An unremarkable century

Which of these is least likely:

A) The Cubs’ current 100-year long championship drought, the longest such drought ever;
B) The Cubs’ current 63-year long championship game/series drought, the longest such drought ever;
C) The Rangers’ franchise-long avoidance of the “Final Four,” the longest drought ever in MLB and second-longest among the sports (the NFL’s Arizona Cardinals are at 60 years); or
D) The Nationals’ avoidance of the playoffs since 1981, not historical by any means?

The math

Much has been made of the Cubs making it a century without sitting on top of the world, but what were the odds of that happening, or more precisely, what were the odds that any franchise would make it from 1909-2008 without a title? The answer lies in binomial distributions, which Dave Studeman used here recently.. In easyish terms, binomial distributions track outcomes of an event; if there’s a 1 in X chance of something happening out of event A, and A happens Y times, what’s the chance I’ll get a certain amount of X? The easy example is coin flips: if I flip a coin 100 times, what are the odds I’ll get heads 100 times, or 57, or 42?

All the results below are from a series of binomial distributions, and I had to do a number of refinements to reflect everything just right, but the procedure is the same for the Cubs question. From 1909-1960, the basic odds of any team winning a championship was 1 in 16 (1 in 8 chance of getting to the postseason, and then a “coin flip” to determine the winner of the postseason series). In 1961, it was 1 in 20 for the AL (10 teams and a coin flip) and 1 in 16 for the NL (8 teams and a coin flip), reverting to 1 in 20 for everyone when the Astros and Mets joined.

Every postseason round adds a coin flip to the equation. Starting in 1969, teams 1969 had a 1 in 6 chance of making the postseason, but it took two coin flips (making it to the Series, THEN winning it) from there. Because of league and division sizes, NL teams were slightly more favored to win championships from 1977-92, when the league was smaller than the AL; they’re slightly disfavored now, and the NL Central has it worst because of division size. For NL Central teams, odds of making the playoffs are 1/6 (division title) plus 1/13 (wild card for the remaining teams), or 24.36 percent. In the AL West, however, it’s 1/4 plus 1/11, or 34.09 percent. Add the three coin flips to the mix, and the Mariners theoretically have a 4.26 percent chance every year of winning the World Series, while the Cubs have a 3.04 percent chance. These sorts of handicaps that heavily influence odds over a long period of time, as we’ll see from…

The results

If you work with all that math, the Cubs had a .50 percent chance of going titleless from 1909-2008; the Cardinals, Reds, and Pirates also possessed the same chance. The original eight AL teams are at .53 percent, except the A’s, whose residence in the 4-team West reduced the chances to .48 percent.

If you’re a Cubs fan, at this point you’re saying, “the odds were 1 in 200 they’d do this? We’re definitely cursed.” But that doesn’t answer the bigger question: what were the odds that any one of the 16 franchises from 1909 would get to here without a title? To calculate that, I took a binomial distribution off the distribution that yielded the .50 percent for the Cubs. We know the odds are .50 percent for the Cubs failing to win 99 tries in a row (not 100 due to 1994), so if you call “failing 99 times in a row” the event at .50 percent odds and try it 16 times — just like rolling a 200-sided die 16 times to try to get a 200 — what are the odds?

Well, they’re better than they seem — 7.80 percent. That doesn’t make it sound great — after all, in 92 percent of possible outcomes, the Cubs would have a title — but it’s the most likely of choices A-D above, and it’s not even close. (What was highly unlikely, however, was the White Sox and Red Sox having similarly long streaks at the same time; the odds of three franchises going from 1919 to 2003 without a title were .07 percent, though it was about a 17 percent chance that any franchise would.)

It’s not even the least likely Cubs-related drought. That the Cubs haven’t been to the World Series for 63 years is far less likely, coming in at .26 percent for the Cubs and 4.11 percent for any of the 16 franchises. This result is intuitive; if a team is twice as likely to make the World Series as they are to win it, then the odds of getting there over 50 years should be the same as winning it over 100 years. As it’s been longer than 50 years, however, this streak was harder to do.

The Expos/Nationals’ streak is even more “impressive” than the Cubs’ two streaks. Any of the 26 teams could have missed the playoffs completely from 1982-2008; the odds of the Nationals missing were .12 percent and any team missing were 3.24 percent. Given that the odds of them making the playoffs under the current system is greater than 1 in 4 every year, that’s pretty amazing. Then again, the ’94 die roll was looking good until it fell off the table and they had to reroll.

