I did good and better/best, so I might as well do bad and worse/worst.
Now, badder isn’t really a word, but clearly baddest is or we wouldn’t have a description for Shaft. But apparently Shaft-describing is the only vestige of what were once real words. Either because they were disliked or just colloquialisms, badder and baddest haven’t been in use for at least three hundred years. Bad itself showed up in the early thirteenth century, first just meaning inferior, then also meaning evil although the latter definition didn’t catch on for another hundred years. It’s thought to come from the Old English insulting term baeddel, which means…well, it’s a derogatory word, let’s just leave it at that.
Like I said, badder and baddest once were the comparative forms of bad. Worse and worst were just more popular. Worse comes from the Old English wiersa/wyrsa, the Proto Germanic wers-izon, and can even be traced to the Proto Indo European wers, which actually means to mix up. Worst has a similar lineage, coming from the Old English wyrresta and Proto Germanic wers-ista and, like worse, the word wers.
Unfortunately, there isn’t much info about why worse and worst were more popular. However it might have something to do with how bad didn’t initially mean evil, but worse and worst did. I’m sure this mess definitely has to do with the fact that English is a language where we all just pick the words we like to say, screw “definitions”.
Tony Jebson’s page on the Origins of Old English