Generally speaking there's a large incumbency advantage. There's been a lot written about that. See e.g. this paper.
I'm quoting this bit because I find it particularly funny/insightful (even though it's not technically about Senators in the first part, although the paper makes that jump):
Even though Congress has low approval ratings overall, according to Gallup polls,
almost half of Americans say they approve of the job their representative is doing. This implies
that the public tends to blame other members of Congress for decisions they dislike, and thus
opens the door for senator reelection. Drain the swamp, sure. But don’t throw out our senator.
But as that paper details, the same principles apply: name recognition, war chests, piggybacking on successes that they might not have contributed to much, etc.
More closely related to your Q though:
candidates with stronger chances of success – usually ones who have been in an
elected office before – tend to run for open seats rather than challenging incumbents.
Alas that paper doesn't discuss that data in detail. There are some such papers though, e.g.
Studying U.S. state legislatures, we find strong evidence of strategic behavior by experienced challengers (consistent with previous studies). However, we also find that such
behavior does not appear to significantly bias the estimated effect of challenger experience or the estimated incumbency advantage. More tentatively, using our estimates,
we find that 30-40% of the incumbency advantage in state legislative races is the result
of “scaring off” experienced challengers.
Alas that's not about the US Senate, so who knows how big the "scaring off" factor is in that case. OTOH what they did study was:
state senate elections, and measure challenger quality in terms
of previous experience as a state representative.
(Using  state senates gives them a larger data set, so they're more likely to get statically significant, thus academically publishable results.)
Also, there's a paper that calculated that the incumbency advantage increases linearly with time in the US Senate. Their data set spanned 1952 to 2008.
And something in there about what I said about statistics and publication-worthiness (but also a list of other factors):
The most striking shortcoming of the incumbency literature is the lack of interest in senatorial elections. [...] The most common justifications used concern
the higher quality of senatorial challengers (Adams and Squire 1997; Hinckley
1980; Lublin 1994; Stewart 1989; Squire 1992; Squire and Smith 1996), the difficulty in establishing a personal relationship with constituents in densely populated
states (Binder, Maltzman, and Sigelman 1998; Hibbing and Alford 1990; Hibbing
and Brandes 1983; Nice 1985; Oppenheimer 1996), and the higher level of media
coverage and exposure that senatorial campaigns generally enjoy (Druckman 2005;
Hess 1986; Sinclair 1990). In brief, virtually all these explanations can be traced to
the fact that senatorial campaigns are held statewide. The unspoken truth, however,
is that the Senate represents a less attractive statistical laboratory than the House:
its members are fewer, they are elected less often, and they win fewer electoral
Some incumbency effect appears in their 2nd term already, and only grows after that; some potential reasons are laid out:
The average share of
the vote obtained by successful non-incumbent candidates is 55.4%. This number
rises to 58.1% after six years or one term in power, 60.2% after two terms, 60.4%
after three terms or 18 years, 62.4% after 4 terms, and 66.5% after five terms or
[...] It might, thus, not only be true that sitting senators receive more votes
at their second bid compared to their first bid: their vote share might also increase
during their third, fourth, and fifth reelection. There are mainly two reasons why
this rationale might be true. First, the longer a senator is in office, the more he or
she can create bonds with his or her constituents. Second, the senators’ political
clout increases with seniority. For example, seniority boosts a senator’s standing
within his or her respective party and renders it more likely that the person will gain
chairmanship of an important committee. Having spent many years in Washington,
Senators are also more likely to gain other informal or formal leadership positions
within the political establishment in the capital; factors that allow him or her to
serve his or her constituents better by, for example, bringing home more “pork.”
Unfortunately, this paper doesn't empirically test the relevance of those putative factors. It does test a few others, but they're kinda "meh" and not in the [causal] direction of interest to this Q, e.g. it concludes that an incumbent senator whose election is contested by a counter-candidate with some elected office experience is more likely to lose their seat than otherwise [ceteris paribus], but this is a rather obvious fact... OTOH, we shouldn't totally discount the relevance of that empirical datum because it lends more credence to the idea that the "scaring off" effect of such counter-candidates [identified in other research] factually matters, i.e. such counter-candidates would indeed be more likely to unseat a Senator.