We often show a greater inclination to assist and avoid harming people identified as those at high risk of great harm than to assist and avoid harming people who will suffer similar harm but are not identified (as yet). Call this the identified person bias. Some ethicists think such bias is justified; others disagree and claim that the bias is discriminatory against statistical people. While the issue is present in public policy and politics, perhaps the most notable examples can be found in medical ethics such as in ICU triage decisions made during the COVID-19 pandemic. The Rule of Rescue, as the application of the identified person bias is sometimes called, states that spending large amounts of resources rescuing identifiable individuals who are in imminent danger is justified. In this paper, I show that our distorted attitudes toward time play a role in identified person bias. I claim that ICU triage decisions are better explained by a preference to treat people sooner rather than later, which is at least partially due to near bias (positive events are to be preferred to be near rather than distant), than by a preference to treat identified lives over statistical lives. Thus, another bias, near bias, is involved in the reasoning behind the identified person bias and the Rule of Rescue.