This paper uses regression analysis to test if the universities performing less well according to Shanghai Jiao Tong University's world universities league tables are able to catch up with the top performers, and to identify national and institutional factors that could affect this catching up process. We have constructed a dataset of 461 universities across 41 countries. We found consistent evidence of a moderate degree of catching up, especially amongst non-US universities. Larger universities as well as universities located in English speaking countries not only perform better on average, but also catch up more over 2003-2009. Universities located in lower income countries are also catching up more. The performance of private universities, as compared to that of public universities, varies substantially between the US and the other countries. (Contains 17 notes, 5 tables and 1 figure.)