This is a guest post by political scientist Ben Highton at the University of California, Davis.

John Walsh is the recently appointed Democratic U.S. senator from Montana.  He replaced Max Baucus, our new ambassador to China.  Walsh has all the rights and privileges provided to all U.S. senators.  So, in one sense he is obviously an “incumbent.”  But, what about when it comes to the Senate election in Montana this fall?  Walsh is running in the special election for Baucus’s seat.  Should he expect to receive the electoral boost from incumbency that incumbent senators who entered the Senate by getting elected – rather than appointed – typically receive?

Our analysis suggests that the answer is no.  The same is true for Tim Scott, the appointed Republican U.S. senator from South Carolina who replaced Jim DeMint.  For Scott, the stakes are much lower because South Carolina is among the most Republican states in the country.  For Walsh, seeking election as a Democrat from a state that has given its electoral votes to the Republicans in 11 of the past 12 presidential elections, the stakes are very different.

In general, the incumbency advantage in congressional elections is well known and reasonably well understood.  In Senate elections our model indicates that over the 1952-2012 period, compared to an open seat, a party receives on average about six percentage points more of the vote when its candidate is an incumbent.  In the more recent 1980-2012 period the incumbent advantage is almost eight percentage points.  The estimates are based on treating only candidates who were previously elected to the Senate as incumbents.  What about the electoral advantage for incumbents (like Walsh and Scott) who were previously appointed to the Senate?

A complete list of appointed senators is available from the U.S. Senate Web site.  A quick look shows that their political careers are not typical of elected incumbents.  A fair number of appointed senators either do not subsequently seek election or lose their party’s primary election.  Focusing on those who do seek election and win their party’s nomination, we can analyze how they do compared to previously elected incumbents who do the same.  (We thank Lily Fitzgerald, a George Washington University undergraduate, for compiling data on the appointed senators for us.)  Over the entire 1952-2012 period, we estimate that appointed senators received less than a percentage point of electoral boost compared to the six points received by previously elected senators.  Focusing on more recent elections, the estimated boost is a bit more, 1.5 percentage points, but significantly less than the eight points received by previously elected incumbents.  And, in neither time period can we confidently rule out the possibility of no electoral boost for appointed senators.

In short, by conventional standards both Walsh (now a former lieutenant governor) and Scott (a former member of the House) are strong, high-quality candidates, which are electoral advantages.  The fact that they are also senators probably doesn’t matter much at all.  Scott should still get elected.  For Walsh, it’s a dicey proposition.  Walsh is a Democrat running in a state where Republican presidential candidates do well, and he’s facing a high-quality GOP opponent in Rep. Steve Daines. As David Parker and Robert Saldin have explained in detail, Walsh is in for a hard-fought battle.