Have you taken into account none of them should make as much as the President of the University.
Really, that's totally irrelevant, and has nothing to do with the proper ways to determine the pay of either the Football Coach or the President. For both, the proper pricing depends on two things. The first is the competitive salaries. How much do you need to pay in order to get the quality you expect? The second is, how much do they contribute directly to the financial and academic success of the University?
For the football coach, it seems that most MAC schools seem to think that in today's market, a starting pay in the $540-625k range is appropriate, and the starting pay for established coaches is not much different. What about looking at the value? A good coach can contribute value in a couple of ways. First, can he put butts in the seats? The second one is harder to determine, and involves the question of how does he affect contributions to the University? Is he a good face of the University, that inspires donations, not just for athletics, but for the general fund as well?
Looking at attendance first, Solich, for a long time, had Ohio's attendance consistently averaging over 21k a game, but that slumped the last few years as attendance slumped nationwide for all teams. How has TA done? Here are numbers for the last few years:
2016 21,190 per home game
2017 19,388
2018 about 16,500 (no attendance numbers available for Howard)
2019 16,566
2021 17,626
2022 17,692
2021 was helped by a big attendance for Syracuse. If we look just at MAC games, in 2021 the average was 15,609, while the 2022 average was 16,781, an increase of 7.5%. If we guess that the average ticket price is $20, then for 6 games Ohio takes in about $2.1 million. A 7.5% increase is about $160k. What if that trend holds, and Ohio can get back to the 21,000 numbers prior to 2018? That would be a difference of over $400k. So, a bad coach can keep the program going, but a good coach that fills the seats is definitely worth more. How is Albin doing? So far, not bad. Attendance in 2022 was the highest since 2017, but it as a ways to go.
What about the argument that the whole program loses money? That's an argument with no basis. In proper cost accounting, you have to look at marginal costs, not average costs. If Coach A costs $400k and keeps things going, while Coach B costs $550k but contributes an extra $200k to revenue, which is the best choice? As for the argument "but the whole program loses money", that's an argument towards the question "should their be a football program at all", not towards the question of how much to pay the coach.
As for the question of how the coach affects giving, that's a question I can't answer. Is TA a good face for the University? Does he stimulate giving in general, not just to athletics? That I can't answer. I do know that traditionally, after a good football or basketball year, general giving rises for a year or two. Will it rise after last year's 10-4 record and bowl win? If things go as they usually do, probably, but I can't say for certain.
Thus, I can't answer the overall question of "how much should TA be paid". All I can do is provide a proper framework. The decision should be made with regard to valid questions, like, how much is he contributing to attendance and giving.