I can 100% guarantee that Brom does not have a greater skill than his opponent. Although it is possible they have the same skill.
Again you are assuming. Firstly you are assuming that because you use cavalry and didn't explicitly train the skill, that yours has never increased. Secondly you are assuming that both characters started at the same base skill level. You can't 100% guarantee it cause you have no idea what level your opponents skill started at or what gains he has made.
