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## Friday, August 10, 2012

#### Pollis: The Mathematical Improbability of Cleveland’s 11-Game Losing Streak

Which is about the same as Lou Camilli going 0 for his first 34 with the Indians, I guess.

Take an average baseball team and let them play 11 games, and the binomial distribution says the chances of them going 0-11 are 0.00049. That’s a 1 in 2,048 chance. If you were to flip a coin 11 times every day and count the number of tails (it’s the same idea if we’re discussing a true-talent .500 team), you’d get 11 heads and no tails only about once every six years.

Okay, but that’s a .500 team; the Indians clearly aren’t that good. So what if we use their current 51-60 record? With a winning percentage of .459, the Tribe’s chances of losing 11 out of 11 are…0.1 percent. That’s a 1 in 869 chance—more than double the odds for a .500 team, but still pretty darn low.

But the Indians have been playing really poorly lately, so perhaps even that’s too generous. What if we call the Tribe a 100-loss true-talent team? It takes a .383 winning percentage to achieve that level of infamous immortality. A 62-100 team would still win at least one of 11 games 99.5 percent of the time. You’d have a 1 in 203 chance of seeing them go 0-11.

...What would it take for a team’s losing 11 straight to be not just possible but probable? For a team to have a greater chance of losing 11 games than winning at least one, its true-talent winning percentage would have to be no better than .061. Such a team would finish with a 10-152 record (yes, you read that correctly). Which is, of course, absolutely ridiculous. Say what you want about how bad the Indians are or how poorly they’ve played or how this always happens to Cleveland sports teams, but snark and sarcasm aside they are not a historically bad team.

Managing to put together an almost statistically impossible losing streak isn’t something to be proud of (I have a lot of feelings about it, but “pride” definitely isn’t up there). But unless you honestly think that this Indians team is worse than the ’62 Mets, then the Tribe’s 11-game losing streak really is pretty incredible. Maybe that will take the sting out.

Repoz Posted: August 10, 2012 at 01:51 PM | 32 comment(s) Login to Bookmark
Tags: indians, sabermetrics

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1. McCoy Posted: August 10, 2012 at 02:01 PM (#4205397)
How often have teams had an 11 game losing streak or worse? Now compare that to how many possible streaks there can be in a season.
2. McCoy Posted: August 10, 2012 at 02:11 PM (#4205407)
From 2002 to 2011 there have been 67 11 game losing streaks. In a 162 games schedule there are 152 sets of 11 games. Assuming all teams played 162 games gives us 4,860 11 game streaks per year. So .14% of all 11 game streaks resulted in a 11 game losing streak.

edit: So I went back and looked and MLB played 22 less games than scheduled so that drops it down to 48,578 streaks and a slightly higher .14%.
3. rombuu Posted: August 10, 2012 at 02:12 PM (#4205410)
As a Royals fan I just assumed every team had an 11 game losing streak every year.
4. Chris Needham Posted: August 10, 2012 at 02:21 PM (#4205424)
Pretty sure Manny Acta is contractually obligated to lose at least 11 in a row each year, as some sort of performance incentive.
5. McCoy Posted: August 10, 2012 at 02:22 PM (#4205427)
So if those % are an accurate reflection of how often this should happen then this year we should have seen 4 such streaks already. We've seen 7 so far this year.
6. Fernigal McGunnigle Posted: August 10, 2012 at 02:32 PM (#4205439)
edit: So I went back and looked and MLB played 22 less games than scheduled so that drops it down to 48,578 streaks and a slightly higher .14%.

And so the binomial distribution tells us that this means that the average team has a true talent of .449, or about 73-89.

EDIT: Or that MLB as a whole has a true talent of .449, or whatever. I'm being flip.
7. Misirlou doesn't live in the restaurant Posted: August 10, 2012 at 02:37 PM (#4205449)
From 2002 to 2011 there have been 67 11 game losing streaks. In a 162 games schedule there are 152 sets of 11 games. Assuming all teams played 162 games gives us 4,860 11 game streaks per year. So .14% of all 11 game streaks resulted in a 11 game losing streak.

edit: So I went back and looked and MLB played 22 less games than scheduled so that drops it down to 48,578 streaks and a slightly higher .14%.

