Influence, the ability to change the beliefs and behaviors of others, is the main currency on social media. Extant studies of influence on social media, however, are limited by publicly available data that record expressions (active engagement of users with content, such as likes and comments), but neglect impressions (exposure to content, such as views) and lack “ground truth” measures of influence. To overcome these limitations, we implemented a social media simulation using an original, web-based micro-blogging platform. We propose three influence models, leveraging expressions and impressions to create a more complete picture of social influence. We demonstrate that impressions are much more important drivers of influence than expressions, and our models accurately identify the most influential accounts in our simulation. Impressions data also allow us to better understand important social media dynamics, including the emergence of small numbers of influential accounts and the formation of opinion echo chambers.