1. A method performed by a data processing apparatus, comprising: receiving, by one or more processors, a request for third-party content, the request including an indication of a resource where the third-party content is to be presented; selecting, by the one or more processors, a plurality of content items eligible for presentation at a plurality of presentation positions of the resource responsive to the request, each presentation position associated with a corresponding position factor indicative of the likelihood of interaction with a content item presented in that presentation position; accessing, by the one or more processors, from a memory, a scaling factor value representing a reduction in the likelihood of interaction with the plurality of content items when presented together on the resource, the scaling factor value specific to the resource; determining, by the one or more processors, a first page value range specifying at least a high page value and a low page value, the high page value exceeding an expected cumulative performance of the plurality of content items computed using historical data associated with each of the plurality of content items and the position factors of the plurality of presentation positions, and the low page value is less than the expected cumulative performance of the plurality of content items and is determined using the high page value and the scaling factor value; determining, by the one or more processors, a first ranking of the plurality of content items based on the high page value and the scaling factor value, the first ranking of the plurality of content items indicative of a first placement of the plurality of content items into the plurality of presentation positions; determining, by the one or more processors, a second ranking of the plurality of content items based on the low page value and the scaling factor value, the second ranking of the plurality of content items indicative of a second placement of the plurality of content items into the plurality of presentation positions; determining, by the one or more processors, that the first ranking of the plurality of content items does not match the second ranking of the plurality of content items; in response to determining that the first ranking does not match the second ranking, determining, by the one or more processors, a second page value range that differs from the first page value range by updating at least one of the high page value and the low page value; determining, by the one or more processors, an updated first ranking of the plurality of content items and an updated second ranking of the plurality of content items based on the second page value range; determining, by the one or more processors, that the updated first ranking matches the updated second ranking; and in response to determining that the updated first ranking matches the updated second ranking, distributing, by the one or more processors, the plurality of content items for display in the plurality of presentation positions based on the updated first ranking.