Someone brought this up in the ATD chat thread, but posting this here for more visibility.
I really struggle in evaluating Bathgate's playoff career. I'm not sure if there's any other Top 100 player who has such an ambiguous record.
The Rangers were terrible during Bathgate's decade on Broadway. They wasted his prime. They only qualified for the playoffs four times during Bathgate's tenure. Three of those matchups were against vastly superior teams (Montreal twice - who finished 26 and 16 points ahead; and the Leafs once - who finished 21 points ahead). That meant the Rangers were huge underdogs. It's reasonable to assume that the Habs/Leafs spent most of their effort trying to contain Bathgate, who was by far New York's best player. It looks like it worked - he was held to just 8 points in 16 games during those three series. How much of that is due to Bathgate being inherently a poor playoff performer, and how much is due to him being the sole star, in very lopsided series? (Not that this is a welcome comparison, but it sounds like a Marcel Dionne situation).
One thing that helps Bathgate's cause - he was very good against Boston in 1958. He scored 5 goals and 8 points in six games (really good for the late 1950's). Yes, the Rangers lost, but it's hard to blame Bathgate when the Rangers allowed 14(!) goals over the final two games. That suggests that, in a closer matchup, Bathgate could have been a strong playoff performer. (Keep in mind how imbalanced the Original Six era was).
It's also hard to evaluate his 1964 playoffs. He had just been traded to the Leafs at the trade deadline. He was still near his peak offensively - he led the league in assists, and was 4th in points. Just by going through the box scores, he looked almost invisible against the much stronger Habs (only 4 points in 7 games, and tied for the worst plus/minus on the team). But he looked good in the SC Finals (primary assist on the tying goal in game 2, forcing OT with less than a minute left; scoring the go-ahead goal which stood as the game winner with 9 minutes left in game 4; getting the primary assist on a big goal with five minutes remaining in game 5; and opening the scoring with an unassisted goal in game 7). I've just looked at the box scores, but it appears that he was quite good in his first trip to the Stanley Cup finals.
The next spring, he was invisible. 1 point in 6 games with the worst plus/minus on the team. But (due to age, injury and/or trouble integrating with the Leafs), he was no longer in his prime (scoring just 45 points in 55 games - his worst total in a decade).
He made the playoffs one final time in 1966. On paper, it looks like a good series for Bathgate - five points (all goals) in six games against a good Chicago team. But he got most of his points in blowouts. Bathgate scored the 4th and 6th goals in a 7-0 route; he also scored in a 5-1 win. He was held to one point in the three one-goal games. Then in the SC Finals he had a solid start, but was held to one absolutely meaningless point in the final four games.
I still don't know how to evaluate Bathgate as a playoff performer. I can only describe his track record as "inconsistent" and "incomplete". Maybe like Paul Kariya?