This article investigates the factors that escalate competition into dangerous conflict. Recent sociological theorizing claims that such escalations are particularly likely in dyads of structurally equivalent people (i.e., actors who have the same relations with the same third parties). Using panel data on Formula One races from 1970 through 2014, we model the probability that two drivers collide on the racetrack (an observable trace of conflict) as a function of their structural equivalence in a dynamic network of competitive relationships. Our main hypothesis, that the likelihood of conflict rises with structural equivalence, receives empirical support. Our findings also show that the positive association between structural equivalence and conflict is neither merely a matter of contention for official position nor an artifact of inherently hostile parties spatially exposed to each other. Our analyses further reveal that this positive association is concentrated in a number of theoretically predictable conditions: among age-similar dyads, among stronger performers, in stable competitive networks, and in safe, rather than dangerous, weather conditions. Implications for future research on conflict, networks, and tournaments are discussed.