Everybody wants to keep such algorithms to themselves. And rather than it being an algorithm it's safer to say it is a set of theories that are then translated to algorithms. The work that goes into these theories is extensive.
Algorithm for Quantifying Chess Personality?

A simple example:
There are sets of openings out there that we could consider opposites of other sets of openings. This already facilitates division, or grouping. Further, we could then say it would be safe to assume that a player who favours certain moves probably belongs to a certain group of openings. Therefore we can learn a lot about a player'sopening choice.
Openings are linked to mid games, and mid games to end games. See where we're headed with this?
I believe masters of the game use the same set of theories when preparing for matches. It would be the team's job to work through such things and recommend a certain prep plan for the master player.
I am aware of the chesspersonality.com quiz endorsed by chess.com.
But does anyone know of an algorithm to automatically quantify a player's personality based on their game(s)? For example, given some FEN and multiple reasonable candidate moves, is a player more likely to open or close a position, are they risk adverse, what does their opening choice say about them, etc. I would be interested in references to any manuscripts on the subject if they are out there.
Personally, I think making such analytics available would be a pretty cool feature to implement on this site. What do others think?