Official Postseason Discussion Thread

[Fresno Bob]

PM me your address, Joe Bob, and prepare to receive a check with lots of obscenities and offensive things written in the For: line.

I'll take a sweet green picture of Abraham Lincoln the next time I see you!

[Mithrandir]

The price to own Madbum has skyrocketed.

[joncarlos]

Well, that ROYALLY sucked.

I'll be here all week.

[Fresno Bob]

and I'll be seeing how good MLB coverage is in China and Australia......

[virgonomic]

"20-1 is too high. There are eight possible outcomes. They occur in roughly equal proportions. The odds on a sweep by a given team is 8-1, absent other considerations. I doubt 20-1 is ever justified."

I wasn't a math major, but that doesn't seem right, forget about tonight.

Truth. It's a binomial probability distribution.

At 0.5 probability of a win:

A sweep can only happen one way: 4 straight wins. The probability is (0.5)^4 = 0.0625.

Winning in 5 games can happen C(4, 1) = 4 ways because the loser must win game 1, 2, 3, or 4.
So the probability is 4(0.5)^4.

Winning in 6 games can happen C(5, 2) = 10 ways because the losing team must win 2 of the first 5 games.
Probability 10(0.5)^5

Winning in 7 games can happen C(6, 3) = 20 ways because the losing team must win 3 of the first 6 games.
Probability 20(0.5)^6

So at 50-50, a longer series is more probable.

[The Feral Slasher]

Truth. It's a binomial probability distribution.

At 0.5 probability of a win:

A sweep can only happen one way: 4 straight wins. The probability is (0.5)^4 = 0.0625.

Winning in 5 games can happen C(4, 1) = 4 ways because the loser must win game 1, 2, 3, or 4.
So the probability is 4(0.5)^4.

Winning in 6 games can happen C(5, 2) = 10 ways because the losing team must win 2 of the first 5 games.
Probability 10(0.5)^5

Winning in 7 games can happen C(6, 3) = 20 ways because the losing team must win 3 of the first 6 games.
Probability 20(0.5)^6

So at 50-50, a longer series is more probable.

For winning in 5, 6, or 7 games I think you need to multiply by one more factor of 0.5 (for the given team to win the last game). Then if you add up the probability of winning in 4, 5, 6, or 7 games it equals 0.5

[onejayhawk]

I was a math major, but that does not enter into it. The distribution is not close to a bell. By observation, sweeps occur more often than a 50/50 chance would occur. For example, from 1953-2002 you get

Gms Times
4 | 8
5 | 8
6 | 10
7 | 24

Why? Certainly the chances of winning game 2, given that you won game 1, would seem to be better than even. Momentum could be a factor, though some statisticians claim there is no such thing. Bottom line, I don't know. A normal (bell) distribution would result in 7 games series at 31.25%, or 15 to 16 out of 50. There are far more than that. The tendency is either blow outs or cliffhangers.

http://www.stat.unc.edu/faculty/rs/s11/aip.htm

Well, that ROYALLY sucked.

I'll be here all week.

That's too bad. The next game is in California.

So much for the sweeps. Does anyone want to bet three straight in SF?

J

[bryanbutler]

something's not right. there have been more than 50 world series played.

and the fact that it doesn't match the theoretical probability is just because it's not a large enough sample. statistical clumping is at work...

you can easily simulate this, and if you use enough trials, you'll get the expected 12.5%, 25%, 31.25%, 31.25% distribution. but if you only use 100 trials, you will regularly get numbers like 5% or 45%. i just ran 1000 trials of 100 series each, and get the following:

games  expected  minimum  maximum
-----  --------  -------  -------
  4     12.5%       2%      22%
  5     25.0%      11%      40%
  6     31.25%     18%      47%
  7     31.25%     18%      47%

[onejayhawk]

something's not right. there have been more than 50 world series played.

and the fact that it doesn't match the theoretical probability is just because it's not a large enough sample. statistical clumping is at work...

you can easily simulate this, and if you use enough trials, you'll get the expected 12.5%, 25%, 31.25%, 31.25% distribution. but if you only use 100 trials, you will regularly get numbers like 5% or 45%. i just ran 1000 trials of 100 series each, and get the following:

games  expected  minimum  maximum
-----  --------  -------  -------
  4     12.5%       2%      22%
  5     25.0%      11%      40%
  6     31.25%     18%      47%
  7     31.25%     18%      47%

Based in your numbers, the premise that the distribution is normal fails at 90% confidence.

There was nothng magical bout that 50 years. It was the most recent 50 WS at the time of the article. Both sweeps and seven game series are much more common than expected. I suspect it has more to do with conditional probabilities than we are allowing. For example, the probability of a sweep, given winning the first two games, would be 25% in a 50/50 scenario. I suspect it is more like 50%.

J

[bryanbutler]

the fact that if you flip a coin 10 times and it comes up tails 8 of the 10, when you "expect" 5, doesn't mean tails is "much more common than expected." it just means you didn't flip the coin often enough.

[The Feral Slasher]

20-1 is too high. There are eight possible outcomes. They occur in roughly equal proportions. The odds on a sweep by a given team is 8-1, absent other considerations. I doubt 20-1 is ever justified.

J

This is just plain wrong, you should stop arguing and try to use your math degree to figure out what you are doing wrong In
stead of arguing about conditional probabilities.

[Pogues]

You all can talk about probabilities when it come to how long a series will go in baseball, but playing baseball games isn't like flipping a coin or drawing a card from a deck of cards. It's quite possible to never get to "expected outcome" because it's more than just pure chance as to who wins a game, and who wins 4 games first.

So really, this conversation is just you guys flexing your brains.

[The Feral Slasher]

You all can talk about probabilities when it come to how long a series will go in baseball, but playing baseball games isn't like flipping a coin or drawing a card from a deck of cards. It's quite possible to never get to "expected outcome" because it's more than just pure chance as to who wins a game, and who wins 4 games first.

So really, this conversation is just you guys flexing your brains.

Maybe if we were vegans we would have something better to do

[Judge Jude]

I have a twin brother, and it happens that we married women who share their birthdays as well (though born in different years).

It's amusing, but people seem to think it's about a 10 million to 1 shot when in fact I think it's what, a 9th grade math question?

The gals were born 180 days apart from our birthdays, which astrology fans would love, I guess.

[bryanbutler]

So really, this conversation is just you guys flexing your brains.

hey, a good brain flex is healthy once in a while .

agreed that it's not 50/50. what would be very interesting is to take, say, the vegas odds and use that as the "expected" outcome for each game, then see how long you expect the series to last. some series are much more evenly matched than others, for sure. at least on paper.