I did this last year. I also live in Ohio (NE). Lots of work, but worth it. I did one 4" drain for each downspout with one exception. That one is two downspouts into a single 4'' drain, the second one "y'd" about 15 feet downstream. Every thing drains fine. By my calculations my two 2"x3" downspouts carry just a little less water than the 4" round pipe., assuming maximum flow. Just calculating the combined area. Using that method, a 4" pipe could not handle more than two downspouts, assuming the maximum flow.
Hope that makes some sense and helps.