Whether and why the Supreme Court agrees to hear cases is among the most important—and well studied—topics in American politics. However, existing theories have overlooked a key player: the advocates. We develop and test a new theory that explicitly incorporates advocates in explaining which cases the Supreme Court is likely to accept. Specifically, we theorize that cert petitions are most likely to be successful when (1) there is great ideological distance between the opposing advocates and (2) the lower-court panel is closest ideologically to the advocate who won at the lower-court level. In these cases, as we explain, the advocate petitioning the Supreme Court to intervene becomes the “Odd Party Out,” a cue that conveys important information about the probability of bias as well as the political importance of the case. We test this theory using a new dataset on the identities and ideologies of advocates and judges. We find strong support for our theory: cert petitions are significantly more likely to be granted when the advocate appealing to the Court is an ideological outlier—that is, when the petitioner is in opposition to an ideologically aligned respondent and lower-court panel.