With the increasing popularity of live streaming services, an intensive competition emerges among streamers who are streaming during the same time period. In this competition, streamers frequently switch their streaming content which drives changes in audience flow. This content switching not only has a direct impact on the audience amount of entrant streamers but also would indirectly influence the incumbent streamers' audience size and thereby lead to disadvantage or advantages for streamers. Based on the dataset we collected from live streaming platform Twitch.tv, we empirically examine how content switching impacts the viewership of incumbent and entrant streamers from a spillover perspective. Our key results show that: 1) The entrant star streamer could benefit from the content switching due to the increasing amount of audience and further benefit the incumbent by a positive spillover. 2) Content switching may lower the audience amount of entrant streamer with limited popularity. This study contributes to literature in the live streaming community from a dynamic and empirical perspective. This study also gives actionable suggestions for streaming strategy and online advertising.