## What's the Magic Number in Baseball?

What's the Magic Number in baseball? It's simply the number of games that the team leading a division needs to win to ensure winning the division. If you're leading the division with ten games remaining and your Magic Number is three, you only need to win three of those ten games to ensure winning the division. Each time you win, your Magic Number goes down by one. Each time your nearest divisional competitor loses, your Magic Number also goes down by one. When your Magic Number hits zero, you've clinched the division.

You calculate your Magic Number by looking at the number of games remaining in the season and assuming that your nearest competitor will win all of their remaining games. Then you see how many games you still need to win to ensure the division title even with your nearest competitor winning all their remaining games.

Since the mighty Minnesota Twins are still atop the AL Central, I thought I'd start tracking their Magic Number. So I searched around on the web and found two different methods of calculation.

One method, endorsed by Major League Baseball is to take the number of games remaining for the division leaders, add 1, then subtract the difference in the number of losses between the leaders and the second place team. In other words:

M = G_{1}+ 1 - ( L_{2}- L_{1})

Another method, which I read on the web here, starts with the number of games remaining for the second place team, again adds 1, then subtracts the difference in the wins between first and second place. Or:

M = G_{2}+ 1 - ( W_{1}- W_{2})

So, is either formula better than the other, or are they equivalent? And how am I just supposed to know how many games these teams have left to play? Well, we can replace the number of remaining games by the total number of games in the regular season (162) minus the number of games played so far, which is just wins plus losses.

For the Major League formula, this becomes:

M = ( 162 - ( W_{1}+ L_{1}) ) + 1 - ( L_{2}- L_{1})

Which expands to:

M = 162 - W_{1}- L_{1}+ 1 - L_{2}+ L_{1}

The L_{1} cancels out, and the 162 and 1 combine, to leave:

M = 163 - W_{1}- L_{2}

For the second method, we get:

M = ( 162 - ( W_{2}+ L_{2}) + 1 - ( W_{1}- W_{2})

Which expands to:

M = 162 - W_{2}- L_{2}+ 1 - W_{1}+ W_{2}

In this case, the W_{2} cancels out. The 162 and 1 still combine, leaving us with:

M = 163 - L_{2}- W_{1}

Which is exactly what we ended up with using the Major League formula.

In closing, the Magic Number for a division-leading Major League Baseball team is simply 163 minus the number of wins the first place team has, then minus the number of losses the second place team has:

##
M = 163 - W_{1} - L_{2}

(More detailed information about baseball standings and number is available from the RIOT Baseball Playoff Races.)