More importantly though, does White have a powerful plan? I can't see a clear one, which is why I can't see how the piece sacrifice is at all effective.
Justifying a Sacrifice
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I think advanced puzzles either have this sort of thing in the solution or in the variations. They would be useful to throw in, and make people more aware of them, but amateurs have enough trouble with the straight forward combinations heh.
If I can sac a piece for two pawns twice in an online blitz game, it's usually fun... but it's interesting how difficult it is to set up sometimes. Of course your opponent isn't looking for it (part of the fun) -- but if you have 4 connected pawns for two pieces it can be a fun kind of imbalanced position for blitz.
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The type of advantage that vies for 1st place against material is activity. In fact I tie all of Silman's imbalances into activity because that's what makes sense to me. This is how I justify any sacrifice. If it's a true sacrifice, it's usually because you're highlighting why they call the relative values relative. The relative values change most frequently due to the relative activity and future activity (i.e. mobility) of the pieces.
Of course activity is important, the hard part is seeing if this advantage in mobility will ultimately lead to greater or at least equal gains than what was sacrificed, or if it will fizzle out once black's development (usually) catches up without allowing a combination 
. At what point do you just assume that your pieces will be active enough to find a tactical way to regain the material or better?
If a move "feels" right to me I'll sac. I just love to sac. However, I do it for the sake of an interesting game. I don't mind losing if a sacrifice leads to an epic exchange 
. But if you do make sacrifices like this, be prepared to lose (and hope for a win)....
This stuff is hard for people much better than me, so I don't want to sound like an expert lol.
But what I look at just depends on the specific position. More pawns is slightly better for knights, slightly worse for other pieces. Extra pieces in general is a bit worse for rooks. Pieces that duplicate powers are bad e.g. two rooks vs whatever equivalent. This fairly common sense sort of stuff + GM games I've played over for some reference.
This is one of the few parts of my game I would describe as intuitive. A big factor is probably that I often analyse "why this move/sequence" "why not that move sequence" with Rybka. I compare the differences in positions and the differences in evaluation and try to link them logically myself. I try out new moves to test my idea, and again watch the evaluation for confirmation. It's sometimes easy to see a lot of Kauffman's (obviously) and human evaluations are present in Rybka. That, and I avoid doing this with tactical situations, so I think this is a useful exercise, at least one that's always made sense to me, before I even knew what I was really doing.
I do use some fractions + intuition e.g. this knight feels about 3.5-3.75 ... I usually don't literally think three-point-seven-five but I might look at it and think ok I have a good knight. Or, my knight is compensation for his _____ or I may go on and intuitively subtract my opponent's negative points and add my positive points. Kind of like guessing the weight of a bucket of water held by the palm of your hand, and you're having trouble balancing it.
I'm biased towards never sacrificing anything for unclear compensation because of the numerous times that I didn't know what to do with my compensation and fell apart.
You could have done Nd5 instead of Bxf6
Estragon wrote:
One of the great things about turn-based games, and old-fashioned snail-mail correspondence games before that, is that it provides a great opportunity to test out pawn sacs.
I attempt to try out pawn sacs as often as I can, to force myself to play actively. Also piece sacs, but not so often, as I want to have a good feeling about my prospects going forward at least, whereas I will often let the pawn go even when I don't think it is a good sac.
There's no prize money riding on these games, so why not use them as a lab to improve my game? Besides, even when the sac turns out bad, it usually means the opponent has defended tenaciously while I attacked, so I was the one having more fun the whole game even if he gets the point.
Thank God analysis board and opening books are allowed in CC.... otherwise my rating would drop to about where my standard rating in live chess is at ~1850 
I am fascinated by this discussion and Mottsauce's insight.
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Psychologically positions that I just can't be sure about (like "unclear" sacrifices) irritate me. I like to be able to figure out if a move is good or not just based on logic or on calculation of a few key variations, but there are some sacrifices of course that are so complicated you can't truly be sure about them until it's played out. Others on the other hand will do anything for an unclear position, but I'm more of a perfectionist.
I would only make an attacking sac if it looked really strong (I can recognize compensation after a sac and have my own methods of doing so but, as a human, nowhere near perfectly), but "unclear" (as these things so often are) wouldn't cut it for me.
Tactics trainer wouldn't put the problems you speak of on because then you don't even know if the "tactic" is a winning (or losing!) one. If you want practice with that, a great option is taking one of many super sharp opening lines (like the latvian gambit) that the haters like to call refuted and then try your best to un refute it
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