A quick thought on the data @Jordu posted above. Those are per game numbers, and since there are more OT minutes in the playoffs, the actual scoring difference between playoffs and regular season (on a per 60 minute basis) is higher. This article by sound of hockey (who I never heard of until today) is pretty interesting, as it talks about regular vs postseason scoring discrepancies, team shooting percentage differences, scoring by defensemen in the postseason, and (for you @tims4wins) PP scoring in the playoffs.
The sound of hockey article also has a link to another piece on penalties in the playoffs. I take some exception to it, however, as from the work I did over multiple seasons (16-17 to 19-20) there was no negligible difference in penalties per 60 minutes between the regular season and the playoffs.
But what I did find was that hits per 60 minutes (from public sources) are up close to 50% in the postseason (see table below). I further looked at the regular season relationship between hits and penalties, including all players with over 500 minutes between the start of the 2016-17 season and 2-26-20 in the study, and found a decent correlation (r = 45%, r^2 = 20.2%) between hits and penalty minutes.

This is important because while hits increase close to 50% in the playoffs, penalties for the most part remain static. The following table shows league average penalties and hits per 60 minutes since the start of the 2016-17 season, along with predicted penalties based on the regular season regression work:
This strongly suggests what many of you have said, that the refs swallow their whistles in the playoffs. Anyway, hopefully the above will spur some more discussion. No math is necessary
Finally, I was talking the other day with an ex scout who is here in Mexico vacationing, and when I asked him the question about what changes in the playoffs, his immediate response was the importance of 4th lines. Interesting. Do you guys have any thoughts on this?
The sound of hockey article also has a link to another piece on penalties in the playoffs. I take some exception to it, however, as from the work I did over multiple seasons (16-17 to 19-20) there was no negligible difference in penalties per 60 minutes between the regular season and the playoffs.
But what I did find was that hits per 60 minutes (from public sources) are up close to 50% in the postseason (see table below). I further looked at the regular season relationship between hits and penalties, including all players with over 500 minutes between the start of the 2016-17 season and 2-26-20 in the study, and found a decent correlation (r = 45%, r^2 = 20.2%) between hits and penalty minutes.

This is important because while hits increase close to 50% in the playoffs, penalties for the most part remain static. The following table shows league average penalties and hits per 60 minutes since the start of the 2016-17 season, along with predicted penalties based on the regular season regression work:
Season | Pen/60 | Hits/60 | Pred Pen/60 |
16-17 Reg | 0.62 | 5.00 | 0.58 |
17-18 Reg | 0.61 | 4.98 | 0.58 |
18-19 Reg | 0.58 | 5.13 | 0.61 |
Thru 2-26-20 Reg | 0.58 | 4.99 | 0.58 |
16-17 Play | 0.62 | 7.41 | 1.09 |
17-18 Play | 0.68 | 7.18 | 1.04 |
18-19 Play | 0.60 | 7.44 | 1.10 |
This strongly suggests what many of you have said, that the refs swallow their whistles in the playoffs. Anyway, hopefully the above will spur some more discussion. No math is necessary
Finally, I was talking the other day with an ex scout who is here in Mexico vacationing, and when I asked him the question about what changes in the playoffs, his immediate response was the importance of 4th lines. Interesting. Do you guys have any thoughts on this?