The blue wave that swept the midterm elections in November along with the continuing investigations into President Donald Trump have led to discussions of a potential Republican primary challenge in 2020. Sen. Susan Collins has said a GOP primary would be a good idea, while outgoing Sen. Jeff Flake and Ohio Gov. John Kasich are being talked up as possible contenders.While Trump himself has said he would welcome the challenge, South Carolina Republicans are discussing the possibility of canceling the presidential primary to avoid a challenger.With Trump still retaining a stranglehold on the GOP base, a successful primary challenge seems unlikely. But if history is any judge, an intraparty battle — even if the challenger is unsuccessful — could be devastating for the incumbent.No sitting President who sought his party’s nomination has been denied it since Chester Arthur in 1884 — Arthur only got the office following President James Garfield’s assassination. And presidents who face a serious re-election challenge have regularly gone down in defeat in the general election.While the story of 19th century presidents is generally a tale of one-termers, presidents since McKinley have been very successful at winning re-election. It’s notable that none of the 13 presidents (including the four VPs who moved up following the death of a president) who won re-election faced a serious primary challenge. They all were essentially handed the ballot line.The presidents who did not win re-election tell a much different tale. Five presidents lost in their quest for another term (in the case of Gerald Ford, it was a first full term). Four of them — all but Herbert Hoover — faced a noteworthy challenge in their party’s primary. In addition, Harry Truman and Lyndon Johnson both pulled out of the race after seeing serious primary challengers emerge.Even when sitting presidents prevailed in the primaries against serious contenders, their authority was often undermined and they went on to lose in the general election. In addition to William Howard Taft in 1912, this was the case for Gerald Ford in 1976, Jimmy Carter in 1980, and George H.W. Bush in 1992.Ford, Carter and Bush all faced difficulties in their first terms, which created an opening for a primary challenger to run. But beyond those challenges, the primary fight forced the President to dirty his hands with politics early on, instead of staying above the fray and focusing on governing.Even worse, it shows that the president does not have complete control over his party. A challenger also pushes the president to take on positions that alienate centrist voters at exactly the time he needs to be wooing independents in the center.