Scoring oddity in compter analysis

I've noticed that when I review chess.com's computer analysis of my games, the score that the computer assigns to the position often changes in my favor after I play my move. This game contains a couple blatant examples:

http://www.chess.com/home/computer_analysis.html?id=48646010&game_type=1

My score improved by 0.65 after 7...c4, and by 0.66 after my entirely pedestrian 15...Nbc6. I don't understand why this should ever happen. My expectation would be that whenever a player plays whatever the computer thinks is the best move then the score should hold constant, and if a player plays any other move then the score should move in his opponent's favor.

The only explanation I can think of is that the move I played was actually better than the computer's recommendation, but the computer only recognized such after searching one ply deeper than before. But if this is really a 2500-level engine like it claims to be, then this shouldn't be happening with such alarming frequency!

Well, the score is based on your current positional advantage, not a turn by turn basis. An advantage is magnified as the pieces are removed from the board. After all, which is better? Being a rook up in the middlegame, or being a rook up in the endgame (as in K+R vs K)? I hope this gives some clarity.

Sorry, it really doesn't. Clearly, the score is, or at least should be, based on more than just the current position. If I just accepted my opponent's queen sacrfice and thereby given him a mate in 4, then I'm losing, no matter how good my position looks heuristically. Similarly, if I'm up a rook in the middlegame and can force an exchange into the endgame, then my score should reflect a rook-up endgame. The way every chess engine I've ever seen works is, it does a minimax search starting from the current position, and applies a quick heuristic to each position it examines, looking at material count, piece mobility, etcetera. The score it returns will be the heuristic score for some node well-down into the tree -- the node which is reached when both sides minimax ideally.

dfranke is right, this is odd.  I've heard other oddities about the sites analysis, such as claiming an equal game in a suggested line where there's a mate in 1 at the end.  (Don't know if they've fixed that stuff, I've been away).

Much better to download a free engine and interface to analyze your games IMO.

If what you're saying is true, then it is odd. I have not experienced this myself, however. Normally, if being a rook up or having a possible mating line leaves you in a disadvantageous position, your opponent has a winning line that trumps your own or simply does not allow you to play your winning line. Have you checked for such a possibility?

The engine I have installed works much like the way I described. Winning a rook in an exchange, for example, will give me a few whole points if it's in the middlegame. However, as the game progresses, this few points tends to accumulate into a better and better score; also, if the exchange is done in an endgame, this few points is more like 10+ points.

I like to think of it as a ratio. The greater your advantage compared to your opponent's, the greater the score will be.

Anyway, those points are my input. It's quite possible that there is something wrong, but I highly recommend looking at these possibilities for such an answer.

That actually makes more sense than what I'm seeing :-). The minimax search has to stop somewhere if you want to get your analysis back before (literally) the heat death of the universe. So in the case you're describing, it probably just stopped at an extremely unfortunate time, when the two sides' positions looked about equally good heuristically despite the mate-in-one. If only it had searched one ply deeper, it would have suggested a different line. The engine could avoid embarrassing itself like that if it withheld the last few moves of its suggested line, but it's more useful the way it is as long as you understand how it works.

You're seeing a horizon effect, where adding one extra ply to the previously quiesscent positions may trigger a substantially deeper search. This can change the computed valuation in either direction.  I remember recently looking at some game where a much better engine changed its valuation of some position by nearly two pawns when it advanced from 16 to 17 plies.

Whatever engine is being used by chess.com, it is likely limited to fairly shallow depths (I would guess somewhere between 12 and 14 at best), so that it returns the analysis in reasonable time. Getting bitten by the horizon effect is not at all surprising.

Here's a short write-up about this and other issues that chess engines have: http://www.chessville.com/misc/Whychessprogramsfindgoodmoves.pdf

LegoPirateSenior, I'm familiar with the horizon effect, but if that's all that's going on here then then I'm either shocked at the magnitude of the effect or deeply skeptical of the 2500 claim. Come to think of it, though, in the game I posted, 12-14 ply would be about right for bringing the fallout from my coming b4 break into scope after 15...Nbc6. So I guess I'm leaning toward "skeptical" rather than "shocked".