Average Marginal Effects interpretation I ran a regression where the dependent variable is winning (1=win)
Given that my regression is probit I want to understand the coefficient.
I've done margins, dydx() for my independent variable (average marginal effects). This yielded a result of -.41. 
What does this mean? Does it mean that the probability of winning goes down by .41 percentage points? and if so, when does it go down by that much?
I just want a lay person's way to explain this .41 value.
 A: The average marginal effect gives you an effect on the probability, i.e. a number between 0 and 1. It is the average change in probability when x increases by one unit. Since a probit is a non-linear model, that effect will differ from individual to individual. What the average marginal effect does is compute it for each individual and than compute the average. To get the effect on the percentage you need to multiply by a 100, so the chance of winning decreases by 41 percentage points.
A: These two links can be checked out for detail explanation. Page 8 in https://cran.r-project.org/web/packages/margins/vignettes/TechnicalDetails.pdf and Appendix A in https://www3.nd.edu/~rwilliam/stats3/Margins02.pdf. 
Briefly, average marginal effect of a variable is the average of predicted changes in fitted values for one unit change in X (if it is continuous) for each X values, i.e., for each observation.   
A: dydx means the difference in the dependent variable (or regressand) Y for a change in the explanatory variable X (regressor). This is to be interpreted as a regression coefficient in a lineair regression (of which the marginal effect is equal to the coefficient, other than in regressions of binary dependent variables). 
A score of .41 means that for a 1 unit increase in X, Y (in a probit, this is your probability), will increase by .41 or 41%-points. eyex would return elasticities.
correct me if I'm wrong
