"While an objective of reform is to remove the concept of deciles, it is for analytical purposes useful to consider the 'hypothetical' decile that each school would move to under a revised funding approach," the paper noted.
"Estimates suggest that two-thirds of schools could move to a different 'hypothetical' decile under a risk factor funding model. About 40 per cent move up or down one 'hypothetical' decile, and 17 per cent move two deciles, 6 per cent move three deciles and 4 per cent move four or more deciles."
The decile system is based on the area from which a school draws its students. But attaching a number to each school has meant some parents avoid lower-decile schools, mistakenly linking a decile number with the quality of education.
Parata has previously said a statistical "risk" index can target funding in a more "fine-grained way" by estimating for each student how at risk of educational underachievement they are.
It uses a range of indicators relating to each child, including how old the mother was at their birth, how many siblings the child has, parental income, father's offending history, and the child's ethnicity.
A law change could be required to allow access to the Statistics NZ database that holds information from a wide range of Government departments and agencies.
The Government is already testing a version of "at-risk" school funding. Schools this year did not get a general increase to operations funding to cover inflation. Instead, schools get $92 in extra funding for each student from a long-term, welfare-dependent background.
The at risk index would be a more sophisticated way to target extra money and would dish out far more money too.
Education union NZEI today said the "at risk" funding system to replace deciles should not be rushed. President Lynda Stuart said progress should be driven by what is best for children, not "fitting in with political timetables".
"The new system being discussed - a predictive risk index - raises huge privacy concerns that we are not convinced have been addressed. The education and privacy of every child in New Zealand is at stake. It's crucial that we get this right," Stuart said.