There are 291 voluntary [not for profit] sector, 232 local authority and 727 private care homes in Scotland.
In the last year, to March 31 2020, there were 158 complaints about voluntary sector homes, 2040 about private homes and 146 about local authority homes.
There are thus 2.5 times as many private as voluntary homes but the level of complaints is 13 times higher.
There are 3.1 times as many private as local authority homes but the level of complaints is 14 times higher.
So, the level of complaints to private homes, taking account of the number there are, is around 4 times higher than in voluntary sector or local authority care homes for the elderly.