New York) is 20 + 130 - 15 + 1 = 136.
Toronto's first-place clinch number is 129.
Toronto must win 129 more games (144 total) to clinch first place.

If Toronto wins 129 more games, their final win total will be at least 144.
The table below shows the best case scenario for each of the other teams if Toronto wins 129 of their remaining 130 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 Toronto' column gives the
minimum number of games that each team will lose to Toronto if Toronto wins 129 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         20	12	130	       7 - 1 = 6	144 *See tie-breaking notes below.
Baltimore        19	11	132	     13 - 1 = 12	139
Boston           18	13	131	     13 - 1 = 12	137
Tampa Bay        14	18	130	       9 - 1 = 8	136

Tie-breakers:
Toronto has won 3 game(s) against New York and lost 3.
There are 7 games left in the series.
In the scenario above, Toronto wins 3 + 6 = 9 games against New York and loses 3 + 1 = 4.

The table above shows that if Toronto wins 129 more games (144 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 129, consider the following scenario in which Toronto wins 128 more games (143 total) but does not finish in first place:

Team             W	L	PCT	GB
New York         144	18	0.889	0.00
Toronto          143	19	0.883	1.00
Tampa Bay        83	79	0.512	61.00
Baltimore        82	80	0.506	62.00
Boston           81	81	0.500	63.00

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 10 additional games against Boston and loses 0.
  Baltimore wins the series 13 games to 0

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

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

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

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

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

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

Toronto currently has 3 wins against New York and 3 losses.
  Toronto wins 5 additional games against New York and loses 2.
  Toronto wins the series 8 games to 5

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 53 games agains teams outside the division and loses 33.
Boston wins 58 games agains teams outside the division and loses 24.
New York wins 89 games agains teams outside the division and loses 1.
Tampa Bay wins 48 games agains teams outside the division and loses 37.
Toronto wins 88 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