there is no single approach to understanding effectiveness. tell me, please, what are the techniques and where they can be found? perhaps there are official methods of authorities of your country?
I recomend an excelent brazilian book called "Como combater a corrupção em licitações: detecção e prevenção de fraudes" (How to fight corruption in bids: fraud detection and prevention), by Franklin Brasil Santos and Kleberson Roberto de Souza. This book was written by two authorities in the Brazilian government who act to fight corruption in bids. There is still no translation of the book into English, but it is one of the best selling books in Brazil in the area of Public Law and presents excellent methods, tools and techniques for biddings.
An interesting tool could be also the World Bank “Benchmarking Public Procurement” . They provide indicators for acessing public procurement regulatort systems and its 2017 version provides the analysis of 180 coutries.
You are right, a general toolbar is missing. If you are doing emprirical/policy research, I can recommend OECD works, they have an excellent team. This is a good benchmark I know: https://www.oecd.org/countries/colombia/towards-efficient-public-procurement-in-colombia-9789264252103-en.htm
Lean management in public procurement to calculate the resource wastage and take corrective action in each process of the public procurement effectiveness.