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Frequently Asked Questions

1. What is the magic number and how is it computed?
2. How are the playoff teams and home-field advantage determined?
3. What happens when there are ties for playoff spots?
4. If RIOT says that my team's first-place elimination number is zero, does that mean my team has clinched first place?

1. What is the magic number and how is it computed?


The so-called magic number is usually defined as the smallest number such that any combination of wins by the first-place team and losses by the second-place team totaling the magic number guarantees that the first-place team will win the division.

The magic number can be computed using the following numbers (see [1] for alternative formulae):
 

• w₁ - the number of games the team currently in first place has won so far
• w₂ - the number of games the team currently in second place has won so far
• g₂ -  the number of games the team currently in second place has left to play


Now, suppose that the first-place team wins x more of its remaining games and the second-place team loses y more of its remaining games (i.e., it wins g₂-y games).  We will now derive a formula for the magic number, x + y.

The team currently in first place will finish with w₁+ x wins and the team currently in second place will finish with w₂ + g₂ - y wins.  The team currently in first place will finish ahead of the team currently in second place as long as w₁ + x > w₂ + g₂- y.  The magic number is the smallest number  x + y  such that x + y > w₂ + g₂ - w₁.

Since we are dealing with integers (whole numbers), the magic number is w₂  + g₂ - w₁+ 1. 

Here is an example using the National League East standings as of 9 am, EST, Sunday September 8 1996:

National League East

					Clinch		Avoid Elim
Team	W	L	GB	Games Left	1st	Play	1st	Play
Atlanta	86	55	-	21	13	9	0	0
Montreal	78	63	8	21	21	17	8	0
Florida	69	74	18	19	*	*	17	9
New York	62	80	24 1/2	20	*	*	Elim	16
Philadelphia	58	85	29	19	*	*	Elim	Elim

The first-place team, Atlanta, has 86 wins and the second-place team, Montreal, has 78 wins and 21 games left to play.  So, w₁= 86, w₂= 78 and g₂= 21. Thus, Atlanta's magic number is 78 + 21 - 86 + 1 = 14.

This means that any combination of wins by Atlanta and losses by Montreal totaling 14 ensures that Atlanta will win the National League East.  For example, if Atlanta wins 14 more games, they will finish with at least 100 wins.  The best Montreal can do is 78 + 21 = 99 wins.  Thus, Atlanta would finish ahead of Montreal.  Likewise, if Montreal were to lose 14 games, they would have 7 games left to play and could finish with at most 78 + 7 = 85 wins.  Since Atlanta already has 86 wins, they would finish ahead of Montreal in this scenario as well. 

Finally, suppose Atlanta wins 4 games and Montreal loses 10 - a combination adding up to the magic number, 14.  In this scenario, Atlanta would have 90 wins and Montreal would have 78 wins with 11 games left to play.  This means that Montreal could finish with at most 78 + 11 = 89 wins and could not catch up with Atlanta.

Notice that RIOT lists Atlanta's first-place clinch number as 13 - one less than the magic number.  In this case, the difference is that first-place clinch number includes ties for first place while the magic number does not.   The first-place clinch number is often just one less than the magic number, but sometimes there is a larger difference.  For example, consider another example from September 8 1996:
 

National League West

					Clinch		Avoid Elim
Team	W	L	GB	Games Left	1st	Play	1st	Play
Los Angeles	78	63	-	21	17	17	4	1
San Diego	78	65	1	19	17	17	4	0
Colorado	71	71	7 1/2	20	*	*	11	7
San Francisco	59	81	18 1/2	22	*	*	Elim	19

Here, Los Angeles' magic number is 78 + 19 - 78 + 1 = 20, but the first-place clinch number is only 17.  What you can't see from the standings is that Los Angeles and San Diego will play each other 7 more times before the end of season.  Thus, if L.A. wins 17 more games, then at least 3 of them will be against San Diego.  Notice that 17 wins for L.A. plus 3 losses for San Diego adds up to the magic number, 20.  This example illustrates how the magic number does not always tell the whole story.

Another drawback with the magic number is that it really only applies to a pair of teams.  For instance, if San Diego loses 20 of its remaining games in the example above it does not necessarily mean that Los Angeles will win the division.  It just means that L.A. will finish ahead of San Diego.  Since Colorado has not yet been eliminated, it is still possible for the Rockies to win the division.   The first-place clinch number, however, is a guarantee; no matter what else happens, the Dodgers will at least clinch a tie for first place if they win 17 more games.

2. How are the wild-card teams determined? 

Each league (American and National) sends five teams to the postseason: the three division winners and two wild card teams. The wild card teams are the two teams in the league with the best records among all teams that are not division winners. In princple the wild card teams are the teams with the 4th and 5th best records in the league, and are the two best second-place teams. However, it's possible that the wild card teams come from the same division, and it's possible that a wild card team could have a better record than the division winner of another division.

3. What happens when there are ties for postseason spots?

This can get quite complicated; see Wikipedia or the official Major League Baseball web site for details.

4. If RIOT says that my team's first-place elimination number is zero, does that mean my team has clinched first place?

References

[1]  M. T. Battista "Mathematics in Baseball." Mathematics Teacher. 86:4. 336-342. 1993