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Old 10-31-2019, 01:36 PM
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Statistical LIklihood for Game 7 of World Series


Someone and I were talking the other day about how it seem like the world series goes to game 7 more than we think would be likely.

I am terrible with statistics, so please help me.

So, the scenario that should most likely lead to a game seven is if the teams were perfectly matched and it were pure chance who won on each night. If that was true, what is the likelihood of going to game seven?

What if one team was only 10 or 20% more likely to win each game?

There have been 110 world series since 1903 (I took four out since they were a best of nine format). An article I just read said there were 40 series that went to game seven. Is that more or less than if the teams were winning by chance?
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Old 10-31-2019, 02:28 PM
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If you and I were repeatedly doing best-of-seven coin flips, we'd need 7 flips 20/64 of the time.

20/64 = .3125

40/110 = .3636...

So real life is only slightly overperforming random chance in getting to 7 games.
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Old 10-31-2019, 02:37 PM
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The 7 games series result from better matched teams, so it's probably out performing chance by a lot for well matched teams if you eliminated the 21 4 game sweeps that clearly indicate a mismatch.
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Old 10-31-2019, 02:41 PM
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I'm not really a baseball watcher but I think the home team lost every game in the World Series this year. is that true? Has that ever happened before?
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Old 10-31-2019, 02:50 PM
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Originally Posted by Tired and Cranky View Post
I'm not really a baseball watcher but I think the home team lost every game in the World Series this year. is that true? Has that ever happened before?
First time last night.
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Old 10-31-2019, 02:51 PM
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I'm not really a baseball watcher but I think the home team lost every game in the World Series this year. is that true? Has that ever happened before?
That is true. Not only has it never happened before in the World Series, it has never happened before in any major U.S. pro sport with a championship series.
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Old 10-31-2019, 02:51 PM
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The 7 games series result from better matched teams, so it's probably out performing chance by a lot for well matched teams if you eliminated the 21 4 game sweeps that clearly indicate a mismatch.
I am just assuming 21 sweeps is way more than the odds would indicate. Probably best to start by calculating the odds for 4,5,6, and 7 game series to see how that differs from the real series.
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Old 10-31-2019, 03:02 PM
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The 7 games series result from better matched teams, so it's probably out performing chance by a lot for well matched teams if you eliminated the 21 4 game sweeps that clearly indicate a mismatch.
I'll just say that if every game is a fair 50/50 coin flip, you'll get a sweep one out of eight times (or around 14 out of 110). So I wouldn't necessarily say that a sweep 'clearly indicates a mismatch'. Especially considering the possibility that even with evenly matched teams, the team that's behind 0-3 may be less effective in the final game and more likely to lose.
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Old 10-31-2019, 03:03 PM
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That is true. Not only has it never happened before in the World Series, it has never happened before in any major U.S. pro sport with a championship series.
They havenít even had the home team lose the first 6, let alone all 7.
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Old 10-31-2019, 03:10 PM
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I'll just say that if every game is a fair 50/50 coin flip, you'll get a sweep one out of eight times (or around 14 out of 110). So I wouldn't necessarily say that a sweep 'clearly indicates a mismatch'. Especially considering the possibility that even with evenly matched teams, the team that's behind 0-3 may be less effective in the final game and more likely to lose.
Ok, that does indicate 21 sweeps is pretty high though. So I'd bet some of those 7 extra sweeps are definitely due to a mismatch. I think it's clearer that in a 7 game series we're looking at well matched teams though.
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Old 10-31-2019, 03:38 PM
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Originally Posted by RTFirefly View Post
If you and I were repeatedly doing best-of-seven coin flips, we'd need 7 flips 20/64 of the time.

20/64 = .3125

40/110 = .3636...

So real life is only slightly overperforming random chance in getting to 7 games.
It certainly didn't pan out this series, but home field advantage is also a factor. Do the odds for a Game 7 increase when you add in a very small boost to the home team? Say 1-2%?
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Old 10-31-2019, 03:51 PM
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Which is more likely: a 7-game series or a 6-game series?

If a series has not ended after the 5th game, it must be 3-2.

If the team that is ahead after game 5 wins game 6, the series ends after 6 games.
If the team that is behind after game 5 wins game six, the series goes to 7 games.

If these are equally likely, then 6-game and 7-game series should have equal probability.

But maybe the team that is ahead after 5 games is ahead because it is the better team? That would make a 6-game series more likely.

Or maybe the team that is behind after 5 games is going to be playing harder and with a greater sense of urgency, because they face elimination in game 6. That would make a 7-game series more likely.

Can anyone tell me whether there have been more 6-game series or 7-game series?
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Old 10-31-2019, 06:53 PM
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Here's an analysis from 2003, updated in 2014, on Are 7-Game World Series More Common Than Expected?
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Old 11-01-2019, 04:17 PM
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Thanks TriPolar and gdave!
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Old 11-01-2019, 07:06 PM
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Here are the answers to questions raised in the OP. As already mentioned, if the teams are evenly matched, then the chances of a 7 game series are 31.25%. If one of the teams has a 45% chance of winning any given game between them, then it is 30.3% and if it is only a 40% chance, then it is 27.6%. The general formula if one team has probability p is 20*((p - p^2)^3). This is pure probability theory, not statistics.

But it is also not realistic, since teams don't have winning percentages as much as pitchers do. So the probabilities vary depending on the starting pitching.
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Old 11-02-2019, 01:41 AM
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But it is also not realistic, since teams don't have winning percentages as much as pitchers do. So the probabilities vary depending on the starting pitching.
I was surprised that the linked article didn't make as big of a deal about pitchers as I would have. The entire game of baseball revolves around the pitcher, and even if teams are evenly matched in the abstract, they will have different quality pitchers who will by more or less effective against the opposing hitters, and so one team would have an advantage each game. By nature of being evenly matched in abstract, these factors must balance out, so it would manifest in there being a greater chance of each side winning equal amounts than compared to each game being a coin flip.
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Old 11-02-2019, 10:03 PM
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Quote:
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But it is also not realistic, since teams don't have winning percentages as much as pitchers do. So the probabilities vary depending on the starting pitching.
No - pitcher win/loss records are mostly meaningless, especially in any individual season. I'll take a team's winning percentage as an indication of future performance well before any particular pitcher's.
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