I have to issue a mea culpa here - in light of further evidence presented by Bruce in the comment thread to my last post on Tony Esposito, I think it is clear that Esposito did play poorly in the playoffs in the early 1970s and most likely contributed to his team's underachieving playoff record. The key here is the contrast between Chicago's record against Boston and Montreal in the regular season and in the playoffs:
Chicago vs. Boston and Montreal in the regular season (1970-1974)
25-24-11, 175 GF, 177 GA
2.92 goals per game
2.95 goals against average
Chicago vs. Boston and Montreal in the playoffs (1970-1974)
7-16, 71 GF, 101 GA
3.09 goals per game
4.39 goals against average
Boston and Montreal were both outstanding offensive teams, but something must have gone very wrong with Chicago for them to allow that many extra goals compared to their seasonal rates. The Hawks were good enough to hold their own during the regular season, but were shellacked in the playoffs 4 times in 5 years. I doubt this was entirely Esposito's fault, but given that unusually high GAA number it is hard to see how he couldn't have contributed to it.
We have one season of save percentage data from the early 1970s (1971), where the numbers indicate that Esposito faced an average of 28 shots per game. Let's say that Chicago allowed an average of 30 shots per game in their regular season games against Boston and Montreal, since they were strong opponents. That would put Esposito at a .902 save percentage, which according to the Hockey Analysis Group was the average save percentage from 1970-1974. Even if Chicago was badly outplayed in the playoffs and allowed an extra 10 shots per game against the same opponents, Esposito's save percentage would still drop to a mediocre .890. If they allowed an extra 5 shots per game, he would be at .875, and if he was still facing the same 30, the stat would be a horrific .854. Of course Esposito didn't play all of those games and there may be some empty netters involved, but the numbers indicate that the goaltending was probably subpar.
Later in his career, Esposito's teams were weak and didn't provide much goal support, which is why he suffered through a string of playoff sweeps and early exits. But the early 1970s Blackhawks were Cup contenders, and could have won a Cup or two with strong goaltending. Esposito had some great games (2nd in playoff shutouts during the period) and series (Chicago twice upset strong Rangers teams), but never played well for an entire series against Boston or Montreal, which is where the Blackhawks repeatedly saw their Cup dreams dashed.