(While we’re here…Brewers fans have every right to complain about league structure. Compared to AL West teams since 1982, they were five times more likely to miss the playoffs completely and over twice as likely as the Nationals. Because of their league-switching, they’ve never been in the smaller of the two leagues, and now they’re in the largest division too. That’s gotta stink.)

But none of that compares to what the Rangers have done. If you count just the divisional era, it was a .14 percent chance that the Rangers would do it and 4.08 percent overall — not likely, but relatively high for this article. However, when you add in the first eight years of their existence (which seems unfair, but the Angels sniffed a pennant or two in that time), the odds of them missing out on the playoffs from 1961-93 and the ALCS from 1995-2008 are a staggeringly low .05 percent for the Rangers and 1.20 percent for the 18 teams existing in 1961. Part of it is how much of an advantage the AL West gives its members; every year the Rangers theoretically have a 17 percent chance of making the ALCS (slightly better than rolling a 6-sided die and getting a 6) and they don’t even come close.

To put it another way, through 1950 there were 47 World Series, or as many World Series as the Rangers have had years to make the final four. In that time, every franchise but the Browns had appeared in the Series twice, and even getting there once was harder to do than the Rangers’ odds of making the ALCS have ever been. I’ve never heard of Rangers fans getting up in arms about how miserable their team’s performance has been historically, maybe because it includes some Senators years, but the Rangers have outdone two Cubs streaks in terms of futility.

The implication and vaguely grim-sounding prophecy

If you’re a non-Cubs fan and are smug that your team doesn’t have a drought that long, don’t be so confident. The current setup of 30 teams and their given odds yields a 58.43 percent chance — majority odds — that at least one team will go a century without a title. There’s a 37.03 percent chance that it will be just one, but a 15.94 percent chance that two will suffer like the Cubs and a 4.42 percent chance it will be three. That’s right; it is twice as likely that two teams will not win the World Series in the next 100 years as it was for the Cubs not to in the previous 100, primarily because there are just so many teams. The Cubs themselves have a 4.54 percent chance of adding another century to their run, as the league structure is against them; that’s nine times greater than their odds of having a first century of futility. Whatever MLB will do to promote competition, it had better work, because left to the whims of fate and statistics, the Cubs’ fate will happen again.

References & Resources
Thanks to Dave for thinking through this with me.

Just so you don’t have to scroll back through this, the odds of the different happenings:

Team not winning the World Series from 1909-2008: 7.80 percent.
Team not winning the World Series from 2009-2108: 58.43 percent.
Team not getting to the World Series from 1946-2008: 4.11 percent.
Team not getting to the World Series from 1961-1968 and then not getting to an LCS from 1969-2008: 1.20 percent.
Team not getting to an LCS from 1969-2008: 4.08 percent.
Team missing the playoffs every year from 1982-2008: 3.24 percent.

Because of the nature of baseball playoffs and because MLB’s been around so much longer in its present form than the other major leagues (the modern NFL, NHL, and NBA are all the same age as the Angels or younger), most of the longest playoff/championship droughts belong to baseball. Here are some various top five lists to put some stuff in context. In each case I’m listing the consecutive years missed, not from title to title, so the years might look a little bit different than you’d expect. Also, for NHL and NBA figures, I used the starting year of the season, so if you’re looking at these teams anywhere else, add 1.

Top 5 Historical Championship Droughts
Cubs                1909-          100
White Sox           1918-2004       87
Red Sox             1919-2003       85
Phillies            1903-1979       77
Orioles             1903-1965       63

Top 5 Active Championship Droughts
Cubs                1909-          100
Cardinals (NFL)     1948-           62
Indians             1949-           60
Kings (NBA)         1951-           58
Giants              1955-           54

Top 6 Historical (also Active) Finals Droughts (World Series, Super Bowl, etc.) 
Cubs                1946-           63
Cardinals (NFL)     1949-           60
Kings (NBA)         1951-           58
Lions (NFL)         1958-           51
Hawks (NBA)         1961-           48
Rangers             1961-           48

Top 7 Historical Missing the Final Four (LCS, Conference Final, etc.)
Cardinals (NFL)     1949-           60
Rangers             1961-           48
Indians             1955-1994       40
A's                 1932-1970       39
Cubs                1946-1983       38
Saints (NFL)        1967-2005       38
Hawks (NBA)         1970-           38

Top 5 Active Missing the Final Four
Cardinals (NFL)     1949-           60
Rangers             1961-           48
Hawks (NBA)         1970-           38
Clippers (NBA)      1970-           38
Warriors (NBA)      1976-           33
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