We've done this before, with batting streaks. The problem is that you really don't have 152 chances to have an 11 game losing streak. In actuality it's much less. If you have a 7 game losing streak and then win one, you've eaten up 8 of your mythical 152 chances in one go.
8. escabeche Posted: August 10, 2012 at 02:40 PM (#4205451)
And so the binomial distribution tells us that this means that the average team has a true talent of .449, or about 73-89.

Maybe he just did the National League.
9. McCoy Posted: August 10, 2012 at 02:47 PM (#4205459)
If you have a 7 game losing streak and then win one, you've eaten up 8 of your mythical 152 chances in one go.

How does that make 152 chances mythical?
10. Misirlou doesn't live in the restaurant Posted: August 10, 2012 at 02:53 PM (#4205466)
How does that make 152 chances mythical?

You lose game one of the season, so you've started a streak. The you lose game 2. That's a continuation of your first streak, not a new one. Then you lose games 3-9, and then win game 10. So your first attempt ended in "failure". But at that point, you don't have 151 more chances.

Hell, even if you lose game 1 and win game 2, thus failing in your first attempt. Starting in game 3 you have only 150 more chances, not 151.

edit: so to answer directly, it's mythical because the only way to have 152 chances is if you win your first 151 games of the season.
11. Never Give an Inge (Dave) Posted: August 10, 2012 at 02:57 PM (#4205472)
From 2002 to 2011 there have been 67 11 game losing streaks. In a 162 games schedule there are 152 sets of 11 games. Assuming all teams played 162 games gives us 4,860 11 game streaks per year. So .14% of all 11 game streaks resulted in a 11 game losing streak.

Does this count a 12-game losing streak (assuming there have been any) as two 11-game losing streaks? Because obviously those two chances are not independent of each other. Which I think gets at what #7 is talking about [EDIT: although now I am not sure after reading #10].

Also, for those who can figure this out, how many 11 game winning streaks have there been?

EDIT #2: removed a sentence because of bad statistics.
12. Misirlou doesn't live in the restaurant Posted: August 10, 2012 at 03:00 PM (#4205474)
Does this count a 12-game losing streak (assuming there have been any) as two 11-game losing streaks? Because obviously those two chances are not independent of each other. Which I think gets at what #7 is talking about [EDIT: although now I am not sure after reading #10]. You theoretically have 152 chances per season, but they are not independent events. A single loss spoils it for 11 different chances.

Yeah, there's that too.
13. McCoy Posted: August 10, 2012 at 03:00 PM (#4205476)
Hell, even if you lose game 1 and win game 2, thus failing in your first attempt. Starting in game 3 you have only 150 more chances, not 151.

Winning in game 2 doesn't just make you fail your first chance but it also makes you fail in your second chance. You've played two games and have a win in your second game. You now have 150 chances to lose 11 games in a row. I'm still not seeing how 152 chances is mythical.

If 152 chances is mythical what are the true amount of chances per season for a team?
14. The usual palaver and twaddle (Met Fan Charlie) Posted: August 10, 2012 at 03:00 PM (#4205477)
The '62 Mets lost 17 straight at one stretch. Put that in your odds and smoke 'em...
15. McCoy Posted: August 10, 2012 at 03:05 PM (#4205483)
Apparently I screwed up since PI includes multiseason streaks. There have been 63 11 games losing streaks (with 11 being exactly 11). So that comes to .13%.
16. Misirlou doesn't live in the restaurant Posted: August 10, 2012 at 03:09 PM (#4205488)
There have been 63 11 games losing streaks (with 11 being exactly 11). So that comes to .13%.

But does that count the 12 game streaks as 2 11's? And the 13's as 3 11's. And so forth. If not, then the percentages will be much much higher. That's why the 152 chances are mythical.
17. McCoy Posted: August 10, 2012 at 03:10 PM (#4205490)
But does that count the 12 game streaks as 2 11's? And the 13's as 3 11's. And so forth. If not, then the percentages will be much much higher. That's why the 152 chances are mythical.

