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Dragging Pieces

I've been wondering about that, too. What you're describing is called a (bonafide) "Fingerfehler" (http://www.nytimes.com/1990/11/04/style/pastimes-chess.html). On my home computer I can just hit the "undo" button if I make such a mistake, which I've done a few times, but I can't do that on the program on this site, and when in a serious game that would be considered cheating. There is probably a workaround for such errors, analogous to hitting the "confirm" button before placing a bid in an online auction, but it would probably take a crusade to get a rule added like that, I believe. (Maybe a move wouldn't be counted until you hit the time clock, or maybe there could be an extra confirmation setting on the clock, or maybe there could be a 3-second rule for adjusting the piece, or something.)

You don't have to drag the pieces. Click on the piece that you intend to move. Then click on the square you plan to place it on. Voila! While there is zero chance of drag error, you just might accidentally choose the wrong square and it might be a legal move, lol.

If the piece is consistently being released prematurely, then somehting is wrong with your mouse/touchpad. My old mouse wouldnt constantly do that, and when I got a new one the problem went away.
So if you're really losing that many games because of this problem, either get a new mouse or use the click & click method instead of drag & drop.

I totally, completely empathize with the OP.
I just lost two games in a tournament because of the "drag effect" that drops pieces one square before where you would like to move them.
Not to mention taking two seconds longer to move on EVERY move than your opponent since you are trying to avoid the problem by placing your piece precisely in the middle of the square to which you want to move it before letting it drop.
In a 40 move game of blitz against a decent opponent, you just lost the game.
I can't even begin to count how many queens and rooks I have lost because of this, or how many games I have lost. Well above 500 games I would venture to guess.
There was one night where there was no lag and no drag and I brought my blitz and bullet scores up by a combined total of over 300 points (which for a low rated player is a lot). It felt like being a person who had always had to walk with stiff metal braces on their legs, and then suddenly they were gone and you could walk normally.
That has never happened before or since.
I have tried chess.com's recommendations and they work sporadically at best. I just call it "the dreaded lag" problem when your mouse moves much faster than your pieces, and to different squares than those to which you intended to move.
What can you do about it? Nothing except complain, in which case you usually get a bunch of people telling you that you don't know how to use a mouse to make a move at computer chess.
Even ignoring your score doesn't help. In chess, 40 brilliant moves can be completely undone by one blunder. When it happens because you screw up you have to learn to take it. But all the examples we are talking about happened because of some electronic glitch, not because of a tactical or strategic error.
That is not so easy to take.
I've lost the last 5 games I have played on here while I was ahead because I went to drag a piece and it released prematurely, completely throwing the game. There needs to be some sort of insurance for draggers. I can't do the click and drop method, it's not in my DNA I'm a dragger and I can't break the habit. It's slitting my motivation by the juggular everytime I come back to try and get into chess and lose games like this.
There needs to be a solution