That's part of the point I mean about not giving enough credit to analysis. These people are supposed to be super geniuses who are impressing everyone with their work. But those super geniuses missed some pretty basic concepts.
I don't know a lot about statistics, but what I do know is that it can't predict the future. It can only accurately predict the probability of something happening. I good prediction model does take into account the miraculous and unusual and assigns a percentage chance of them happening.
When they went beyond the end of the war to multiple generations down the line revolting, that was pretty absurd. And it makes statistical analysis itself look like some sort of useless voodoo.
I don't find it a problem that Bashir could get behind properly done statistical analysis, but the way it's presented here doesn't seem properly done. And credibility of the characters presenting it doesn't help either.
Another minor issue with the episode is that the set-up is rather unbelievable, Dukat and Sisko being on the same ship, travelling on its own near the Cardassian border, then they escape together to a habitable planet as two of only a handful of survivors? It's a bit outlandish.
As Dukat recounted the events that lead him and Sisko to be conveniently marooned together, I kept thinking of Zap Brannigan tricking Leela into thinking they were crash landed on another planet and he had saved her. After getting past my amusement at the thought of Dukat attempting to woo Sisko, I realized that's pretty much what he's doing. He's not trying to woo Sisko romantically, but his main goal is to get Sisko to like him.
Since the situation is so disbelievable, I also wonder whether Dukat was telling the truth about how he and Sisko go there. What if the 3rd guy wasn't accidentally killed? What if Dukat killed him or just left him behind?
I kind of wish the Defiant scenes had been used to give a sense of believability to the situation by doing something like showing the rest of the crew had survived and implying Dukat had purposely taken his escape pod as far from the others as he could or purposely found a place sensors wouldn't detect them on the same planet as some of the others. Even so, I can still get past it.