These are the two sets of stats (ORR and DfT) for 2013/14.
In the DfT stats the net Northern figure is 12.5 p/mile, which equates to the ORR figure of 7.79 p/km.
http://orr.gov.uk/__data/assets/pdf_file/0007/14497/rail-finance-statistical-release-2013-14.pdf
https://www.gov.uk/government/publications/rail-subsidy-per-passenger-mile
On a pence per mile basis (in the DfT document), the Northern PTE grant is 13.3, and the network grant is 25.7.
That's how you get to 51.5 pence per passenger mile.
So the PTEs pay Northern more than DfT does in subsidy, and the network grant doubles both those figures.
What's more these figures are going up by about 10% a year, so the Northern problem is getting worse.
It is interesting to delve further into these figures. The total subsidy of 51.5p PPM was actually a fall of 3% from the previous year, due to a 12% reduction in the Network Grant PPM apportioned to Northern. So that part of the "Northern problem" is
not getting worse. The direct DfT subsidy PPM to Northern, net of revenue share, increased by 9% year on year, from 11.5p to 12.5p, while the PTE subsidy PPM increased by 7%, from 12.4p to 13.3p.
The PTE grant, like the others, is divided by Northern's
total annual route miles to get the PPM figure, whereas this grant is really just for the route miles
within the PTE areas. I do not know what proportion of Northern's route mileage is in the PTE areas, but these figures suggest that the "Northern problem" may be mainly a problem of the suburban services, rather than, as some have suggested, the far-flung rural services. If so, the high subsidy levels might be due more to low revenue yield (low fares and ticketless travel) than to high operating costs.
Greater Manchester alone absorbed 39% of the PTE grant. Yet Manchester Metrolink, operating on similar routes to Northern's Manchester suburban services, achieved an operating surplus. This seems to me to indicate that investment in improved infrastructure and rolling stock is the way to turn things around.