Abbott & Morrison at the core of Aged Care Disasters, page-24

There is no denying that Vics private and not for profit aged care is concentrated in Melbourne which would push the statewide ratio of 9 to 1 private/public much closer to 100%.
Little wonder near 100% of the covid cases from aged care were from private facilities.

It does not prove public facilities at the time had better covid measures in place when most public aged care beds are in the country areas.