Any studies on what chess tactics occur most frequently?

It seems that a study which calculates tactics that occur most frequently, tactics that result in a win most often, and tactics that are missed the most would useful.

It would also be interesting to see the difference between amateur and titled-players.

First try listing the tactics in a thorough, organized way. Then you can think about trying step #2.

You might search the chesstempo.com forums as someone may have already explored this. They do a lot of work with algorithms exploring tactics from the databases, I believe.

Something tells me it's a pin, but I've no empirical evidence. 

I suspect it's hanging pieces (which is one of the motifs in Tactics Trainer).

https://www.amazon.com/Invisible-Chess-Moves-Discover-Overlooking/dp/9056913689

That's partly what I'm getting at: there exist multiple types of pins, only some of which are tactical (https://www.chess.com/forum/view/general/is-a-pin-a-tactic), and the fact that nobody seems to even know that fact is evidence that even listing tactics is a prohibitive task at the current time.

another problem is that the tactic might "occur" in a sense that in order to avoid it from happening, a player might have to give up some other advantage.  So the tactical theme doesnt actually end up on the board but plays its role on the game nonetheless. 

The knight fork was probably the first tactic I learned.  I am not counting the 'hanging piece' tactic.

But most frequent in every game?  Probably the fork.

Lately I've been trying to go even more basic, and think about mentally categorizing types of tactical moves in terms of threats.

One of the most common (for both the winning side and defending side) is to remove a threat while simultaneously making the biggest threat possible... this might sound obvious, but trying to find all the ways of doing this for an individual move can be difficult. For example a knight is threatened, so I move it and give a check, super obvious, but if you calculate that line and it doesn't work out, you need to find an actual threat, and sometimes it's a "quiet" move that threatens a sequence instead of something 1 ply in advance.

Anyway, the basic mechanics of tactics seems to be:
1) Side to move makes a threat
2) Opponent removes threat
repeat until tactic is finished.

It seems to me that what's useful during calculation is being able to quickly find all candidate moves that do one or the other... especially when removing threats (I think people tend to be better at creating threats).

For example can you name all the general ways to remove a threat? I haven't given it a lot of thought, but sometimes I go through a list like

1) Capture the piece making the threat
2) Add a defender to the square/piece under threat
3) Make a counter threat equal to or bigger than current threat
4) Interfere with a line of force (move a piece between threatener and threatened) or pinning the piece making the threat
5) Retreat the piece away from the threat

Most tactical moves seem to be a move that can combine 3+5. Quiet moves are 2+3, surprising moves 4+3 (often a temporary sacrifice), obvious moves are 1+3 (but you need calculation to find the best capturing sequence or maybe we could say the biggest threat). Oh, and some surprising moves are just 3... a really big 3 you didn't consider because it looks suicidal and doesn't actually take away their ability to execute the original threat.

Here's a list of tactics to get you thinking:

https://www.chess.com/article/view/chess-tactics--definitions-and-examples#matingnet

I would bet that the pin is most often used, then removal of defender, then double attack.

Just suggestions, I have no data to back this statement up.

Yeah, those exhaustive lists of patterns seem counter productive to me. A lot of them can be in multiple categories I assume... just looking at the example of "overloading" from that link... you could also call this removing the defender or decoy sac or even fork.

Although... I guess as long as new players aren't intimidated by such a huge list (and realize it's ok that some of them will overlap) it is useful to see the different ideas.

According to Paul Georghiou, the Spanish Monk Ruy Lopez invented a tactic I've not seen very often- arranging the board so that the light is in your opponent's eyes the whole game!

That's probably the least common, "blinding"

the double attack is most common chess tactic