The advantage of incumbency in American elections is well-documented, but the source of this advantage remains unclear. I combine quasi-random variation in state-level gubernatorial term limits with a standard regression discontinuity design for close elections to distinguish between individual-level and party-level incumbency effects. I find that incumbency advantages are concentrated entirely among individual officeholders, while political parties themselves are electorally penalized by incumbency, all else equal. These findings may help shed light on a perennial riddle of American politics: why incumbents are typically rewarded at the ballot box even while their parties are punished in midterm elections. Moreover, my estimates imply that states without term limits will experience longer-lasting consequences of a single electoral victory and meaningfully longer streaks of one-party control.