1824: What if Andrew Jackson Did Not Run for President

[Frodo]

Let us suppose that Andrew Jackson decided in 1822 not to run in the 1824 presidential election, choosing instead to heed his wife Rachel's wishes to avoid the political spotlight for a time, and focus on his family.  In all likelihood, then-War Secretary John C. Calhoun would not have dropped out of the race, so he would have been among the main candidates contesting the election with John Quincy Adams, Henry Clay, and William Crawford.  Bear in mind, he did not become the states' rights, limited government, nullification proponent (though he was always pro-slavery) we know him today until later that decade, so in 1824 he would have been still a nationalist more in tune with Henry Clay's preferred policies (at least I think so).  

How would the 1824 election have turned out?  Could Calhoun have won?