Remember Me?

 Straight Dope Message Board Remember Me?

#1
10-31-2019, 01:36 PM
 Guest Join Date: Jan 2004 Posts: 2,631

## 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.

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?
#2
10-31-2019, 02:28 PM
 Charter Member Join Date: Apr 1999 Location: Maryland Posts: 40,031
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.
#3
10-31-2019, 02:37 PM
 Guest Join Date: Oct 2007 Location: rhode island Posts: 41,200
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.
#4
10-31-2019, 02:41 PM
 Guest Join Date: Dec 2014 Posts: 1,651
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?
#5
10-31-2019, 02:50 PM
 Guest Join Date: Oct 2007 Location: rhode island Posts: 41,200
Quote:
 Originally Posted by Tired and Cranky 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.
#6
10-31-2019, 02:51 PM
 Guest Join Date: May 2018 Posts: 247
Quote:
 Originally Posted by Tired and Cranky 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.
#7
10-31-2019, 02:51 PM
 Guest Join Date: Oct 2007 Location: rhode island Posts: 41,200
Quote:
 Originally Posted by TriPolar 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.
#8
10-31-2019, 03:02 PM
 Guest Join Date: Dec 2000 Location: temperate forest Posts: 7,218
Quote:
 Originally Posted by TriPolar 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.
#9
10-31-2019, 03:03 PM
 Member Join Date: Sep 2009 Posts: 4,755
Quote:
 Originally Posted by gdave 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 haven’t even had the home team lose the first 6, let alone all 7.
#10
10-31-2019, 03:10 PM
 Guest Join Date: Oct 2007 Location: rhode island Posts: 41,200
Quote:
 Originally Posted by Quercus 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.
#11
10-31-2019, 03:38 PM
 Guest Join Date: Mar 2000 Location: Parts Unknown Posts: 22,266
Quote:
 Originally Posted by RTFirefly 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%?
#12
10-31-2019, 03:51 PM
 Charter Member Join Date: May 2000 Location: Lincoln, IL Posts: 27,891
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?
#13
10-31-2019, 06:53 PM
 SD Curator of Critters Moderator Join Date: Oct 2000 Location: Panama Posts: 43,612
Here's an analysis from 2003, updated in 2014, on Are 7-Game World Series More Common Than Expected?
#14
11-01-2019, 04:17 PM
 Guest Join Date: Dec 2014 Posts: 1,651
Thanks TriPolar and gdave!
#15
11-01-2019, 07:06 PM
 Member Join Date: Mar 2002 Location: Trantor Posts: 13,231
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.
#16
11-02-2019, 01:41 AM
 Guest Join Date: Aug 2008 Posts: 2,223
Quote:
 Originally Posted by Hari Seldon 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.
#17
11-02-2019, 10:03 PM
 Guest Join Date: Mar 2000 Location: Parts Unknown Posts: 22,266
Quote:
 Originally Posted by Hari Seldon 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.

 Bookmarks

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is Off HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Main     About This Message Board     Comments on Cecil's Columns/Staff Reports     General Questions     Great Debates     Elections     Cafe Society     The Game Room     Thread Games     In My Humble Opinion (IMHO)     Mundane Pointless Stuff I Must Share (MPSIMS)     Marketplace     The BBQ Pit

All times are GMT -5. The time now is 08:15 PM.

 -- Straight Dope v3.7.3 -- Sultantheme's Responsive vB3-blue Contact Us - Straight Dope Homepage - Archive - Top

Send questions for Cecil Adams to: cecil@straightdope.com