We combine analysis of rivalry with consideration of a possible selection b
ias. We discover that what makes great powers more likely to be rivals is s
tatistically related to their propensity to experience war. A censored prob
it allows simultaneous estimation of the influence of six covariates on the
probability great powers experience rivalry and war, while controlling for
statistical linkage between the two dependent variables. Consequently, we
recast some past research. For example, contiguity and parity actually redu
ce the probability of war between great power rivals once we control for th
eir influence on the probability great powers are rivals in the first place
. Our results compliment other research highlighting various problems of se
lection bias in world politics and suggest a new direction for future resea
rch on rivalry.