As you may have heard, a certain team recently ended a World Series drought of 108 seasons. In a clash of two historically unfortunate teams, the Chicago Cubs ended their record-setting (across all sports, even) streak of futility. And like I wrote about it at the time, this World Series was a historic meeting that will remain at the top of its category for some time. It's mathematically guaranteed until 2047, at the very least. And even in just comparing the misfortunes of individual teams, the Cleveland Indians have another four decades until they match where the Cubs just were. Even the second-longest drought of all time, that of the Cubs' crosstown rivals the White Sox, fell two decades short. It seems like such an outlier in all regards, doesn't it?
Yes, it will be sometime before we see another World Series drought in similar length to the Cubs'...but it is almost guaranteed to fall, and probably sooner than you would first believe. Even that record-setting 174 years of combined drought in World Series competitors is probably less safe than it seems like it should be, and could very likely fall within your lifetime. Historic droughts are going to start becoming more common; it's really just a simple question of math.
Just think of the question as a basic algebra question. There are currently 30 teams in Major League Baseball, so let's give them each a given probability of 1/30 for winning it all in any given year, or approximately 3.33% if you prefer it in percentage form. That might seem overly simplistic; you wouldn't give, say, the Cubs and the Braves equal chances in 2017. But if we take a long-term view of things, the odds even out pretty well. We have zero clue what the 2026 versions of either team will look like, so just assigning every team a 1/30 probability is probably a reasonable assumption.
Conversely, that would mean that any team has a 29/30 chance of not winning in a random year, or 96.67%. Now, if we wanted to see the odds of a team not winning in either year one or year two, we'd just multiply the probability of not winning in either year, or 29/30^2. That gets us to a 93.44% chance of a given team not winning in either of two seasons in a row.
So let's extrapolate from there. The chance of a given team not winning for 100 years in a row would be 29/30^100, which works out to about 3.37%. If your first reaction to that might be "that's not so bad", compare that to the initial 1/30 odds. That means there is a (marginally) better than 1-in-30 chance of a team going a century without, which, given that there are currently 30 teams, means that you would expect (on average, if you could set it up like an experiment and run it a bunch of times) at least one to go 100 straight seasons without winning it all.
And that's just using the most simplistic view of the problem. In real life, we have several confounding factors to deal with. For example, not every team is going in to every season with 1/30 teams; a team that gets saddled with below-average management will see even worse odds for some years in that stretch. Additionally, Major League Baseball isn't done expanding just yet. We've been hearing some rumblings of possible new teams for a little bit now, which makes sense given that 1998 (the last season with new teams) to the present represents the longest the league has gone without growing since the initial 1961 expansion. As soon as we hit 32 or 34 or more teams, each individual team's odds will continue to drop.
On top of that, each team isn't starting at the same place. If we had thirty brand new teams in a hypothetical competitor league start this season, we'd (on average) expect one to have a barren century. But not all MLB teams are starting at zero. The Indians, as mentioned, would only need to go four more decades to match the Cubs, which works out to just over a one-in-four chance (25.77%). The Rangers and Astros, at 56 and 55 respective years without a championship, come in at just under one-in-six, and then there's a trio of teams approaching the half-century mark on top of them.
That's not to say that they'll be quite as...extraordinary as the Cubs' streak. After all, the Cubs pulled off half of that in a pre-expansion era of only sixteen teams. A "mere" fifty years of not winning with 1/16 odds (6.25%) is actually roughly as likely as not winning for a hundred years in a thirty-team league, so any future "hundred-year rebuilding plans" won't have been as statistically improbable as the Cubs' recently-ended one unless the new team eclipses their mark in length. Of course, I'm sure that fact will do a lot to comfort whichever team's fans finds themselves on the wrong end of a century of ultimately coming up short.