David Richard-US PRESSWIRE

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

Something amazing happened Wednesday: the Cleveland Indians won a game. For the first time in almost two weeks, the ninth inning ended and the Tribe had the lead. The win snapped the Indians’ losing streak at 11 games as they avoided getting swept for the fourth consecutive series. The 2012 season is almost certainly lost now, but boy was it a relief to see Cleveland actually pull one out.

But, unbelievable as the win felt after roughly a fortnight of consecutive failures, the Indians have now accomplished another feat that is actually far more incredible: Losing 11 games in a row.

Rick Osentoski-US PRESSWIRE

It’s easy to roll your eyes and sigh. Sports is synonymous with misery for most Clevelanders, and the Indians have played poorly for more than a month now. Some overly jaded fans probably think that dropping almost a dozen games in a row was inevitable. But it’s not. In fact, the odds of a losing streak lasting this long are so small it’ll knock your socks off.

The odds that a team will win a given number of games in a given number of opportunities can be expressed via the binomial probability distribution. The binomial distribution is a basic function that calculates the chances that a sample of n independent trials with p odds of success each time will end up with x successes. One can perhaps quibble the idea that games are independent trials (i.e., that the outcome of the first game has no predictive power for the result of the second game beyond the pre-established value of p), but this is pretty basic statistics. Nothing controversial or ambiguous.

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.

Let’s turn to the worst team since World War II and everyone’s go-to example of a completely hapless ballclub: the 1962 New York Mets. Maybe we’re just as bad as them? (Cleveland’s record is way better than the infamous Mets’ 40-120 standing, but skeptical Tribe fans can be prone to exaggeration.) But even a team with a .250 winning percentage would have just a 4.2 percent chance (1 in 24) of losing 11 straight.

How bad would a team have to be for a slide like Cleveland’s to be a realistic possibility? A general rule of thumb for statistical significance is 5 percent. The best true-talent winning percentage a team could have to reach that threshold is .238. Such a team would go 39-123 over a full season, the worst record since the Philadelphia Athletics went 36-117 in 1916.

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.

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Tags: Cleveland Indians

  • Guest17

    I think you are leaving out an important part of the equations. Teams have multiple opportunities to go 0-11 every season. For a sufficiently long season (which the current 162 game season is not even close), it actually becomes unlikely a good team won’t go 0-11 at some point.

    Still, I agree that the losing streak is less indicative of the team’s true talent level and more indicative of the team’s luck. I mean, losing Sizemore, Hernadez’s identity troubles, Chisenhall’s season ending injury, etc. Why not an 11 game losing streak to just make the point absolute? I think we are at the point where we can say random chance disfavors the Indians, even if that is paradox.

    • http://twitter.com/LewsOnFirst Lewie Pollis

      Of course. My point was just to demonstrate the unlikelihood of a team going 0-11 in a given 11-game sample size, not over the course of the season. Obviously the odds are much higher over the course of the season.

    • Matthias_Kullowatz

      Since I have nothing better to do…

      I ran a simulation of an average baseball team playing 1000 consecutive seasons, and I recorded each losing streak. Here is a summary of the results.

      Longest losing streak: 14 (.004 per season)
      Streaks of 11 or more losses: 48 (.048 per season)
      Streaks of 5 or more losses: 2562 (2.56 per season)

      How about a team that wins 45.9% of its games?

      Longest losing streak: 16 (.002 per season)
      Streaks of 11 or more losses: 80 (.08 per season)
      Streaks of 5 or more losses: 3490 (3.49 per season)

      It is still very hard to lose 11 in a row!

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