The recent proliferation of post-season playoff series means that most career post-season records are held by recent players. The question looked at here is "How many more post-season games does the average player play in?"

Let's begin with the "expected length" of a post-season series.
Assume that each team is equally likely to win each game.
Then the expected length of the series is easy to compute.
This is not entirely accurrate, but the probabilities rarely deviate much
from 50%, so the actual values should not have a large impact on expected series length.
The expected lengths are as follows:

**5 game series**: 4.125
**7 game series**: 5.8125
**9 game series**: 7.5390625

The table lists the seasons,
followed by the expected number of post-season games for a "random" team,
which is then followed by the expected number of World Series games.

Years PS WS 1903 0.942 0.942 1905-1918 0.727 0.727 1919-1921 0.942 0.942 1922-1960 0.727 0.727 1961NL 0.727 0.727 1961AL 0.581 0.581 1962-1968 0.581 0.581 1969-1976 1.172 0.484 1976-1984NL 1.172 0.484 1977-1984AL 1.004 0.415 1985-1992NL 1.453 0.484 1993NL 1.246 0.415 1985-1993AL 1.246 0.415 1995-1997 in 5 team div. 2.333 0.400 in 4 team div. 2.653 0.454 1998-2002 AL in 5 team div. 2.333 0.400 AL in 4 team div. 2.653 0.454 NL in 6 team div. 1.989 0.341 NL in 5 team div. 2.200 0.377

Length of a

Length of a

Length of a

Length of a

Letting a wild-card team into the playoffs complicates the expected value computation.
Making the simplifying assumption that teams are equally distributed allows for
an approximate expected value to be computed.

The equal distribution assumption means that it is assumed that the team with the best record
in a 14 team league has probability of 5/14 of being in a particular 5 team division, and
probability 4/14 of being in a four team division.

They will be in a five team division with probability (10/14)*(4/13).

They will be in the four team division with probability (4/14)*(3/13).

This somputation can be repeated for teams with the third best and fourth best records.

Wild-card 5 team division 2nd best (10/14)*(4/13) 3rd best (10/14)*(5/13)*(8/12)+(10/14)*(4/13)*(7/12)+(4/14)*(10/13)*(4/12) 4th best (10/14)*(5/13)*(4/12)*(8/11)+(10/14)*(4/13)*(5/12)*(8/11)+(4/14)*(10/13)*(5/12)*(8/11) Wild-card 4 team division 2nd best (4/14)*(3/13) 3rd best (10/14)*(4/13)*(3/12) + (4/14)*(10/13)*(3/12) 4th best (10/14)*(5/13)*(4/12)*(3/11)+(10/14)*(4/13)*(5/12)*(3/11) + (4/14)*(10/13)*(5/12)*(3/11)Simplifying these sums;

wild-card 5 team div. 4 team div. 2nd best 20/91 6/91 3rd best 30/91 10/91 4th best 200/1001 75/1001 Total 750/1001 251/1001So, the expected number of playoff teams from 5 team divisions is 2+750/1001=2752/1001.

The expected number of playoff appearances for each of the teams is (2752/1001)/10=1376/5005.

The expected number of playoff teams from a 4 team division is 1+251/1001=1252/1001.

The expected number of playoff appearance for each of the teams is (1252/1001)/4=313/1001.

These teams will play in the 5 game division series, expected number of games: 4.125 games.

Half of them will play in the LCS, expected number of games: (5.8125)/2.

One-quarter of the teams will play in the World Series, expected number of games: (5.8125)/4.

Wild-card 5 team division 2nd best (10/16)*(4/15) 3rd best (10/16)*(5/15)*(8/14)+(10/16)*(6/15)*(9/14)+(6/16)*(10/15)*(9/14) 4th best (10/16)*(5/15)*(6/14)*(8/13)+(10/16)*(6/15)*(5/14)*(8/13)+(6/16)*(10/15)*(5/14)*(8/13) Wild-card 6 team division 2nd best (6/16)*(5/15) 3rd best (10/16)*(6/15)*(5/14)+(6/16)*(10/15)*(5/14) 4th best (10/16)*(5/15)*(6/14)*(5/13)+(10/16)*(6/15)*(5/14)*(5/13)+(6/16)*(10/15)*(5/14)*(5/13)Simplifying these sums;

wild-card 5 team div. 6 team div. 2nd best 1/6 1/8 3rd best 11/42 5/28 4th best 15/91 75/728 Total 54/91 37/91The expected number of playoff teams from 5 team divisions is 2+54/91=236/91.

The expected number of playoff appearances for each of the teams is (236/91)/10 = 118/455.

The expected number of playoff teams from the 6 team division is 1+37/91=128/91.

The expected number of playoff appearances for each of the teams is (128/91)/6 = 64/273.

These teams will play in the 5 game division series, expected number of games: 4.125 games.

Half of them will play in the LCS, expected number of games: (5.8125)/2.

One-quarter of the teams will play in the World Series, expected number of games: (5.8125)/4.

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