Analysis should include position volatility

We can define volatility (per white's position or black's) roughly by some function of the number of moves which result in a similar (or better) positional evaluation.

For example, in the fried liver attack, white's volatility is low since white can make a lot of fairly natural looking moves (whether they add to the attack it doesn't matter) which result in no significant loss in the evaluation of the position. With black in the same attack, the volatility is high since black has to make very accurate moves in order to maintain equality or a better position.

I haven't seen any engine measuring this volatility, but I think it is important because you can mislead your opponent into thinking he has a better position but if his position is highly volatile, you have many chances to take advantage.

I get what you're saying, where volatility has an inverse relationship with the amount of good moves for the side playing. It's an interesting concept, but it would take a very large amount of CPU time to perform.

Maybe put this one on the back burner for when lichess has greater resources.

Is there any chess engine measuring volatility already?
I think the analysis provided by the site is done by Stockfish, wich is a free open-source chess engine.

Seems like Stockfish does not provide volatility analysis, but it will be hard to get a great license-free chess engine with new features to make the site work with.