The World Series

Date: 10/22/2000 at 11:23:03
From: Erin Ramsey
Subject: Probability of Yankees and Mets in World Series

What is the probability of the Yankees and the Mets playing each other 
in the World Series?

Thanks so much!

Date: 10/22/2000 at 11:27:44
From: Doctor Robert
Subject: Re: Probability of Yankees and Mets in World Series

The probability is 1. They ARE in the World Series.

- Doctor Robert, The Math Forum
  http://mathforum.org/dr.math/   

Date: 10/22/2000 at 13:04:58
From: Erin Ramsey
Subject: Re: Probability of Yankees and Mets in World Series

Dr. Math:

Thanks, but I think that my algebra teacher means what is the 
probability of the Yankees and the Mets playing each other in the 
World Series at the beginning of the season, before any league games 
are held. 

Thanks for all of your help. If you can help me with this, I would 
greatly appreciate it. I have spent several hours working on this. I 
know that there are 30 teams, but I don't know if I need to "figure 
in" how many games each teams plays.

Thanks again,
Erin

Date: 10/23/2000 at 12:35:30
From: Doctor TWE
Subject: Re: Probability of Yankees and Mets playing each other

Hi - thanks for writing to Dr. Math.

This is not strictly a math question. The probability of a team making 
it to the Series depends on their talent, luck, the amount of money 
they can spend on free agents, team "chemistry," and the strength of 
their scouting and minor league operations, among other factors.

The World Series pits the champions of the American and National 
Leagues against each other. For a team to be its league's champion, of 
course, it has to either win its division or win the wild card spot. 
Since the divisions don't have the same number of teams, the chances 
of winning the division are not the same.

For simplicity, however, let's assume every team has an equal chance 
of winning its league. Currently there are 16 teams in the NL and 
14 teams in the AL. Thus, in our simplified approach, we'll assume 
that the Mets' probability of winning the NL is 1/16, and the Yankees 
probability of winning the AL is 1/14. Since these are independent 
events, the probability of both happening is:

     p = (1/16) * (1/14) = 1/224 ~= 0.004464 or about 0.45%

We could use a more complex model, assuming that each team's chance 
of winning its division is equal, and each non-division-winner has 
an equal chance of winning the wild card. We'll also assume that each 
team in the playoffs has an equal chance of winning each series. (This 
last assumption is probably not true - home field advantage, pitching 
rotations, and the fact that the wild card won fewer games than the 
divisional winner, probably give an advantage to one team or the 
other.) In this case, the Mets' chance of winning their division is 
1/5, and their chance of winning the wild card is:

     p = (4/5) * (1/13) = 4/65

The 4/5 is the Mets' team's chance of NOT winning their division, and 
the 1/13 is their chance of winning the wildcard given that they did 
not win the division (there are 13 teams that did not win their 
division in the NL.) Thus, the Mets' chance of making it to the World 
Series using this model is:

     p = [(1/5)+(4/65)] * (1/2) * (1/2) = 17/260

We add the chance of the Mets winning their division and the wild card 
(this is their chance of making it into the post-season), and then we 
multiply that by their chance of winning the divisional series and 
the league championship series (which we're assuming are 1/2 each.)

Similarly, the Yankees' chance of winning their division is 1/5, and 
their chance of winning the wild card is

     p = (4/5) * (1/11) = 4/55

Again, the 4/5 is their chance of NOT winning their division, and the 
1/11 is their chances of winning the wildcard given that they did not 
win the division (there are 11 teams that did not win their division 
in the AL.) Thus, the Yankees' chance of making it to the World 
Series using this model is:

     p = [(1/5)+(4/55)] * (1/2) * (1/2) = 3/44

Then the chances of both teams making it to the World Series are:

     p = (17/260) * (3/44) = 51/11440 ~= 0.004458 or again about 0.45%

Of course, the Mets and Yankees have two of the top six payrolls in 
baseball - they have each gone out and signed free agents or traded 
for the players they needed to make their team championship caliber, 
so their chances of making it to, and advancing in, the playoffs are 
probably better than even. I don't think teams like the Expos, Devil 
Rays or Twins had the same chance of winning as either of these two.

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/