So when the time comes for them to run for their own term as governor, do they actually win?
The short answer is yes -- far more often than not. We looked through the election track record for the 18 governors who took office through succession from 2000 to 2014 (those who served as "acting governors" in states like New Jersey and Massachusetts were not included), and here's what we found:
Turns out that governors who took office through succession do a good job of getting elected, winning their own terms more than half the time overall and winning 75 percent of them time when they actually run. Those who run and lose -- Scott McCallum (R) in Wisconsin, Joseph Kernan (R) in Indiana and Olene Walker in Utah (R) -- are the exceptions.
Two of the governors opted not to run were in office for less than a year: Idaho's Jim Risch (R) and Missouri's Roger Wilson (D). (Risch, for what it's worth, is now a U.S. senator.) Paterson briefly ran before dropping out thanks in part to low poll numbers.
Brown, for what it's worth, will have two years to prove her mettle before a 2016 special election, so it's not like she'll be a complete stranger to Oregon voters. She also has the advantage of being an incumbent Democrat in a blue state where Republicans haven't won a governor's race since 1978.
Here are the 18 governors used to determine election trends:
Correction: An earlier version of this post misstated the year of Oregon's next gubernatorial election.