Astros are trailing 0 games to 2 behind the Nationals
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There are 15 possible combinations of wins and losses for the remaining games. Of those 15 games, 10 of them produce a Series win for Walgreens, and 5 produce a Series win for the Astros.
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The Astros have a 1 in 3 chance of winning the World Series
Feel free to correct my analysis if you see an error.
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wessimo said:

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You are assuming every game is a coin flip.

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yes .....this analysis is the Mathematical Odds. Every game is won by one, or the other team. Mathematically, there is a 50% chance for either team to win a game.

This thread is giving me a nosebleed.

Username checks out

3 Toed Pete said:

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Beats the days of figuring out how many more losses until the Astros were mathematically eliminated from making the playoffs.

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In July.

And we're also all using the word odds incorrectly. Everyone has actually been talking probability.

In your 3rd, 4th, 6th, 7th, 8th, 9th, and 10th odds, the second win you list for the Astros is in a game the odds say has a 0% chance of taking place.

BMX Bandit said:

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NoseBleed said:

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wessimo said:

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You are assuming every game is a coin flip.

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yes .....this analysis is the Mathematical Odds. Every game is won by one, or the other team. Mathematically, there is a 50% chance for either team to win a game.

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this is not true, even for Mathematical odds

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Correct

We have a much lower chance than 1/3 assuming 50% win chance per game

I think I found the correct formula online

The odds of Astros winning 4 of next 5 games, assuming a win probability of 55% for each game

20.6%

If you say each game is a coin flip, out odds are 15.6%

Wabs said:

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lda6339 said:

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There will not be another World Series baseball game played in Houston this year. Book it.

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Won't be another one played in Arlington either. Book it.

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If you're gonna pretend this is clever or funny at least go through my post history to figure out I'm not a rangers fan so you can attack the correct team you melon.

The OP actually assumes that each entire sequence of outcomes is equally likely, not that each game is a coinflip.

In reality (assuming coinflip games), the scenarios that are shorter are more likely to occur. For example, the scenario where the Nationals win the next two, the probability of that is .5 x .5 = 25% whereas the scenario where the Astros win 4 in a row is .5 x .5 x .5 x .5 = 6.25%. All 7 game scenarios (8 of the 15 outcomes) have a 3.125% chance of happening. All of the 6 game scenarios (4 out of 15) have a 6.25% chance. Both of the two 5 game scenarios have a 12.5% chance of happening, and (as mentioned) a Nationals sweep would have a 25% chance of happening.

Total odds assuming coinflip games are 81.25% Nationals vs 18.75% chance Astros.

Fangraphs has the odds at 65% Nationals 35% Astros

In order to get to Fangraphs current series odds, the implied probability for each game would need to be 61% towards the Astros.

Correct

JJxvi said:

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The OP actually assumes that each entire sequence of outcomes is equally likely, not that each game is a coinflip.

In reality (assuming coinflip games), the scenarios that are shorter are more likely to occur. For example, the scenario where the Nationals win the next two, the probability of that is .5 x .5 = 25% whereas the scenario where the Astros win 4 in a row is .5 x .5 x .5 x .5 = 6.25%. All 7 game scenarios (8 of the 15 outcomes) have a 3.125% chance of happening. All of the 6 game scenarios (4 out of 15) have a 6.25% chance. Both of the two 5 game scenarios have a 12.5% chance of happening, and (as mentioned) a Nationals sweep would have a 25% chance of happening.

Total odds assuming coinflip games are 81.25% Nationals vs 18.75% chance Astros.

Fangraphs has the odds at 65% Nationals 35% Astros

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This article is a few years old now, but seems to concur with your analysis:
https://sabr.org/research/world-series-game-situation-winning-probabilities-how-often-do-teams-come-back-behind

The stros. are ass my dude

wessimo said:

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You are assuming every game is a coin flip.

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Not even doing it right.

As the coin flips:

1/4 result in Washington winning in 4.
1/2 result in 3-1 Washington after 4.
1/4 result in 2-2 after 4

From there (after 5)
1/4 of 3/4 more end 4-1 Washington (7/16)
1/2 of 3/4 are 3-2 Washington (3/8)
1/4 of 3/4 are 3-2 Astros (3/16)

Now (after 6)
1/2 of 3/8 more end 4-2 Washington (5/8)
1/2 of 3/16 end 4-2 Astros (3/32)
And the rest go to game 7. (9/32)

After game 7
49/64 go to Washington
15/64 go to Houston

So, as a coin flip, Houston has just under a 25% chance of winning the best of 7.

Good thing baseball isn't a coin flip.

Jjxvi is correct

18.75% chance for Astros assuming coin flip

Y'all really can't math, huh?

TexasRebel said:

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Y'all really can't math, huh?

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I concede

I didn't account for chance we could win 4 straight in my binomial probability calculator

You win

15/64

TexasRebel said:

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wessimo said:

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You are assuming every game is a coin flip.

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Not even doing it right.

As the coin flips:

1/4 result in Washington winning in 4.
1/2 result in 3-1 Washington after 4.
1/4 result in 2-2 after 4

From there (after 5)
1/4 of 3/4 more end 4-1 Washington (7/16)
1/2 of 3/4 are 3-2 Washington (3/8)
1/4 of 3/4 are 3-2 Astros (3/16)

Now (after 6)
1/2 of 3/8 more end 4-2 Washington (5/8)
1/2 of 3/16 end 4-2 Astros (3/32)
And the rest go to game 7. (9/32)

After game 7
49/64 go to Washington
15/64 go to Houston

So, as a coin flip, Houston has just under a 25% chance of winning the best of 7.

Good thing baseball isn't a coin flip.

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My math is correct.

After Game 4 your numbers are fine

1/4 chance Washington wins
1/2 chance (3-1)
1/4 chance (2-2)

But after Game 5

1/4 chance Washington wins 4-1 (1/2 of 1/2)
3/8 chance of 3-2 (1/2 of 1/2 and 1/2 of 1/4)
1/8 chance of 2-3 (1/2 of 1/4)

After Game 6

3/16 chance of Washington 4-2 (1/2 of 3/8)
1/16 chance of Houston 2-4 (1/2 of 1/8)
4/16 chance of 3-3 (1/2 of 3/8 and 1/2 of 1/8)

After Game 7

4/32 chance of Washington 4-3 (1/2 of 4/16)
4/32 chance of Houston 3-4 (same)


Add up the Washington in bold. 1/4 + 1/4 + 3/16 + 4/32 = 13/16 (81.25%)
Add up the Houston in italics. 1/16 + 4/32 = 3/16 (18.75%)

I played game 5 twice.

In game 5 (3/4):
2-2(1/4) becomes 3-2(1/8) or 2-3(1/8)
3-1(1/2) becomes 4-1(1/4) or 3-2(1/4)

In game 6 (1/2):
3-2(3/8) becomes 4-2(3/16) or 3-3(3/16)
2-3(1/8) becomes 3-3(1/16) or 2-4(1/16)

In game 7(1/4):
1/8 goes each way.

3/16.

How does 1/4 of 3/4 get to 7/16

How does 1/2 of 3/8 make 5/8

NoseBleed said:

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Go to

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I went today.

I was wondering where the 64s came from.

Even checked twice. Just had a 5a and 5b.