Political scientists have developed increasingly sophisticated understandings of the influences on Supreme Court decision making. Yet, much less attention has been paid to empirical measures of the Court's ideological output. We develop a theory of the interactions between rational litigants, lower court judges, and Supreme Court justices. We argue that the most common measure of the Supreme Court's ideological output—whether the Court's decision is liberal or conservative—suffers from systematic bias. We trace this bias empirically and explain the undesirable consequences it has for empirical analyses of judicial behavior. Specifically, we show that, although the Court's preferences are positively correlated with the ideological direction of the justices’ decision to reverse a lower court, the attitudes of the justices are negatively related—and significantly so—to the ideological direction of outcomes that affirm lower court decisions. We also offer a solution that allows scholars to work around this “affirmance bias.”