Why? I'm not looking at the odds that a team will lose exactly 11 games. I'm looking at the odds that a team will lose 11 in a row at some point. And again if 152 chances is mythical what is the right amount of chances?
18. Never Give an Inge (Dave) Posted: August 10, 2012 at 03:10 PM (#4205491)

Have there been 63 streaks of 11-or-more losses? Or have there been 63 sequences of LLLLLLLLLLL? You don't want to count a 12-game losing streak twice, but you do want to count it at least once.
19. Joey B. is counting the days to Trea Turner Posted: August 10, 2012 at 03:12 PM (#4205494)
The Orioles of course famously lost their first 21 games in '88, but I THINK the '61 Phillies still have the all time record with their incredible 23 in a row.
20. Never Give an Inge (Dave) Posted: August 10, 2012 at 03:13 PM (#4205497)

There are 152 chances, you just can't treat them as independent.
21. Misirlou doesn't live in the restaurant Posted: August 10, 2012 at 03:20 PM (#4205512)
There are 152 chances, you just can't treat them as independent.

Yeah, I guess that's what I was getting at. Without saying, or even realizing it, my point was there aren't 152 independent chances. a 12 game losing streak is a 12 game losing streak, not 2 11's. For a team, the chances of losing 11 in a row, and then losing the next game to make two 11 game streaks, are not remotely the same. For a true talent .500 team, the odds for the former is (using the odds from the excerpt), are .049%. For the latter it's 50%.
22. TomH Posted: August 10, 2012 at 03:26 PM (#4205523)
It's highly improbable that the particular person who won the lottery last week should have won the lottery. Ergo math is wrong. Except for batting averages, and Jack Morris' game 7 clutchiness.
23. McCoy Posted: August 10, 2012 at 03:28 PM (#4205525)
I never made the claim that there are 152 independent chances.
24. Misirlou doesn't live in the restaurant Posted: August 10, 2012 at 03:31 PM (#4205529)
And again if 152 chances is mythical what is the right amount of chances?

As for this, it depends. It's not a question that can be answered a priori. It depends on the distribution of wins and losses, with a lower bound I suppose of 14 (a team which loses 10 and then wins 1, loses 10, wins one... for the entire season), and an upper bound of 152 (the afore mentioned 151-0 team).
25. Misirlou doesn't live in the restaurant Posted: August 10, 2012 at 03:34 PM (#4205535)
I never made the claim that there are 152 independent chances.

Perhaps, but you're treating them as independent in #2.
26. Never Give an Inge (Dave) Posted: August 10, 2012 at 03:35 PM (#4205537)
.
27. void*** (SC) Posted: August 10, 2012 at 03:39 PM (#4205540)
Teams are not created equal, a 60-win team have much bigger chance of pulling off a 11-loss streak than a 100-win team.

An equal mix of 61-win teams and 101-win teams have about 8 times more 11-loss streaks than a group of 81-win teams.

EDIT: My point is that approximating the win probability with 50% is going to be wrong by orders of magnitude (one here, if you got the Astros in the league, more).
28. Curse of the Andino Posted: August 10, 2012 at 11:45 PM (#4205925)
The Orioles of course famously lost their first 21 games in '88, but I THINK the '61 Phillies still have the all time record with their incredible 23 in a row.

1899 Spiders lost 24 in a row.

/I was there in '88, so we were wondering if we might just get that record.
29. Voros McCracken of Pinkus Posted: August 11, 2012 at 03:47 AM (#4206005)
That 1899 Spiders team is probably one of the more important individual teams in baseball history and I think would make a fantastic movie.
30. PepTech Posted: August 11, 2012 at 04:16 AM (#4206007)
I know I tried to erase it from my memory, but I seem to recall the Mariners losing 17 straight last July. When it started they were at .500.
31. Sunday silence Posted: August 11, 2012 at 04:20 AM (#4206009)
can some of the statistics guys here tell me if the Reds are ever going to lose another game??
32. something like a train wreck Posted: August 11, 2012 at 09:18 AM (#4206041)
My math ends with arithmetic, but if you define "success" as an 11th consecutive loss, every win eliminates the next 10 possible successes. (If you are looking only for exactly 11 losses, not 12 ..., then the 11th loss has the same effect.) No therefore, it is just clearer for me to frame the problem that way.

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