In reading both fiction and nonfiction materials over the years, involving Egyptian, Roman, Persian, Greek, and Jewish cultures, I have seen statements to the effect that the locals believed their war was won because the god of preference in the story was stronger and determined the outcome. Recently, I thought I could find a simple, concise statement by some scholar that the concept was ubiquitous in ancient cultures (and by some people, believed modernly). However, in researching the basic question, "did ancient people generally believe that the strongest god was instrumental in winning the war", it is a case of being unable to see the forest for the trees.
I have been surprised how difficult is to get a general statement, although the web is full of individual debates about the wars within specific pantheons, the belief systems and origins of various cultures, and the modern world of gaming describing the powers of the gods. There are thousands of links to Ares, Mars, Týr, Anann, Horus, Istar, etc. But a general statement about a widely held belief among the ancients to the effect that the wars' outcome was dependent on which god was stronger, has been elusive.
Thank you for your insight into the problem.