Baltimore Orioles First-Place Clinch Scenario

Baltimore's traditional magic number (relative to first-place New York) is 20 + 130 - 19 + 1 = 132.
Baltimore's first-place clinch number is 127.
Baltimore must win 127 more games (146 total) to clinch first place.

If Baltimore wins 127 more games, their final win total will be at least 146.
The table below shows the best case scenario for each of the other teams if Baltimore wins 127 of their remaining 132 games and loses the other 5.
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 Baltimore' column gives the
minimum number of games that each team will lose to Baltimore if Baltimore wins 127 more games. Assuming that a team wins all of its remaining games except for
the games it loses to Baltimore, the resulting maximum number of wins is shown in the 'Maximum W' column.

Team             W	L	GL	Losses to Baltimore	Maximum W
New York         20	12	130	      10 - 5 = 5	145
Boston           18	13	131	      10 - 5 = 5	144
Toronto          15	17	130	      13 - 5 = 8	137
Tampa Bay        14	18	130	      13 - 5 = 8	136

The table above shows that if Baltimore wins 127 more games (146 total), then they will finish the season in first place in the division.

To see that Baltimore's first-place clinch number cannot be less than 127, consider the following scenario in which Baltimore wins 126 more games (145 total) but does not finish in first place:

Team             W	L	PCT	GB
New York         146	16	0.901	0.00
Baltimore        145	17	0.895	1.00
Boston           120	42	0.741	26.00
Toronto          59	103	0.364	87.00
Tampa Bay        37	125	0.228	109.00

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

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

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

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

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

New York currently has 1 wins against Baltimore and 2 losses.
  New York wins 6 additional games against Baltimore and loses 4.
  New York wins the series 7 games to 6

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

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

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 86 games agains teams outside the division and loses 0.
Boston wins 76 games agains teams outside the division and loses 6.
New York wins 90 games agains teams outside the division and loses 0.
Tampa Bay wins 23 games agains teams outside the division and loses 62.
Toronto wins 35 games agains teams outside the division and loses 53.

Combining the current standings with the wins and losses from the scenario results in the final standings listed above.
# Baltimore Orioles' magic number
# Baltimore's magic number
# Orioles' magic number
# MLB Playoff Race