The Cubs last won the World Series in 1908, 107 years ago. The Curse of the Billy Goat could be to a blame, bad management could be responsible, or the club has just consistently gotten unlucky (which could be interpreted as being caused by the curse, that's up to you/Cubs fans). However, it's really hard to win a World Series - so is 107 consecutive years an extremely unexpected drought?
It would make sense to approximate a team's chances at winning it all in a given season by simply giving them a 1 in n chance, with n being the number of teams in the league. This isn't all that straight-forward of a calculation, since MLB has expanded multiple times in the past century (so it's not just (1/30)^107). Since there used to be fewer teams (and thus 1 in n was higher), the resulting figure is very low that the Cubs would go that long without winning the title: 0.41%.
However, there's an even more unlikely event that's occurred during that time span: the Cubs not winning the National League. In this case, the last time they won the pennant was 1945, 70 years ago. There is only a 0.17% chance that they would never win the NL in that span. Of course, the infamous Bartman incident in 2003 contributed to this, and those probabilities are so low... maybe the Cubs really are cursed.
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