This seems wrong: an even exchange does not change absolute balance but magnifies relative balance, which you do not want if you're behind.
Let's say your "strength" is simply the sum of the value of your pieces. The losing side has a strength of l and the winning side has a strength of L.
The losing side loses by l-L in absolute terms, or (l-L)/(l+L) in relative terms.
An even exchange of value k makes it go to (l-k)-(L-k) = l-k in absolute terms (no change); and to (l-L)/(l+L-2k) in relative terms. (l-L)/(l+L-2k) < (l-L)/(l+L).
To take an example, if the situation is white : two pawns and black: one pawn, going to white: one pawn and black: nothing is a bad deal for black (the losing side)!
Let's say your "strength" is simply the sum of the value of your pieces. The losing side has a strength of l and the winning side has a strength of L.
The losing side loses by l-L in absolute terms, or (l-L)/(l+L) in relative terms.
An even exchange of value k makes it go to (l-k)-(L-k) = l-k in absolute terms (no change); and to (l-L)/(l+L-2k) in relative terms. (l-L)/(l+L-2k) < (l-L)/(l+L).
To take an example, if the situation is white : two pawns and black: one pawn, going to white: one pawn and black: nothing is a bad deal for black (the losing side)!