Thanks to the 2015-16 Diving/Embellishment List on Scouting the Refs and the easily accessible data on Corsica, I made a quick graph of how 5v5 player penalty rates break down depending on whether the player had either 0, 1, 2, or 3 diving/embellishment calls in 2015-16 or had been fined by the league for the same offenses.
Taken together, the data seems to suggest that players who are called or fined for embellishment / diving penalties are more frequently involved in penalty calls (both for and against) than those who are not. More so, the increase for penalties drawn appears slightly larger than that for penalties taken.
Now there are significant shortcomings to using this data that should be further investigated before making any strong claims. The largest issue at hand is the sample size. While there were a total of 666 player records investigated in this analysis, only 68 of them had some sort of diving/embellishment call or fine. Of them, 55 had one offense, 11 had two offenses, and 2 had three offenses. While the data may be reliable at the single offense level, anything beyond them will likely be subject to volatility in the data.
Another important factor is teasing out how a player’s conduct might influence an on-ice official’s calling of penalties involving the player. The most substantiated case of this is the Burrows-Auger incident from the early 10’s. And there certainly are players in the league today who arguably have their penalty rates affected by their reputation. Thomas Holmstrom is perhaps the most famous case of that in recent memory. That all said, further analysis would be needed to see how a player’s penalty rates might change with their reputation, e.g., how their penalty rates change after receiving their first diving/embellishment call, after their second, etc.
Finally, it would be nice to expand the data set back into previous years, but the league has seemed to change how frequently they would like these calls made. At most, this data set could probably be made to include 2014-15 data, but I would not go back further.