Statistically speaking, VPs who complete another president's term are much more likely to win reelection than regular presidents.

44 people have been president, counting the current president. Of those, 16 won two consecutive terms and one won two non-consecutive terms, giving an overall reelection rate of about 38%. This can be a misleading number, as 13 of these presidents didn't run for a second term (counting Donald Trump whose first term isn't over but is running for election later this year).

Out of the 31 presidents who ran for two or more terms in office, 17 won. This gives a much more impressive success rate of 55%. This number is inflated by two groups of presidents who were unusually likely to be reelected, and one of them is the very group you are interested in: VPs who complete another president's term.

First I want to talk about the other group: early presidents. Every one of the first seven presidents ran for reelection and five of them won, an astronomical success rate of over 70%. However these elections were very different from later elections. Here's what happened the reelection bids of the first seven presidents:

1792 - George Washington runs unopposed.

1800 - John Adams loses to Thomas Jefferson in a competitive race.

1804 - Thomas Jefferson defeats Charles Pickney in the largest popular vote victory in history in which two major parties ran candidates. Jefferson carries 15 of the 17 states and wins the popular vote by 45%.

1812 - James Madison defeats DeWitt Clinton, a member of his own party. No Federalist runs for election in 1812.

1820 - James Monroe runs functionally unopposed.

1828 - John Q. Adams loses to Andrew Jackson in a competitive race.

1832 - Andrew Jackson defeats three challengers in a competitive race.

Many of these elections worked very differently than modern elections. I don't want to get into this too much because it's a tangent from your area of interest, but the modern two-party system didn't really exist before 1828 and scholars often consider the first six presidents separately from the rest when talking about electoral politics. I will follow that convention and separate the first six presidents (though not Andrew Jackson!) from the rest.

Of the 25 later presidents who ran for reelection, five of them had ascended to their first term through the Vice Presidency: Teddy Roosevelt, Calvin Coolidge, Harry Truman, Lyndon Johnson, and Gerald Ford. Of these five men, the only one to lose was Gerald Ford.

So now we have the following breakdown:

• 6 early presidents, 5 of whom won reelection (83%).
• 20 later presidents who won their first term and ran for reelection, 8 of whom won (40%).
• 5 later presidents who ascended from being VP, 4 of whom won (80%).
• 9 later presidents who won their first term and didn't run for reelection
• 4 later presidents who ascended from being VP and didn't run for reelection.

This is certainly a resounding win for the ascended VPs, but it would be unwise to draw any causal connection. There are also some complicating details, such as FDR winning more than two elections and Teddy Roosevelt running for a third term and losing. It's hard to speak of the "typical public perception" of such a small sample across two hundred years. Instead, I'll go into a bit of detail about the one man who ran for reelection after assuming the vice presidency and lost: Gerald Ford.

Gerald Ford not only was never elected president he was never elected vice president either. In a scandal unrelated to Watergate, Nixon's first VP resigned early in Nixon's second term. Nixon chose Speaker of the House Gerald Ford to be the replacement VP. Ford was VP for only six months before Nixon resigned. This is one of my favorite US politics trivia fact: Ford is the only US President to never win a national election of any kind.

Ford faced four major challenges during his reelection campaign. Firstly, he was challenged in the primaries by future president Ronald Regan. Regan rallied the conservative arm of the party and fiercely criticized Ford on foreign policy, especially pulling troops out of South Vietnam and his conciliatory approach to the USSR. The primary was so close that it wasn't until the actual convention vote that Ford became the party candidate. Ford won 52% of the votes at the convention. Secondly, his pardon of Nixon was widely unpopular. Many Americans wondered if Ford hadn't struck a deal with Nixon in which Nixon would resign in exchange for a pardon and one of Nixon's political appointees even resigned in protest of the pardon. Thirdly, Ford struggled with an economic downturn and the fall of South Vietnam in the last year of his presidency. While neither of these were directly Ford's fault, they caused dismay and dissatisfaction in the American public. Fourthly, Ford made a major misstep in a televised debate when he said "there is no Soviet domination of Eastern Europe and there never will be under a Ford administration." While he had been steadily gaining in the polls for months, his momentum stopped after this debate inflamed doubts about his approach to the USSR that had been previously raised in the primary campaign.

Despite these challenges, his reelection campaign was quite close. Ford won 48% of the popular vote and 45% of the electoral college votes. His journey was rather typical of presidents who fail to be reelected, regardless of how they go their first term. He benefited from the official station of his office, suffered from downturns in current events, and ultimately lost a close race. While people were displeased with how he became president, it was out of desire to see Nixon brought to justice and worry about the impropriety of the pardon rather than anything that would generalize to other VPs who assume the presidency.