The literature
According to conventional political science, the greatest advantage a U.S. senator has is incumbency. However, it is uncertain if the advantage held by elected senators extends to those who are appointed.
Several studies examine the incumbency advantage; David R. Mayhew’s Congressional Elections: The Case of the Vanishing Marginals is one. Peter Tuckel has written two articles: "Length of Incumbency And the Reelection chances of U.S. Senators" and "The Initial Re-Election Chances of Appointed & Elected United States Senators". Other books are Treadmill to Oblivion: The Fate of Appointed Senators by William D. Morris and Rodger H. Marz and The Electoral (Mis)Fortunes of Appointed Senators and the Source of the Incumbency Advantage, by Jennifer A. Steen and Jonathan Koppell.
Mayhew
In Congressional Elections: The Case of the Vanishing Marginals, Mayhew compiled House seat swing data from 1956 to 1972 and wondered if House members receive more benefits from federal programs. He suggests that they have become more skilled at taking positions on issues, possibly due to an increase in polling technology and resources. His study explains that incumbency becomes an advantage due to experience.
Tuckel
Tuckel examined incumbency in "Length of Incumbency and the Reelection Chances of U.S. Senators" and "The Initial Re-Election Chances of Appointed & Elected United States Senators". He found that 24 percent of senators who are appointed remain in office, compared to 65.4 percent of those who are elected. Excluding appointed incumbents who relinquish their role voluntarily, Tuckel wrote that 56.5 percent of appointees win an election; 76 percent of elected office holders are reelected. He also suggested that the reason for the difference in electoral chances between appointed and elected senators is the amount of experience.
Morris and Marz
In Morris and Marz's Treadmill to Oblivion: The Fate of Appointed Senators, voters tend to see appointed senators as illegitimate; this weakens the power of incumbency. None of the nine appointed senators who stood for election were victorious, and seven of their nine successful opponents had more political experience. Morris and Marz conclude that Senate appointees cannot make effective reelection efforts while doing committee work and conducting other Senate business for less than one term.
Steen and Koppell
In The Electoral (Mis)Fortunes of Appointed Senators and The Source of Incumbency Advantage, Steen and Koppell suggest two often-overlooked factors in the incumbency advantage: incumbents are reelected because of qualities they had before they were elected the first time, and reelected incumbents have successfully honed their skills and connections. The incumbency advantage is due more to previous election than to holding the office.
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