Probabilities on U.S. presidential elections

I'm not a pollster, so my expectations for who will win a U.S. presidential election hinges mostly on basic probability analysis. Currently, U.S. presidential elections are dominated by candidates labeled either Democrat or Republican, a pattern which began a century and a half ago with the election of 1868, and while the exact meanings of those labels has evolved over time, for this analysis I'll ignore the particulars and only consider the labels of incumbents and winners in the abstract.

Including the election of 1868, the United States has held 39 presidental elections, 17 of which were won by a Democrat (44%), 22 by a Republican (56%):

The parties don't just split the number of elections, they also alternate semi-regularly, with neither side winning more than three elections in a row for the last eighty years. To me, that suggests the electorate likes to oust a party after a few cycles in power. Here are the probabilities of keeping the incumbent party versus switching:

While Republican candidates are more likely to win regardless of which party is incumbent, note how often the electorate chooses to switch the party in power. Even for Republicans, being rejected 4 out of 10 times is hardly solid affirmation.

Despite the high odds of switching parties, a sitting Democrat is more likely to be re-elected (47%) than a sitting Republican (36%), a bias that's still present even without FDR's second and third re-elections.

Keen-eyed readers will notice in the above statistics that the odds of a Democrat being re-elected are exactly the same as the odds of Democrats keeping the White House (47%). That's not a coincidence, which brings us to perhaps the most curious fact in this analysis: despite a Democrat's slightly better chances of being re-elected, a Democrat has never been elected when a different Democrat was president. Meanwhile, 5 Republicans have succeeded members of their own party. The only times a Democrat has followed another Democrat as president have been due to a predecessor's death in office.

Presidential elections are infrequent, so we're dealing in a very small sample set. The minor ups and downs for each party may be due less to the wishes of the electorate and more to the law of large numbers not kicking in. Nevertheless, if I had to invent explanations for these stats, I might suppose the following:

1. The electorate doesn't want either a Democratic or a Republican agenda running the country long-term, and it attempts to create some sort of aggregate platform over time by alternating between parties.
2. Democrats win based on their personalities, making it easier for a given president to be re-elected but harder for them to be followed by another member of their party.
3. Republicans win based on their principles, making it easier for one member of the party to follow another but jeopardizing re-election for presidents whose actions don't live up to their advertised principles.

Of course, explanations #2 and #3 surely break down under historical scrutiny. No doubt each president has been elected based on both their personality and principles, and failures to be re-elected have more unique explanations than failure to act on principle.

Explanation #1 is more interesting to consider. I don't think it holds either, in particular since it assigns a single mentality to the country's diverse population of voters, a population that over a century and a half has been completely replaced by new voters at least once. Whether the wisdom of crowds is valid or not, we can't assign the masses a strategic will. A much more likely source of strategic will is the politicians, who each election formulate a platform that erodes the incumbent candidate or party, eroding it enough to win about half the time.

Still, the fact that a Democrat has never followed a different Democrat in office intrigues me. It might be easy to invent narratives about presidents sabotaging candidates from their own party in order to elevate themselves, but I have a hard time believing that such people are vastly more likely to be Democrats or that Republicans are bad at it. If you have a more systemic or statistical explanation, I'd be glad to hear it, so feel free email me.