Contests between rivals placing similar value on the resource at stake are commonly won by the rival having greater 'resource holding potential' (RHP). Mutual assessment of RHP difference between rivals is usually expected as an economical means of resolution; weaker rivals can retreat when they detect their relative inferiority, thereby avoiding costly, futile persistence. Models of contest resolution that entail retreat decisions based on estimates of RHP difference predict that contest duration diminishes as RHP difference between rivals increases because the asymmetry is more readily detected. This prediction appears to have been fulfilled in contests of diverse taxa, generating widespread support for assessment of RHP differences in contests. But few studies have considered alternatives in which each rival simply persists in accord with its own RHP ('own RHP-dependent persistence'). In contests decided by own RHP-dependent persistence, in which costs accrue only through each rival's own actions, weaker rivals retreat first because they are inherently less persistent, and contest duration depends primarily on the weaker (losing) rival's RHP rather than RHP difference between the rivals. We show here that the analyses most commonly used to detect effects of RHP difference cannot discriminate between these alternatives. Because RHP difference between rivals tends to be correlated with RHP of the weaker rival in a pair, a negative relation between RHP difference and contest duration may be generated even when decisions of retreat are not based on estimated RHP difference. Many studies purporting to show a negative relation between RHP difference and contest duration may actually reflect an incidental association between weaker rival RHP and RHP difference. We suggest statistical and experimental approaches that may help to discriminate between effects of weaker rival RHP and true effects of RHP difference. We also discuss whether 'true' negative effects of RHP difference on contest duration always reflect retreat decisions based on estimated RHP differences.