The Red Sox were definitely not a middling/bad team before that. They were simply the red-headed stepchildren to the Yankees. The wild card was effectively created for the Red Sox & Yankees so that both could make the playoffs every year, and the strategy worked. They've gobbled up the lion's share of those WC's in their respective leagues when they didn't make the playoffs outright. But the Red Sox were a perennial top team who were most famous for "the Curse". They weren't by any means the Cubs (who just manage to just generally suck year in and year out).
And they had the Bucks at like $300-$350 million. They sold for $550 million. Then there was Brooklyn. It's been this way for years. At this point, when I look up the valuation of a sports franchise by mainstream sources, I just tack on 50% to whatever estimate they make, and assume that's the minimum.