Seven out of the ten US presidents in the period from 1869 to 1923 were from the state of Ohio, yet before or since not a single other president has been. Was this just a coincidence?

In his paper “Broken Cradle: Why is Ohio No Longer the Mother of Presidents?”, political science professor James Melcher identifies six factors in Ohio’s dominance at the presidential level during this period:
1) It was “a pivotal state in national elections” and something of a battleground state. Although Melcher admits that the state leaned decidedly Republican, it still featured more “partisan competitiveness” than most others during the era. It worked as a bellwether for the Republican Party at the national level at the time, which is the party that all those Ohio presidents came from. If the Republicans could do well in Ohio, they could win the Presidential election.
2) Ohio politicians of the era tended to be described at the time as “bland” and “nonideological”, and not as partisan as politicians from other areas of the country. Melcher posits that this might be due to Ohio having multiple large population centers, which meant that statewide officeholders in Ohio had to appeal to a broader electorate than in other states. This translated well to winning national elections.
3) Because Ohio politicians were skilled at building coalitions, they tended to perform well at nominating conventions at a time that candidates were picked at the conventions among the delegates there. Ohioans often came out as a consensus candidate inoffensive to more ideological members of the party. Conventions “rewarded a candidate with” skills at “strong party organization” which Ohio politicians of the era tended to have.
4) Ohio’s geographic location helped it as well, with the West being so sparsely populated for most of this era, and elections won by appealing to the electorate East of the Mississippi. Due to intra-migration in the country, Ohioans were good at speaking for the country as a whole, inoffensive to more of the country than most other populated locations, where divisions and rivalries could be more hostile (especially South v. Northeast).
5) Ohio had a lot of Civil War military veterans-turned-politicians, who, up until that era, were often candidates (and often successful candidates) for national office.
6) Once Ohio was identified as this new cradle of the presidency, Melcher says this created “momentum” for future candidates. Ohioans had kept winning the office, so might as well nominate another Ohioan. This argument was being made at the time, for instance, in this Western Magazine article preceding the 1920 election when both major candidates came from Ohio.
In “Sectionalism and Presidential Politics: Voting Patterns in Illinois, Indiana, and Ohio” by authors Fred M. Shelley and J. Clark Archer, they make several of the same points, though broadening the scope to include Illinois and Indiana, too. Between 1856 and 1920, 8 of 12 men elected President came from one of these three state which “illustrates the sensitivity” the Republicans had “to the importance of mobilizing popular support in these states”. The authors also say these three states had demographic similarities to the South and Northeast that those two sections of the country didn’t have to each other: these Midwestern states were rapidly urbanizing with immigrant populations like the Northeast was, but they also had a significant rural population with ties to the South.
In “U.S. Presidential Elections in the Nineteenth Century: Why Culture and the Economy Both Mattered” by G. Patrick Lynch, the author also echoes some of what Melcher said. Ohio had elected Democrats to the governorship and their legislature in the 1870s, and Republicans found themselves in a dogfight for political dominance during the period. Indeed, Ohio’s shift almost proved fatal: the Republicans won Ohio in 1876 by less than 1.2% of the vote, which, if switched, they would have lost the election (and barely won it anyway, due to the contested Florida vote). The Republicans needed Ohio to secure a Presidential win.
This agrees with a statistical analysis done by John R. Wright in “Pivotal States in the Electoral College, 1880 to 2004”, which identified Ohio as one of the most perennially pivotal states to win in elections in that period. Most specifically, Wright identifies Ohio as being the most pivotal state in the 1896 outcome, and the second-most pivotal state in the 1888 election, two elections won in the period by Ohioans.
This electoral college importance is also offered as the explanation for Ohio’s dominance of the era in the 1965 biography The Available Man: The Life Behind the Masks of Warren G. Harding by Andrew Sinclair.
In the book Ohio and Its People by George W. Knepper, the author echoes Melcher’s point about Ohio being the source of compromise among Republicans at the conventions, their politicians often considered safe, and pointing in particular to James A. Garfield’s 1880 nomination during a particularly split convention as the best example.
In the book The Ohio Presidents: Eight Men and a Binding Political Philosophy in the White House, 1841-1923 by Quentin R. Skrabec, Jr., the author makes an argument that echoes Melcher’s factor that Ohioans made good compromise candidates. Due to the socioeconomic make-up of the state, Ohioans tended to embody Republican Party and republican (small “r”) values of the time better than most. On both social issues and economic issues, they followed the Republican Party closely, and Ohio was something of a microcosm of the social conditions of the U.S. as a whole during the period. The state experienced significant growth through immigration, and became more urban, so Ohio politicians had experience appealing to a constituency that was very much like the national electorate. The book also talks about Ohio’s electoral college importance as a battleground state, and it often acting as a bellwether of the national political mood.