Thus, it's really only necessary to encode three of the four possibilities as dummy variables, and in fact if all four possibilities are encoded, the overall model becomes non-identifiable.
By introducing dummy variables, any formula in prenex normal form can be converted into a sentence where existential and universal quantifiers alternate.
I used the 269 matches with available stats that he played against those 66 opponents, to find coefficients for the 66 opponents, plus dummy variables for each year.
I also used a dummy variable for cases where an outsider candidate or unusually weak candidate (the two aren't necessarily coterminous) was nominated in an otherwise competitive race.