Creating an expression that tells marginal impact of moving one independent variable to another independent variable.

[Alan Blach]

I have been working on a project over the last few months. The idea of this project is looking at MLB payrolls for teams and finding a way to maximize winning by allocating payroll between batting and pitching. In my project so far I have found how to maximize spending for both pitching and batting controlling for both year and team, as well as logit and OLS models in an attempt to make a working model to predict winning percentages for a team given their payroll spending.

My main problem with this project is that I need to make an expression that explains the marginal effect of taking money from batters and moving it to pitchers. An example would be the following:

$50 million in pitching, $50 million in batting results in a __ winning percentage
If I were to move $1 million from pitching to batting ($49 million and $51 million, respectively), what is the marginal impact on winning percentage?

I have been working in Stata throughout this project and although I know what the end result may look like, I am clueless as to how this is achievable. I have been working with the margins command throughout this project but am not sure how/if I can use this command to achieve my question. I have been using margins to look at how a $1 million dollar increase in payroll for batting and pitching impacts winning percentage, and I am not sure if I can somehow apply this to my issue of moving it from one to the other. Has anyone ever attempted this sort of problem or have any idea how to make this happen? I have been working on this issue but cannot find much to help me.

This is my first post here so I apologize if I am being vague with my issue or if it doesn't apply to this type of forum. Thank you to anyone who can help!

[Clyde Schechter]

I doubt anybody can give you concrete advice without seeing example data, your regression models, and what you have already done with -margins-.

In general terms, you could do something like this. Instead of using the salaries for pitching and batting as the variables in your model, create two new variables: one is the total of pitching + batting salaries, and the other is the difference between them. Then switching $X from one to the other is the same as keeping the total constant but increasing (or decreasing, depending on the direction of the switch) the difference by $2X. The impact of that would then be 2X times the marginal effect of the difference variable.