Individuals exhibit different forms of judgment biases in daily life. Many of these biases can be attributed to a general cause – people are insensitive to the relevance of given information. In this research, we adopt the theory of relevance insensitivity to test a new bias: people are insensitive to the relevancy of the start of an event. Across two studies, we find that people tend to over-rely on the start in outcome predictions when it is of low relevance to the final outcome. On the other hand, people tend to under-rely on the start when it is highly relevant to the final outcome. In both circumstances, relevance insensitivity to the start can lead to biased outcome predictions. We also find that when people are made sensitive to the relevance of the start, it is possible to attenuate the biases. Finally, we discuss the limitations and implications of this research.