Is Factor Analysis what I am looking for? I have a calls dataset with ~20 variables and I'm trying to determine what combination of variables lead to a "Win" or a "Loss". For example, when variable A is high and variable B is high, that leads to wins. Is this factor analysis?

No, at least not directly.
You're interested in predicting one variable based on other variables, which factor analysis won't give you. The most common approach to prediction would be a regression model. Because your outcome is binomial (it has two categorical levels, "win" and "loss"), you'd want to use a logistic regression.
20 variables is a relatively large number of predictors -- depending on your sample size and how highly intercorrelated these are, this can cause problems with fitting a model or with the results being generalizable. One solution to this would be stepwise logistic regression, which can identify a smaller number of predictors with optimal predictive power. This works by adding predictors one by one until additional predictors no longer improve prediction (forward stepwise), or by starting with the full model and removing predictors until doing so no longer reduces predictive power (backward stepwise). An alternative method to look into would be a penalized regression model, such as ridge or lasso regression.
Another approach would be a dimensionality reduction method, such as (yes) factor analysis. Factor analysis attempts to explain patterns of intercorrelation among a large number of variables in terms of a smaller number of underlying (or "latent") variables. It can provide estimates of these latent variables (factor scores), which you can then include as predictors in your regression model. This could be appropriate, especially if you have reason to believe that your 20 variables are assessing a smaller number of underlying traits / processes / whatever. Without knowing more about your dataset, though, stepwise regression would probably be a simpler place to start.
