Let's say I have two variables $a$ and $b$, such that $a+b=10$. Their values chan change with time, so I would like to express the contribution of each to the total at each time. At time $t=1$, for example, $a_1=2$, therefore it contributes 20% to the total. It gets tricky now, because at later times, $a$ becomes negative and larger than the total in magnitude. If $a=-20$, then necessarily $b=30$ so that the sum still equals to 10. Now, how to express the percentage contribution of $a$ to $a+b$ in this case? A contribution of $-200$% to a total sounds very strange to me and difficult to interpret. Any creative meaningful ways to represent the contribution of $a$ to $a+b$ in this case?
ED1: Sometimes $b$ can be very small. So a ratio $a/b$ wouldn't be ideal. I am looking for something to express a contribution of one of the parts to the total.
Another way of representing the contribution of $a$ to $a+b$ is by defining the contribution as $\frac{a}{|b|}$. Note that this also changes the value (and interpretation) of cases where both values are strictly positive. Furthermore, $b$ must be nonzero.
The interpreation of this definition is by which percentage the sum $a+b$ is larger than before $a$ was added. For instance, when $a=2$ and $b=8$, the contribution of $a$ is $\frac{2}{|8|}=0.25$, because the total ($10$) is $25\%$ larger than just $b$. Similarly, the contribution of $b$ is $4$, because $10$ is $400\%$ larger than $2$.
For $a=-20$ and $b=30$, the contributions would be $\frac{-20}{|30|}=-\frac{2}{3}$, $\frac{30}{|-20|}=1.5$ for $a$ and $b$ respectively.