How do the engines and the players say if a side is winning or not? What are the key factors they consider while assigning a score to each side?
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It depends, some computers can know things like “bishops that have long unobstructed paths in multiple directions and exist on the same coloured square as the king are valuable” and assign value to pieces based on meta analysis of game position based on a certain amount of data it has. They can advance the position several moves forward and use that analysis to focus on certain lines. For example the computer won’t deeply analyse the line of black opening h6/a6 pawn move because it has the data that it’s a bad move. The more powerful this type of computer is the farther along it can develop more lines (this is also why you sometimes see the evaluation bar randomly move as a very strange line that at first based on the rules the computer uses to prioritise lines it analyses is actually really strong).
The number is supposed to be pawns worth of value (1 for a pawn, 3 for a bishop etc). It’s not strictly material as positionally one can be ahead and the weighting that positioning can vary a little bit across analysis programs with the same position depending on the depth they analyse to (a 20 move deep analysis might see greater value in a piece than a 10 move deep)
They get stronger the larger the dataset they have is so that they can know what good positions look like so they prefer those. That’s how most analysis computers will work, as far as the super computers that far outstrip the masters go, they’re literally playing out millions of games to make their positions.
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