The need to reform research assessment processes related to career advancement at research institutions has become increasingly recognized in recent years, especially to better foster open and responsible research practices. Current assessment criteria are believed to focus too heavily on inappropriate criteria related to productivity and quantity as opposed to quality, collaborative open research practices, and the socioeconomic impact of research. Evidence of the extent of these issues is urgently needed to inform actions for reform, however. We analyze current practices as revealed by documentation on institutional review, promotion, and tenure (RPT) processes in seven countries (Austria, Brazil, Germany, India, Portugal, the United Kingdom and the United States). Through systematic coding and analysis of 143 RPT policy documents from 107 institutions for the prevalence of 17 criteria (including those related to qualitative or quantitative assessment of research, service to the institution or profession, and open and responsible research practices), we compare assessment practices across a range of international institutions to significantly broaden this evidence base. Although the prevalence of indicators varies considerably between countries, overall we find that currently open and responsible research practices are minimally rewarded and problematic practices of quantification continue to dominate.