This paper extends Taagepera's (2007) Seat Product Model and shows that the effective number of seat-wining parties and vote winning parties can both be predicted with institutional variables alone, namely district magnitude, assembly size, and upper-tier seat share. The expected coefficients are remarkably stable across different samples. Including the further information of ethnic diversity in the models hardly improves the estimate of the effective number of parties, and thus the institutions-only models are preferable on the grounds of parsimony and the applicability to electoral-system design or “engineering”. •Taagepera's seat product is accurate for estimating the effective number of parties.•Effective number of parties can be estimated accurately from institutions alone.•Inclusion of ethnic diversity improves fit for few countries.