Clarke always underwhelmed me as far as a postseason player goes. I'm open to hearing the counter to that.
I looked at Clarke more in depth to see if anything stood out in the playoffs, good or bad.
Offense:
Clarke was a very consistent scorer. He showed up and got his points regardless of the quality of opposition. Incredibly, he only played 12 career playoff games against teams with a losing record. I would have expected that total to be quite a bit higher given Philadelphia's strong regular seasons coupled with a high percentage of teams qualifying for the playoffs from 1975 onwards. The only punching bags Clarke ever saw were in brief preliminary round series against the late 70's Rockies, Canucks, and first-year Oilers. Overall, Clarke played 110 playoff games from 1973-1980, what we would probably consider his prime. 53 of those games came against what I would consider elite Cup-contender opposition.
Broken down by individual series, it's almost uncanny how consistent his production was. In 19 best-of-seven series, he produced between four and seven points on 15 occasions. The closest thing we ever saw to an offensive outburst from Clarke was 8 points in 5 games against the 1980 North Stars. The only dud series was a disastrous 0-point, minus-11 series against the Rangers in 1979 (which is so bad compared to every other series he ever played that I have to suspect he was injured).
Bottom line is, Clarke was never going to steal you a series on the basis of his offense, but he showed up and gave his teams a chance in that regard almost every time. He could be contained offensively, but very rarely shut down.
Defense:
I decided to take a look at what the opposition's #1 center did against the Flyers during Clarke's prime years. This is an inexact science; I don't know how often Clarke was directly matched against the players below, others may be able to chime in here. But whether he was directly matched or not, I think it is fair to say that the job of the #1 center is usually to outplay the opposition's #1 center in a playoff series.
1973
Flyers lost a reasonably close 5-game series to the 120-point eventual champion Canadiens. I'm not sure who of Lemaire, Richard, or Mahovlich he'd have seen the bulk of his ice time against. Clarke scored 3 ES points, but was a -2. Henri Richard had a strong series and may have gotten the better of him. Lemaire's stat line is non-descript, and Mahovlich was bad at -4 with no ES points.
1974
Clarke looks pretty ordinary against the Rangers in the semi final, (4 points, -1), but absolutely buried Jean Ratelle, who went -6 without any ES points. Clear win for Clarke here.
Phil Esposito fares little better in the famous upset in the SC Final. His -3 is directly opposite to Clarke's +3, and Espo only had two ES points in the series, which is one of the worst in his career.
1975
The Flyers washed Toronto in the quarter-final, Darryl Sittler with 0 ES points, -4.
Not sure about the semi-final. Clarke and Denis Potvin both had a good series. The Islanders didn't have any elite centers on their roster at this time.
Neither Clarke nor Perreault gave up much at ES. Clarke did his scoring on the PP, Perreault did little at either ES or PP, but did finish +1 despite the lack of scoring. Both players were better at home than on the road in this series.
1976
Sittler gets his points (5 at ES), but it seems they must have come at somebody else's expense. Clarke scored well too, and was a +6, while Sittler had an ugly -5.
Clarke seems to have dominated Jean Ratelle again, now a Boston Bruin. Just two ES points and a -3 for Ratelle as Philly beat the Bruins easily.
The Final against Montreal (127 point season) might be Clarke's first match-up loss since those same Habs in 1973. Clarke and Lemaire were both -1, while Peter Mahovlich ended up +4 with 3 ES points. Depending who mainly went against Clarke, it's either a saw-off or a loss.
1977
Sittler is again a victim here, -3 despite scoring a good amount of points again. +4 for Clarke.
Ratelle and Boston get their revenge. Clarke is a -4, with Ratelle (5 ES points, +5) appearing to be the benefactor.
1978
Clarke doesn't look great, going -1 against Buffalo. But Perreault is held in check with just 1 ESP and a -3 rating.
Ratelle kills the Flyers for the second year in a row. Clarke is -3.
1979
That awful series I alluded to above. I'm not sure who Clarke was playing against here, but he was -11 in a 5-game loss. Instinctively you'd think Esposito, but Phil was only an Even plus/minus player despite score 6 ES points.
1980
Clarke (+1) appears to have outplayed young Gretzky (-3) in a preliminary round.
He definitely outplayed old Phil Esposito (-2) in this series. +2 despite just two points would indicate a strong defensive effort.
Clarke was good in the Final as well (7 points, +3), and closed the playoffs +10 despite a somewhat modest (for that era) 20 points in 19 games. Trottier and Goring both had a solid series, neither finished a minus player. Hard to say exactly who was playing who in this one.
Conclusion:
Up through 1976, there is little not to like about Clarke in the post-season. It is often remarked that an offensive player did or did not outscore their defensive deficiencies. I think this is a case where we can say the opposite. Clarke's defensive play was so strong that it easily covered for his weak-ish (by standards of the players in this vote) offensive production.
This seems to have stopped quite abruptly in the spring of 1977, however. Clarke all of a sudden has a string of 19 games spread over four playoff series where he's a hideous -19. 13 points in these games is a drop in production, but it's really not a huge step down from where he was at before. Nowhere near big enough to explain that minus-19.
Clarke returned to previous form in 1980 though. He seems to have been no less effective in this almost-Cup win than in 1974-1976. His play remained strong throughout the rest of his career, though the Flyers never went deep in the playoffs again. He had 16 points/+6 in the last 22 games of his playoff career.
Possible Explanation for the "Down Years"?:
It's difficult to look past the fact that Clarke's best playoff series line up so well with years where Bernie Parent was in net. He was there in 1974, 1975, and 1976...but was injured against Boston that year and didn't play most of the semi-final or any of the final. In 1977 he only played three games, and that's right when we see Clarke experience this sudden drop in goal prevention. He was back for all of 1978, however. In 1979 (the year of that awful series), Parent was done for good and didn't play at all in the playoffs. Pete Peeters and then Pelle Lindbergh re-established stability at the goaltender position from 1980 onwards, where Clarke's defensive play seems to have returned to form. The flip side of this argument is, just give Clarke a solid netminder, and he'll do great things...but I must admit, the strong overlap of Clarke's great numbers with years of good/great goaltending is a little concerning for me.