Understanding both contact and probability of transmission given contact are key to managing wildlife disease. However, wildlife disease research tends to focus on contact heterogeneity, in part because the probability of transmission given contact is notoriously difficult to measure. Here, we present a first step towards empirically investigating the probability of transmission given contact in free-ranging wildlife. We used measured contact networks to test whether bighorn sheep demographic states vary systematically in infectiousness or susceptibility to Mycoplasma ovipneumoniae, an agent responsible for bighorn sheep pneumonia. We built covariates using contact network metrics, demographic information and infection status, and used logistic regression to relate those covariates to lamb survival. The covariate set contained degree, a classic network metric describing node centrality, but also included covariates breaking the network metrics into subsets that differentiated between contacts with yearlings, ewes with lambs, and ewes without lambs, and animals with and without active infections. Yearlings, ewes with lambs, and ewes without lambs showed similar group membership patterns, but direct interactions involving touch occurred at a rate two orders of magnitude higher between lambs and reproductive ewes than between any classes of adults or yearlings, and one order of magnitude higher than direct interactions between multiple lambs. Although yearlings and non-reproductive bighorn ewes regularly carried M. ovipneumoniae, our models suggest that a contact with an infected reproductive ewe had approximately five times the odds of producing a lamb mortality event of an identical contact with an infected dry ewe or yearling. Consequently, management actions targeting infected animals might lead to unnecessary removal of young animals that carry pathogens but rarely transmit. This analysis demonstrates a simple logistic regression approach for testing a priori hypotheses about variation in the odds of transmission given contact for free-ranging hosts, and may be broadly applicable for investigations in wildlife disease ecology.