Political Science I am trying to formulate a hypothesis based on the recent economic sanctions against Russia. From this,...

We can look at your hypothesis development at two levels, namely (a) a conceptual discussion of the proper elements of a mathematically expressed hypothesis, and (b) a specific discussion of the dynamic you are attempting to model and analyze.

First off, it is assumed that the test of this hypothesis will involve obtaining actual data points and applying statistical tests to determine the ability of the independent variables to explain (correlate with) the dependent ones. Generally speaking, your model will need to incorporate all material independent variables in order for any correlations to have real explanatory meaning. If significant determinants of state behavior are left out, you risk having (1) a lack of correlation due to other underlying factors which you did not incorporate (i.e. your data points were “apples and oranges”) or (2) correlations shown in the model that do not have explanatory power, because they are either coincidental or correlated with other variables not included (“spurious correlation”).

I think your inclusion of the length of sanctions to be problematic. Sanctions tend to be imposed on the basis that they will be continued until they bring about the desired change in behavior. They typically are not predefined. In fact the length observed for a particular sanction tends to be a dependent variable, not an independent one.  Perhaps what would be more meaningful would be some measure of the perceived willingness of the imposer of the sanctions to persevere with them. This in turn could be defined as how much the sanctions cost the imposer of them. For example, forbidding your domestic companies from participating in certain markets, in order to harm the other actors in those markets (think the US approach to Cuba or Iran) clearly costs those corporations business and profits, which in turn creates political pressure in the imposing state to limit if or how long those sanctions are kept in place.

Finally, remember that it will be a challenge creating actual metrics for some of these variables (especially the degree of aggression), and the data for those metrics may be very difficult to obtain. This is not to dissuade you, as there can be a lot learned from qualitative discussion using a well-defined model as a framework. Just think about the practicality of rigorous statistical analysis before allocating your time down that path.